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A
A PRIORI/A POSTERIORI
A distinction between kinds of knowledge that can be acquired
independently of experience
(such as that 2 + 2 = 4 or that bachelors are unmarried)
and that can be secured only on the
basis of experience (such as that there are four apples
in the basket or that John is a
bachelor). Often defined relative to analytic/synthetic
and necessary/contingent distinctions.
ABDUCTION
Inference involving the generation and evaluation of explanatory
hypotheses. In its strict
sense, a mode of creative conjecture introduced by C. S.
Peirce. In its looser sense, a
species of inductive inference, still associated with Peirce,
also known as "inference to the
best explanation," which involves selecting one member
from a set of alternative hypotheses
as the alternative providing the best explanation of the
available evidence. Hypotheses that
explain more of the available relevant evidence are preferable
to those that explain less.
Hypotheses that are preferable are also acceptable when
sufficient evidence becomes
available. Hypotheses that are incompatible with the evidence
are rejected as false.
Hypotheses may be false even when they are acceptable, which
makes inference of this kind
fallible, but they remain the most rational among the alternatives
considered.
ABDUCTIVE INFERENCE see ABDUCTION
ABSTRACT DATA TYPE see DATA ABSTRACTION
ABSTRACTION
(The result of) a process of simplification, to describe
something at a more general level than
the level of detail seen from another point of view. This
is often achieved by omitting details
specific to individual cases or to methods of implementation.
For example, a realtor's
description of a house may leave out architectural detail
so that it is an abstraction of an
architect's description. In computer science, language abstraction
is the use of high-level
language programs allowing computational processes to be
described without reference to
any particular machine, hence more simply. See also ABSTRACTION,
FULL and
ABSTRACTIONS/IDEALIZATIONS.
ABSTRACTION, FULL
A semantics for a programming language is fully abstract
if it does not distinguish programs,
or program phrases, which are observationally equivalent.
See also ABSTRACTION and
ABSTRACTIONS/IDEALIZATIONS.
ABSTRACTION, PROCEDURAL
The separation of a computational procedure A's use from
its definition, so that another
procedure B can call A to get something accomplished while
remaining ignorant of how A
accomplishes its task.
ABSTRACTION/IDEALIZATION
The axioms and theorems of formal systems in pure mathematics
make assertions about
abstract entities that do not exist in space/time, such
as points and lines in Euclidean
geometry. The truth or falsity of these hypotheses seems
to be analytic and a priori. If those
formal systems are provided an empirical interpretation
and those entities are identified with
things that may have instances in space/time, such as the
paths of rays of light, the results
belong to applied mathematics. The truth or falsity of these
hypotheses seems to be synthetic
and a posteriori. Idealizations, by comparison, are special
cases of physical phenomena that
might or might not have any instances during the history
of the world, such as frictionless
planes and perfect spheres. See also ABSTRACTION
and ABSTRACTION, FULL.
AI see ARTIFICIAL INTELLIGENCE
AI, STRONG
In one sense, the difference between "weak" and
"strong" AI is that between the use of
machines as a tool that is useful in the study of the mind
and the claim that these machines
actually do possess minds. Alternatively, the difference
between "weak" and "strong" AI is that
between how we do think (the descriptive thesis) and AI
as studying how we should think (the prescriptive thesis).
ALETHIC
Of true or false value.
ALGOL
A programming language, developed in the late 1950s, which
established many of the
features of modern programming languages.
ALGORITHM
Any well-defined sequence of steps (procedure or routine)
that takes some value as input and guarantees a value as
output in some finite number of steps. See also DECISION
PROCEDURE.
ANALOGY see REASONING, ANALOGICAL
ANALYTIC/SYNTHETIC
The distinction has typically been drawn between different
kinds of hypotheses as possible
objects of knowledge, where sentences are qualified as analytic
when (i) their predicates are
contained in their subjects, (ii) they are logical truths
or are reducible to logical truths when
synonyms are substituted for synonyms, or else (iii) their
negations are contradictory. Other
sentences are said to be synthetic. The history of this
distinction is important enough to
deserve discussion. Hume distinguished knowledge of relations
between ideas (when one
idea includes or excludes another; for example, the notion
of being a bachelor includes the
notion of being unmarried) from knowledge of matters of
fact (where that is not the case; for
example, the height, weight, and color of hair of a person
who happens to be a bachelor are
not included in the notion that he is a bachelor). Thus,
knowledge of relations between ideas
has been viewed as analytic, while knowledge of matters
of fact has been viewed as
synthetic. Similarly, Kant, who introduced these terms,
distinguished knowledge of conceptual
connections (when one concept is contained in another) as
analytic and knowledge that is
informative about the world as synthetic. While Kant asserted
the existence of synthetic a
priori knowledge that is both informative about the world
and also knowable independently of
experience due to the mode of function of the human mind,
that position distinguishes specific
forms of rationalism and has been rejected by all forms
of empiricism.
ARTIFICIAL INTELLIGENCE (abbrev. AI)
Branch of computer science that investigates the extent
to which computers can perform
tasks that require intelligence when done by people (or,
more weakly, by animals). AI is
closely associated to cognitive science. See also AI,
STRONG.
ASSIGNMENT
The process whereby a variable in a program acquires a new
value, thereby losing whatever
old value it had compositionally. A semantics is compositional
if the values it gives to
composite entities can be constructed from the values of
the components of those entities.
ATTRACTOR
Region of a phase space into which all trajectories departing
from an adjacent region ("basin
of attraction") tend to converge. Example: fixed point,
limit cycle, deterministic chaos.
AUTOASSOCIATIVE NETWORKS
Connectionist networks (or artificial neural networks) in
which each unit (or node) is
connected to every other unit, including itself.
AUTOCATALYSIS
Self-catalysis, catalysis of a chemical reaction by one
of the products of the reaction.
B
BACKPROPAGATION
Also known as "the generalized Delta rule," it
is a supervised learning algorithm for weight
change. It is frequently used in multilayered connectionist
networks (or artificial neural
networks). The actual output activation pattern for a given
input activation pattern is compared
with the desired output. The difference between the two
- the error measure - is then
propagated back into whatever connections were used to get
the actual output activation
pattern. The connections among units that contributed to
the actual output are strengthened
(increased in weight) when the match is good and are reduced
in strength (decreased in
weight) when it is poor. The weights of connections among
units (or nodes) are thus adjusted
so as to reduce the margin of error between the actual output
and the desired one.
BAYES' THEOREM
Derivable from the definition of conditional probability
as a feature of the calculus of
probability, where P(h/e) - the probability of hypothesis
h, given evidence e - equals the
product of the probability of evidence e, given hypothesis
h (which is also known as a
"likelihood") multiplied by the probability of
hypothesis h divided by the probability of evidence
e. That is, P(h/e) = P(e/h) o P(h)/P(e), where P(h) and
P(e) are known as "unconditional" (or
as absolute) probabilities, insofar as they are not formalized
as "conditional" (or relative to)
specific conditions. In order for the theorem (in this or
more complex forms) to be applied, it is
necessary to fix the values of the probabilities on the
right-hand side to calculate the value of
the probability on the left-hand side. The fashion in which
this is supposed to be done is what
divides species of Bayesianism. See also BAYESIANISM.
BAYESIANISM
A theory of knowledge maintaining that Bayes' theorem captures
the fundamental principle of
scientific reasoning. According to this view, adequate measures
of evidential support must
satisfy certain mathematical relationships characteristic
of the calculus of probability. The
cumulative influence of acquired evidence is taken to be
determined by a process of
conditionalization.
BELIEF
The state of accepting an hypothesis as true. Beliefs appear
capable of variation in strength,
where a person might hold some beliefs more strongly than
others. Some quantitative
theories supply a means for measuring the strength of beliefs,
especially in terms of betting
odds that one would accept under certain special conditions.
The importance of beliefs arises
because (a) we explain and predict events that occur during
the course of the world's history
on the basis of our beliefs, which thereby supply the foundation
for our understanding of
nature; and (b) we tend to act on the basis of our beliefs
relative to the contexts in which we
find ourselves, where these "contexts" consist
of our other beliefs, our motives, our ethics, our
abilities, and our capabilities. Alternatively, the state
of accepting an hypothesis as true or
alternatively as rationally worthy of adoption.
BELIEF, DEGREES OF
A person's measure of credibility (or strength of conviction)
that something is the case, where
those degrees of belief are usually measured by means of
betting odds. For example, if a
person were willing to bet even money at odds of 2:1 against
Duke University repeating as
the basketball champion of the NCAA, that would presumably
make the person's degree of
belief that Duke will win equal to 1/3 (or 33 percent) and
that Duke will lose equal to 2/3 (or 66
percent). Theories of knowledge that do without acceptance
and rejection rules tend to make
this a basic concept.
BESTAND
A term used by Heidegger to name the way the world appears
in technological perspective.
Modern technology makes the world appear as "Bestand"
or "resources" to be manipulated.
Also sometimes translated as "standing-reserve."
In ordinary German, the word also means
"stock" or "supply."
BEST-MATCH PROBLEMS
Minsky and Papert's term for problems whose solution involves
assessing the satisfaction of
multiple soft (i.e., nonmandatory) constraints. A problem
that arises for procedures for solving
best-match problems is that of avoiding local maxima of
goodness of constraint fit. It can be
characterized as an energy minimization problem. The analog
of the goodness maximum is
the energy minimum, and the analogs of local goodness maxima
are local energy minima.
The situation is easy to visualize as an energy landscape.
In an energy landscape, the
goodness maximum corresponds to the lowest valley in the
landscape, while local goodness
minima correspond to local valleys in the landscape. The
problem of avoiding local goodness
maxima is thus the problem of avoiding settling into a local
valley, rather than into the lowest
valley in the energy landscape. See also BOLTZMANN MACHINE.
BOLTZMANN MACHINE
An interactive connectionist network designed by Hinton
and Sejnowski (and named after the
physicist Ludwig Boltzmann) that is especially efficient
at solving best-match problems. To
handle the problem of local maxima of goodness of constraint
fit, the Boltzmann machine
employs a computational analog of the metallurgical process
of annealing, a process whereby
metals are heated to a little below their melting point
and then cooled very slowly so that all
their atoms have time to settle into a single orientation.
The analog of temperature in the
Boltzmann machine is random noise that is introduced into
network activity. The function of
the noise is to jar the network out of local energy landscape
valleys, so that it can explore
other parts of the energy landscape to find the lowest valley,
thereby achieving the global
maximum of fit. When the network reaches a stable state,
it has settled or relaxed into a
solution. Given sufficient time, the Boltzmann machine can
find the energy minimum for any
best-match problem. See also BEST-MATCH PROBLEMS.
BOOLEAN see BOOLEAN ALGEBRA
BOOLEAN ALGEBRA
Set of algebraic rules, named after George Boole, in which
"true" and "false" are equated to 0
and 1. Boolean algebra includes a series of operators ("and,"
"or," "not," "nand," "nor,"
and
"xor") which can be used to manipulate "true"
and "false" values. In modern notation, a
Boolean algebra is any 6-tuple {B, Å, Ä, Ø,
0, 1} that satisfies the following conditions:
1. B is a set of elements;
2. Å and Ä are two binary operations on B (a
binary operation on a set B is a function
from B ´ B to Å, for example the truth tables
for "or" and "and") that are
2.1. commutative, a binary operation * on B is said to be
commutative if and only if "x "y
(((x Î B) Ù (y Î B)) ® (x * y = y
* x))
2.2. associative, a binary operation * on B is said to be
associative if and only if
"x "y "z ((((x Î B) Ù (y Î
B)) Ù (z Î B)) ® (x * (y * z) = (x * y)
* z))
2.3. idempotent, a binary operation * on B is said to be
idempotent if and only if
"x ((x Î B) ® (x * x = x));
3. each binary operation is distributive over the other:
a binary operation Ä is said to be distributive over
a binary operation Å on a set B if
"x "y "z ((((x Î B) Ù (y Î
B)) Ù (z Î B)) ® (w Ä (y Å z)
= (w Ä y) Å (w Ä z)));
4. the constant 0 is the identity for Å and the constant
1 is the identity for Ä
an identity for a binary operation * on B is an element
e in B for which
"x ((x Î B) ® (x * e = x = e * x));
5. the complement operation Ø is a unary operation
satisfying the condition
"x (x Î B ® ((x Å Ø x = 1) Ù
(x Ä Ø x = 0))).
Since propositional logic, interpreted as a 6-tuple {{F,
T }, Ú, Ù, Ø, T, F}, can be shown to
satisfy such conditions, it qualifies as a Boolean algebra,
and this holds true in set theory as
well, where B is the set of subsets of a given set, the
operations of intersection (Ç) and union
(È) replace Ù and Ú respectively, and
the set complement plays the role of Boolean algebra
complement. The question then becomes how we implement a
Boolean algebra
electronically. We need electronic switches arranged into
logical gates, which can be
assembled as components of larger functional units. Once
this is achieved, it becomes a
matter of technological progress to construct increasingly
efficient logic gates that are smaller
and faster.
BOOLEAN NETWORK
A network comprised of some number of binary variables.
The state of each variable at each
step in discrete time is governed by some logical switching
or "Boolean" function applied to
the states of some specific set of other variables in the
network.
BUTTERFLY EFFECT
Said of initial, small, and local causes leading to unpredictable,
large, and global effects in
chaotic system. See also DETERMINISTIC CHAOS.
C
CATALYSIS
A modification (usually an increase) in the rate of a chemical
reaction that is induced by a
substance (e.g. a catalyst like an enzyme) that alters the
speed of, or makes possible, a
biochemical or chemical reaction while remaining unchanged
at the end of the reaction.
CAUSAL RELATIONS
The relations that obtain between two events when one is
the cause of the other. It is
sometimes assumed that indeterminism implies noncausation;
on other views, causal
relations can be deterministic or indeterministic. Sentences
that describe causal relations
between events may occur in causal explanations. See also
CAUSATION.
CAUSATION
A process or a property by virtue of which one event brings
about (or "produces") another.
The producing event is known as the cause and the event
produced as its effect. One of the
most difficult concepts in epistemology and the philosophy
of science, causes are usually
assumed to be temporally prior to, as well as spatially
contiguous with, their effects, where the
occurrence of a cause makes its effect necessary (or probable).
Although Newton's theory of
gravitation appears to violate this conception by introducing
action-at-a-distance,
contemporary theories of gravitation appeal to the notion
of gravitational waves propagated at
finite velocities. According to Einstein's special theory
of relativity, furthermore, no causal
process can occur at a rate faster than that of the speed
of light. Quantum mechanics poses
puzzling phenomena that may or may not violate this assumption.
The strongest conceptions
of causation are those associated with determinism, according
to which the same outcome is
invariably produced as an effect when the same cause occurs
("same cause, same effect").
But this turns out to be the case only when causes are given
descriptions that are nomically
complete (by including a specification of the presence or
the absence of every property
whose presence or absence makes a difference to the occurrence
of that outcome).
Somewhat weaker conceptions of causation are associated
with indeterminism, where one or
another outcome in the same fixed set of possible outcomes
variably occurs but with constant
probability.
CELLULAR AUTOMATON (pl. AUTOMATA)
Systems consisting of arrays (a regular spatial lattice)
of connected individuals, known as
"cells," each of which follows some simple "local"
rule or program and can be in any one of a
finite number of states. The states of all the cells in
the lattice are updated simultaneously and
the state of the entire lattice advances in discrete time
steps. The state of each cell in the
lattice is updated according to a local rule that may depend
on the state of the cell and its
neighbors at the previous time step. Each cell in a cellular
automaton could be considered to
be a finite state machine, which takes its neighbors' states
as input and outputs its own state.
Cellular automata are often offered as examples of how global
patterns can arise from purely
local interaction, with Conway's "Game of Life"
given as a common example.
CETERIS PARIBUS
Latin for "other things equal." Ceteris paribus
clauses are nonstrict generalizations but
generalizations that hold when other things are equal. They
typically occur conjoined with
incomplete descriptions of the factors whose presence or
absence bring about an outcome.
Thus, ceteris paribus, striking a match will cause it to
light (but not if the match is wet, if there
is insufficient oxygen present, or if it is struck in a
peculiar fashion).
CHAT
A variety of synchronous systems, including IRC (Internet
Relay Chat) and ICQ ("I seek you"),
which allow two or more people to exchange text messages
in real time, in contrast with
asynchronous systems such as e-mail. See also CHATROOMS.
CHATROOMS
Conversational "spaces" made possible by chat
software. Users log on (often under a selfchosen
pseudonym) to a chatroom of specific interest (e.g., concerning
technical issues)
and/or populated by specified users (teenagers, seniors,
science fiction fans, etc.) and can
then engage in both public and private chat with other users
who are also logged on to the
chatroom. See also CHAT.
CHINESE ROOM
An argument advanced by John Searle to illustrate the thesis
that similar input/output
behavior is insufficient to demonstrate that two systems
are systems of the same kind in
relation to their modes of operation. The Chinese room consists
of an enclosure around a
person who knows no Chinese but is equipped with a set of
directions (or "dictionary") that
instructs him or her what Chinese characters ought to be
sent out when other Chinese
characters are sent in. Although the person in the room
knows no Chinese, his or her
input/output behavior is said to be identical with that
of someone fluent in Chinese. A
counterexample to the Turing test, Searle's argument has
been the subject of a voluminous
literature. See also EMULATION; REPLICATION;
SIMULATION; TURING TEST.
CHURCH'S THEOREM
Theorem proved by Alonzo Church showing that there is no
mechanical routine (or decision
procedure) for establishing the validity of arguments in
quantificational logic with relations and
multiple quantifiers.
CHURCH-TURING THESIS (abbrev. CTT)
Broadly speaking, CTT suggests that the intuitive but informal
notion of "effectively
computable function" can be replaced by the more precise
notion of "TM-computable function"
(where "TM" equals Turing machine). CTT holds
that if a computational problem cannot be
solved by a TM then it cannot be solved by an algorithmic
system. See ALGORITHM;
COMPUTABILITY; DECISION PROCEDURE; TURING
MACHINE.
CLOSED-WORLD ASSUMPTION
A metalinguistic rule concerning how database queries are
to be handled. The closed-world
assumption allows the inference of a negative literal P(t1,
…, Pn) from a failure to infer its
positive counterpart P(t1, …, Pn). Although the rule
is formally unsound, it does allow for
defeasible inference, in that if the literal P(t1, …,
Pn) were to be added to the database, P(t1,
…, Pn) would no longer be inferred.
CLOSURE
A set of objects S is closed under an operation R when for
every member x of the set S, if x is
R-related to y, then y is a member of set S.
COGNITION
Any instance of any mental operation at any time where something
stands for something else
in some respect or other. Ordinary instances thereof include
perception, recognition,
inference, memory, and problem-solving. Alternatively, a
causal process that occurs when a
system that has the ability to use signs of a certain kind
becomes conscious of the presence
of a sign in relation to its other internal states. When
the system becomes conscious of
something that functions as a sign for the system, cognition
occurs as an effect of interaction
between that sign and those states. Alternatively, any mental
state that requires or involves
representations.
COGNITIVE FUNCTIONS
According to the computational theory of mind, cognitive
(mental) abilities are exercised by
means of the computation of cognitive functions. An example
of a cognitive function in lowlevel
vision is a function that maps patterns of retinal stimulation
onto representations of
scenes before the visual observer's eyes.
COGNITIVE MODELING
The use of computers to simulate aspects of human thinking.
COGNITIVE SCIENCE
Study of the nature and laws of cognition in human beings,
other animals, and possibly
machines. Cognitive science is an interdisciplinary field
embracing philosophy, psychology,
artificial intelligence, neuroscience, information theory,
linguistics, and anthropology. The
dominant paradigm within cognitive science has been the
computational conception, which
assumes that human beings and digital computers operate
according to the same principles,
at some suitable level. More recently, connectionist conceptions
of the brain as a neural
network have supplied the foundation for alternative theories
of cognition, which may afford
new solutions to the nature of mind and the mind/body problem.
While computers may be
useful within cognitive science, they are not essential
to its being. A science of cognition could
still be pursued even in the absence of these machines.
COHERENTISM
A theory of justified belief according to which justification
for a belief (or a set of beliefs)
derives from confirmation or agreement from other beliefs
already in the set.
COMBINATORIAL OPTIMIZATION
A combinatorial optimization problem takes the form of minimizing
the cost of certain solutions
to a given type of task; a typical such task is to maximize
the flow of goods in a road network,
given that each road has a maximum capacity.
COMBINATORICS
The area of mathematics concerned with counting classes
of finite structures.
COMPACTNESS THEOREM
A fundamental result about the nature and expressive limitations
of classical first-order logic:
it states that a set G of sentences is consistent if and
only if every finite subset G0 of G is
consistent. Together with the Löwenheim-Skolem property,
it characterizes first-order logic.
COMPETITIVE NETWORKS
Connectionist networks (or artificial neural networks) in
which units (or nodes) form pools. The
units in a pool are all mutually inhibitory, while units
outside of the pool bear excitatory
connections to one or more units in the pool.
COMPILER
A programming tool that translates a program written in
a familiar high-level language like
Basic, C++, or Java, into, typically, the machine language
of a computer, which is composed
only of zeroes and ones.
COMPLETENESS THEOREM
A feature of classical first-order logic according to which
a sentence f is a logical
consequence of a set G of sentences if and only if there
is a formal proof of f all of whose
assumptions are drawn from G.
COMPUTABILITY
The class of problems that can be solved by means of the
application of algorithms to formal
systems. The Church-Turing thesis establishes that a universal
Turing machine has the
capacity to imitate any formal system, which implies that
the boundaries of computability are
the same as those of problems that can be solved by universal
Turing machines. A parallel
thesis about the nature of thought maintains that all thinking
is computation because
computability itself defines the boundaries of thought.
See also CHURCH-TURING THESIS.
COMPUTATION, THEORY OF
The mathematical analysis of data structures and algorithms.
COMPUTATIONAL PROCESS
Generically, any form of behavior or pattern of actions
instantiating a formal specification and
resulting in a state transition from input conditions to
output conditions. For example, the
process by which a card player arranges cards in her hand,
and the process by which a
computer sorts names in a customer list, though they share
nothing in common physically,
may nevertheless embody the same computational process.
See also ALGORITHM;
COMPUTABILITY; DECISION PROCEDURE.
COMPUTER SCIENCE
The science concerned with the study of computational processes
and with the design and
implementation of hardware and of software to solve problems,
characteristically by means of
algorithms (or effective procedures) implemented in the
form of programs.
CONCEPTS
What words stand for, signify, or mean, especially when
meanings are taken to be in our
heads rather than in the world. Words that are synonymous
stand for the same concept.
When sentences are synonymous, then they may be said to
stand for the same proposition.
Concepts are sometimes analyzed as complex forms of dispositions
or habits of mind and
habits of action that instantiate different meanings.
CONCEPTUALIZATION
An abstract, simplified view of some domain that we wish
to represent for some purpose. See
also ABSTRACTION.
CONDITIONALIZATION
A process of changing degrees of belief under the influence
of new information in accordance
with (a special application of) Bayes' theorem. If "Pn"
stands for the new probability
distribution ("posterior" to or subsequent to
the acquisition of some new information E) and
"Po" stands for the old distribution ("prior"
to the acquisition of that new information E), then
according to the principle of conditionalization, Pn(X)
= Po(X/E) = Po(E/X) o Po(X)/Po(E).
Given this interpretation, Bayes' theorem functions as a
dynamic requirement that must be
satisfied by sets of beliefs as they change across time
as opposed to its normal use as a
static requirement of a set of beliefs at one time. See
also BAYESIANISM; BAYES'
THEOREM.
CONDITIONALS
Complex sentences of "If . . . then ___" form,
where the ". . ." sentence is known as the
antecedent and the "___" sentence as the consequent.
While many kinds of conditionals
occur in English, logicians focus on certain varieties in
constructing models for understanding
arguments. The simplest kind of conditional is the material
or "truth-functional" conditional,
where the truth or falsity of a sentence of this form depends
exclusively upon the truth-value
of its components. When either the antecedent is false or
the consequent is true, sentences
of this kind are said to be true. A second kind of conditional
is the subjunctive (or
"were"/"would") conditional, which characterizes
how things would be on the assumption that
the antecedent were true. Thus, the sentences, "If
this stick of dynamite were ignited, then it
would explode," and "If this stick of dynamite
were ignited, then it would not explode," as
material conditionals, might both be true as long as their
antecedents are false. But as
subjunctive conditionals, they cannot both be true, since
they characterized different ways
things would be on the assumption that their antecedents
were true. Subjunctives with false
antecedents are also called counterfactual conditionals.
Among various kinds of conditionals
that are also studied by philosophers of science are causal
conditionals, nomic conditionals,
and probabilistic conditionals.
CONFIRMATION VS. TRUTH
Evidence that confirms an hypothesis does not thereby guarantee
its truth. Truth appears to
be a relation involving sentences in a language where a
sentence is true when what that
sentence asserts to be the case is the case. But a sentence
can be confirmed even if it is
false and can be true even if it is never confirmed. The
hypothesis of the existence of
intelligent life elsewhere in the universe may be true,
yet remain unconfirmed. Newtonian
mechanics was among the best-confirmed theories in science,
yet it no longer appears to be
true. Truth is a semantic (or ontic) concept, but confirmation
is a pragmatic (or epistemic)
concept. For theories, such as coherence theories, that
reject more traditional conceptions of
truth, belief sets that satisfy specific relations of coherence
among themselves, in particular,
may be viewed as confirmed or as true (or both).
CONJUNCTIVE
Pertaining to conjunction, as in A & B, where both A
and B are true.
CONNECTED PROBLEMS
Problems that do not divide into independently solvable
subproblems. A paradigm example is
the traveling salesman problem. The goal is to find the
shortest route that a salesman can
take to visit each of a number of cities, while visiting
each city only once. Since which city the
salesman visits depends on which cities he has already visited,
the problem does not divide
into independently solvable subproblems. Connected problems
represent a limit to the
parallelization of solution procedures.
CONNECTIONISM
An approach to computation, cognitive science, and philosophy
of mind that views the brain
as a neural network of numerous nodes that are capable of
activation. These nodes can be
connected to other nodes where, depending on their levels
of activation, they might bring
about increases or decreases in the levels of activation
of those other nodes. These patterns
of activation, in turn, can function as signs for the larger
systems, of which they are otherwise
meaningless parts, by coming to stand for other things for
the systems of which they are
elements. This process is known as learning, conditioning,
or reinforcement, where the impact
of experience in the shaping of behavior depends upon the
causal tendencies instantiated by
a specific connectionist system. Connectionist architectures
of the brain differ from traditional
conceptions in many respects. One is that connectionist
brains are capable of parallel
processing, which means that more than one stream of data,
information, or knowledge may
be processed at the same time. Traditional machines can
be arranged to process data
simultaneously, but each machine can only process one stream
of data sequentially. More
important is that connectionist brains are capable of distributed
processing, which means that
the bearers of information or knowledge in connectionist
systems are patterns of activation
rather than individual nodes. Some versions of connectionist
system make individual nodes
(or units) the bearers of information, but they fail to
exploit what may be the greatest
advantage of the connectionist approach. Additionally, different
kinds of connectionist
systems seem to typify different species. Thus, connectionism
offers an approach that
promises to clarify and illuminate the mental properties
of other species. This is the dominant
research program in cognitive science today.
CONSCIOUSNESS
A state of awareness capable of degrees, where a person
(animal, machine) might be
conscious of some phenomena but not conscious of other phenomena.
The range of possible
awareness appears to be determined by neurophysiological
capacities under the influence of
environmental histories. Thus, with respect to signs (marks,
symbols), for example, a person
may be said to be conscious with respect to signs (marks,
symbols) of some kind when they
have the ability to use those symbols and they are not incapacitated
from exercising that
ability. When a sign (mark, symbol) of that kind occurs
within suitable causal proximity, then
cognition results. Consciousness should be distinguished
from self-consciousness, which is
an awareness of one's own self. Self-consciousness, like
consciousness, is amenable to
degrees, where some persons are more self-conscious (self-aware
or self-knowing) than
others.
CONSTRUCTIVISM
Ernst von Glasersfeld defined as "radical constructivism"
the claim that knowledge is actively
built up by the knowing subject. Thus, the external world
does not exist independently of the
subject, as a separate ontological reality; on the contrary,
it exists as the world of the subject's
experience.
CONVENTIONS
Shared habits, tendencies, and dispositions qualify as conventions
when they are reinforced
or explicitly endorsed by the community, as in the case
of natural languages taught by public
schools.
COOKIE
File placed on a user's computer when the user visits a
website. The file allows the website to
keep track of subsequent visits. Cookies can be sent without
the user's knowledge or
consent.
COUNTERFACTUAL SUPPORT
A generalization is said to be counterfactual-supporting
if it is not only true of its instances, but
also would be true of relevant non-instances. For example,
the generalization "metals expand
on heating" is counterfactual-supporting because it
not only says something true about what
happens to heated metals, but also says something true about
what would happen to
unheated metals, were they heated (contrary to actual fact).
In contrast, "everything in Nelson
Goodman's pocket on VE Day was silver" is not counterfactual-supporting
because, even if all
the things in Nelson Goodman's pocket on VE Day were in
fact silver, there are many
nonsilver objects that might have been in Nelson Goodman's
pocket on VE Day. It is widely
thought to be a requirement on nomic generalizations (as
opposed to mere accidentally true
generalizations) that they support counterfactuals.
COVARIATION (OF PROPERTIES)
Properties P and Q covary just in case P is instantiated
if and only if Q is instantiated.
CRYPTOLOGY
The study of the mathematics of secret codes or cryptosystems.
It encompasses
cryptography, the art of designing cryptosystems, and cryptanalysis,
the art of breaking
cryptosystems.
CURRY-HOWARD CORRESPONDENCE
A correspondence between terms in the calculus and proofs
in intuitionist logic
CUT
A formal property of classical first-order logic and many
defeasible systems (more precisely:
of the associated consequence relations) according to which
adding a previously reached
conclusion to the premise-set does not lead to any increase
in inferential power.
CYBORG
A short form of "cybernetic organism," that is,
some machine-animal hybrid.
D
DASEIN
Heidegger's name for human being. The German literally means
"being there" or "there
being." Because of its technical philosophical meaning,
it is usually not translated.
DATA ABSTRACTION
The specification of computational objects (like customers,
recipes, flight plans, chatrooms,
etc.) and all operations that can be performed on them,
without reference to the details of
their implementation in terms of other data types. Such
objects, called data types, once they
become implemented, assume their place among integers, arrays,
and so on as legitimate
objects in the computational world, with their representation
details, which are necessarily
more machine-oriented, being invisible to their users.
DATA
Normally, information is conveyed by large clusters of well-formed,
codified data, usually
alphanumeric, which are heavily constrained syntactically
and already very rich semantically.
However, in its simplest form a datum is any lack of uniformity
or anything that makes a
difference: a light in the dark, a black dot on a white
page, a 1 opposed to a 0, a sound in the
silence, the difference between the presence and the absence
of a signal. In Chapter 4, data
are also defined as constraining affordances or answers
without questions: 12 is a sign that
makes a difference (datum), but it is not yet informative,
for it could be the number of the
astrological signs, the size of a pair of shoes, or the
name of a bus route in London, we do not
know which. Computers certainly treat and "understand"
data. It is controversial whether there
is any reasonable sense in which they can be said to treat
and understand information.
DATA STRUCTURE
A way to store and organize data in order to facilitate
access and modifications.
DATAGLOVE
A glove-like device containing sensors that provides computer
input concerning the
movements of the user's hand, allowing the manipulation
of computer-generated objects in
virtual reality.
DEBUGGING
The process of eliminating errors (or "bugs")
from a computer program.
DECISION PROBLEM (ENTSCHEIDUNGSPROBLEM)
Formulated by Hilbert, the decision problem for a given
formal system is the problem of
providing a formal algorithm to determine whether a sentence
j can be inferred from a given
knowledge base in the system. More broadly, a decision problem
takes the form of a family of
problem instances, for each of which a "yes" or
"no" answer is required. In the case of the
decision problem for predicate logic, the instances take
the form of sentences of firstorder
logic, for which we want to know the answer: "Is this
sentence satisfiable?" Th e decision
problem for classical first-order logic was proved to be
unsolvable by Church and Turing in
1936. See also ALGORITHM and DECISION PROCEDURE.
DECISION PROCEDURE (Also known as "effective
procedure.")
A routine or procedure that can be carried out in a finite
sequence that in every case yields a
definite answer ("Yes" or "No") to a
question within a specific domain of inquiry. The discovery
of a decision procedure for a fixed class of problems is
known as the decision problem. Once
a decision procedure has been found, the problem is solvable
and those questions are
decidable. See also ALGORITHM and DECISION PROBLEM.
DELTA RULE
A supervised learning algorithm for weight change in connectionist
networks (or artificial
neural networks). The algorithm changes the weights leading
from units (or nodes) sending
signals to output units on the basis of the discrepancy
between the actual output and the
desired one so as to lesson the difference.
DERIVABILITY, SYNTACTIC
A formula of a formal system is syntactically derivable
from a set of formulae of a formal
system (as premises) when it follows from those premises
in accordance with an accepted
rule of inference of that system. When those premises are
axioms of the system, such a
formula is said to be a theorem. Rules of inference are
formal insofar as their application
depends exclusively upon the formal properties (of shape
and size, etc.) of the marks that
constitute (what is usually called) the vocabulary of that
system, without concern for possible
interpretations that make those formulae meaningful or true.
The construction of a formal
system, however, is normally motivated by the desire to
reflect corresponding relations of
semantic entailment with respect to the objects and relations
of some abstract or physical
domain.
DETERMINISTIC CHAOS
Attractor of a dynamical system with nonlinear dynamics,
nonperiodic and bounded
trajectories, and exponential dependence on initial conditions.
See also BUTTERFLY
EFFECT.
DIGITAL
A description of data or information that is stored or transmitted
as a sequence of discrete
symbols from a finite set. Most commonly, this means binary
data represented using
electronic or electromagnetic signals. In Chapter 13 a digital
property (or process or system)
is one that is finitely recursive.
DOMAIN ONTOLOGY
The extension or specification of a top-level ontology with
axioms and definitions pertaining to
the objects in some given domain.
DYNAMICAL SYSTEMS THEORY
Popularly known as chaos theory, the study of the iterative
dynamics of classes of
mathematical functions, and their applications. A central
focus of dynamical systems theory
has been iterated mathematical functions that show "sensitivity
to initial conditions": when the
output of the function is repeatedly taken as input, initial
conditions that are arbitrarily close
produce results arbitrarily far apart, something known as
the "butterfly effect" (q.v.).
E
EFFECTIVE PROCEDURE see DECISION PROCEDURE.
EMERGENCE
Synergetic and macroscopic phenomena of dynamical systems
explained by collective and
nonlinear interactions of their elements.
EMULATION
One system emulates another when they stand in a relation
of replication and are composed
of the same material. Thus, if humans and machines can not
only simulate each others
input/output behavior but also share the same modes of operation,
then they can stand in a
relation of replication. But only systems that are composed
of the same components - such
as metal and silicon or flesh and blood - can stand in a
relation of emulation. In relating
systems on the basis of their input/output behavior, their
modes of operation, and their
material of composition, this is the strongest possible
relationship between systems. See also
REPLICATION; SIMULATION; TURING TEST.
ENTAILMENT (SEMANTIC)
A set of interpreted formulae of a formal system (the premises)
semantically entails another
interpreted formula (the conclusion) when the conclusion
cannot be untrue if the premises are
true (the use of "untrue" instead of "false"
is meant to avoid ruling out many-valued versions
of entailments). The construction of a formal system tends
to be motivated by the desire to
establish relations of syntactic derivability reflecting
corresponding relations of semantic
entailment. Within sentential logic, for example, an argument
is syntactically valid if and only if
its corresponding conditional, that is a conditional formed
by taking the conjunction of its
premises as its antecedent and its conclusion as its consequent,
is a logical truth.
EPISTEMIC
Of or pertaining to knowledge or justification.
EPISTEMOLOGY see ONTOLOGY/EPISTEMOLOGY
ERGODIC SOURCE
A stochastic source of an unlimited number (or ensemble
of unlimited sequences) of symbols
(messages) which satisfies two properties: (i) the statistical
nature of its messages does not
change with time (the source is stationary); and (ii) the
statistics based on one message apply
equally well to all messages that the source generates.
A tossed coin is an ergodic source.
EROTETIC LOGIC
The logic of questions, answers, and the formal relations
between them.
EUKARYOTE
One of the two major groupings into which all organisms
are divided (the other is prokaryote).
Included are all organisms, except bacteria and cyanobacteria.
The cells of eukaryotes
possess a clearly defined nucleus, bounded by a membrane,
within which DNA is formed into
distinct chromosomes. Eukaryotic cells also contain mitochondria,
chloroplasts, and other
structures (organelles) that, together with a defined nucleus,
are lacking in the cells of
prokaryotes.
EXPERT SYSTEM
In its narrower sense, expert systems are restricted to
production systems of condition/action
rules, where when certain conditions are fulfilled, a certain
action is taken (or recommended).
In a broader sense, expert systems are any systems that
are based upon domain-specific
knowledge acquired by an expert. In this sense, scripts
and frames and semantic networks
may qualify, too. Typically, the construction of an expert
system is envisioned as a process of
knowledge acquisition, knowledge representation, and knowledge
utilization. Perhaps the
most important problem encountered in the development of
expert systems is picking the right
expert.
EXPONENTIAL
If F(n) is a quantity depending on a numerical parameter
n, then we say that F(n) is
exponential in n if there is a constant c > 0 so that
F(n) > 2cn for infinitely many n. For
example, the truthtable method for deciding satisfiability
of propositional formulas requires
exponentially many steps as a function of the number of
variables in a formula.
EXTENSION OF A THEORY
In defeasible reasoning, an extension is a maximally consistent
set of defeasible conclusions
that reasoners could be regarded as warranted in inferring
from the theory. In many
formalisms, theories can have zero, one, or more extensions.
EXTERNALISM
The view that at least some of the conditions that make
knowledge possible may forever lie
beyond or external to the ken of the would-be knower.
F
FEEDBACK
Informally speaking, the return of a signal that indicates
the effect of an action, in order to
determine further action by a (mechanical, electrical, electronic)
system. Negative feedback is
distinguished from positive feedback. In the first case
the returning signal is error correcting;
in the second case, it is error amplifying.
FEEDFORWARD NETWORKS
A non-interactive connectionist network (or artificial neural
network) in which activation flows
in one direction only, from input units (or nodes) through
however many layers of hidden units
the network contains to output units. The Hamming net is
a widely used feed-forward network
with three layers of units, one of which is a layer of hidden
units.
FIXED POINT
In a phase space, a point that is attractor of all trajectories
of a dynamical system.
FLOATING-POINT OPERATION
The hardware of current conventional computers (and pocket
calculators) is designed to
perform "floating-point arithmetic," that is,
their basic arithmetical circuits perform additions
and multiplications of numbers represented in "scientific
notation," as in the case of
Avogadro's number N = 6.02252 × 1023. A common measure
of speed for supercomputers is
the number of floating-point operations performed per second;
a speed of one megaflop
represents one million floating-point operations per second.
In June 2000, the IBM RS/6000
SP supercomputer had a performance in excess of 1 teraflop
(a trillion [1012] floating-point
operations per second). In 2003, NEC's supercomputer, named
"Earth Simulator," could
perform 35.9 trillion calculations per second.
FORMAL PROGRAM VERIFICATION
The process of determining whether a program conforms to
its specification, not by
empirically testing the program to observe its behavior,
but by mathematically reasoning
about its algorithm as a formal, abstract object.
FORMAL PROGRAM VERIFICATION DEBATE
The debate over whether formal program verification can
offer guarantees of program
correctness and reliability. Opponents of formal program
verification claim that it can offer no
such guarantees. Proponents believe that it can largely
replace program testing in the
identification of program bugs (errors).
FORTRAN
A programming language, designed in the 1950s, intended
for the solution of scientific
problems.
FOUNDATIONALISM
The view that some beliefs are not justified by other beliefs,
but by experience, selfjustification,
or some source other than relation to other beliefs.
FRAME PROBLEM
There appear to be several versions. The most restricted
version takes it as the problem of
designing and implementing a program for anticipating what
will and what will not change
about a situation (or state of affairs) across time. A less
restricted version takes it as the
problem of discovering the kind of knowledge that would
provide the foundation for designing
and implementing a program for solving the first version.
Moreover, some theoreticians
maintain that the problem concerns common sense rather than
scientific knowledge, whereas
others, with some justification, contend that scientific
knowledge is required to resolve it.
FUNCTIONAL
A mathematical function whose domain is a set of functions.
For example, definite integration
is a functional which, when given a function, returns a
number (the integral of that function
over a particular interval).
FUNCTIONAL PROGRAMMING
A programming language is functional if it has no assignment
statements: this makes its
semantics particular tractable.
FUNCTIONALISM
There are at least two principal varieties. The first is
machine-state functionalism, which
maintains that human beings can be properly understood as
special instances of computing
machines, and mental activity involves functional transitions
from one state to another. This
position was advocated by Hilary Putnam in some of his early
work. The second is causal-role
functionalism, which maintains that the meaning of a mental
representation (symbol, sign)
either is or is not determined by its causal role in influencing
behavior. Machine-state
functionalism is not widely advocated at present, but causal-role
functionalism is popular.
G
GELASSENHEIT
German for calmness, composure, tranquility. Used by
Meister Erkhart to name mystical
detachment or releasement. Heidegger picks up the term and
presents the Gelassenheit as
the opposite of the technological attitude toward the world.
GESTELL
A German word that in everyday parlance means "stand,"
"rack," "shelf," etc., which
Heidegger adopts as a technical term for what he calls the
essence of modern technology, its
enframing of the world, transforming the world into Bestand
or resources.
GOFAI
Good Old-Fashioned Artificial Intelligence; see AI, STRONG.
H
HEBB RULE
A learning algorithm for weight change in a connectionist
network (or artificial neural network).
The Hebb Rule is based on Donald Hebb's hypothesis that
the connections between two
neurons might strengthen whenever they fire simultaneously.
According to Rumelhart and
McClelland's formulation of the Hebb rule, the weight of
a connection between units should be
increased or decreased in proportion to the products of
their simultaneous activations.
HALTING PROBLEM
The problem of deciding whether a particular computer program
will ultimately halt or not.
This was historically the first undecidable problem to be
discovered. See also DECISION
PROBLEM.
HAPTIC
Pertaining to the sense of touch. In the context of computers,
haptic feedback can refer to the
simple feel of a keyboard or mouse, or to more sophisticated
forms of tactile feedback
employed by some virtual-reality systems.
HEAD-MOUNTED DISPLAY
A helmet or goggle-like device that provides computer input
concerning the user's head and
eye movements which are then used to change and update virtual-reality
displays in ways
appropriate to those head and eye movements.
HERMENEUTICS
From the name for the Greek messenger god, Hermes, hermeneutics
is the study of
messages or the science of (textual) interpretation.
HEURISTICS
In the absence of algorithms, generalizations or "rules
of thumb" that are useful but have
exceptions can turn out to be very helpful in dealing with
problems that might not otherwise be
resolved. Since inductive generalizations are amenable to
exceptions, due to their fallible
character as the conclusions of arguments that are ampliative,
and nondemonstrative, a
terminological decision has to be arrived at as to whether
reliance upon induction is or is not a
matter of heuristics.
HOLISM OF BELIEF FIXATION
The claim that it is impossible to fix, or come to, a given
belief without holding in place a
number of other beliefs at the same time. According to this
view, an experimental datum
confirms (i.e. verifies, gives us some reason to believe)
a given statement only in conjunction
with one's other theoretical commitments, background assumptions
about the experiment,
and assumptions about the logical and mathematical apparatus
connecting the datum to
these other beliefs.
HOMEOSTASIS
Self-regulation, the ability or tendency of an organism
or a cell to maintain internal equilibrium
by adjusting its physiological processes and their variables,
such as body temperature or
blood pressure, which are important for the survival or
health of living organisms.
HYPERDIGITAL
A hyperdigital property (or process or system) is one that
is transfinitely recursive.
I
ICONS
In the theory of signs advanced by Charles S. Peirce, icons
are things that stand for that for
which they stand by virtue of a relation of resemblance
that obtains between that sign and
that for which it stands. Thus, photographs, paintings,
and statues are familiar icons.
ICQ ("I seek you") see CHAT
ICT
Digital information and communication technologies.
IMITATION GAME
A game in which a thing of one kind is pitted against a
thing of another kind to see if it can
cause a contestant to mistake it for the other kind. At
a party, a man might be paired up
against a woman, where a contestant might be asked to guess
which is which based strictly
upon their answers to questions. If the man were trying
to pose as a woman, then he would
be permitted to give false answers, but not the woman. As
a serious test, a machine might be
paired up with a human being, where a contestant might be
asked to guess which is which
based strictly upon their answers to questions. The machine
would also be permitted to give
answers that were false. The presumption is that a machine
that could fool a human
contestant into thinking that it were human would be equal
to its human counterpart with
respect to the characteristic tested. Yet even if the man
were to fool a contestant into thinking
he was a woman, that would not change his sex. See also
EMULATION;
REPLICATION; SIMULATION; TURING TEST.
INDICES
In the theory of signs elaborated by Charles S. Peirce,
indices are signs that stand for that for
which they stand by virtue of being causes or effects of
that for which they stand. Thus,
smoke is an index of fire and fire is an index of smoke.
Excellent examples of indices in this
sense are symptoms in relation to a disease.
INDUCTION, MATHEMATICAL
Its name notwithstanding, mathematical induction is a special
case of deductive reasoning
and a fundamental principle of mathematical reasoning for
the natural numbers. Mathematical
induction allows one to prove that, if 0 has the property
P and, whenever a number has P, so
does its successor, then every number has the property P.
Variants of mathematical induction
apply to other well-ordered or recursively defined collections.
INFERENCE
The process of drawing conclusions from premises, especially
when that process could be
justified on the basis of logic. Thus, the free association
of ideas does not properly qualify as
inference. Rules of deduction and induction are called rules
of inference.
INFERENCE TO THE BEST EXPLANATION see ABDUCTION
INFERENCE, RULES OF
Both deductive and inductive reasoning are governed by rules
of inference, which specify
what follows from what (in the case of deductive rules),
and what supports what (in the case
of inductive rules). A familiar deductive rules of inference
is modus ponens. According to this
rule, given "if p then q" and "p," infer
"q," where the conclusion cannot be false if the
premises
are true. A familiar inductive rule of inference is the
straight rule, which is also known as
induction by enumeration: if m/n observed As have been Bs,
infer that m/n As are Bs, when a
large number of As have been observed over a wide variety
of conditions. But inductive
conclusions can still be false even when their premises
are true.
INFORMATION (SEMANTIC)
Chapters 4 and 9 follow Floridi's definition: in its weaker
sense, semantic information is wellformed, meaningful data;
in its stronger sense, well-formed and meaningful data that
is
truthful. See also DATA.
INFORMATION CARRYING
According to Dretske, a signal r carries the information
that p just in case the conditional
probability of p, given r (and k , the knowledge of the
receiver of r), is 1 (but given k alone, less
than 1).
INFORMATION SYSTEMS ONTOLOGY
A concise and unambiguous description of principal, relevant
entities of an application
domain. A dictionary of terms formulated in a canonical
syntax and with commonly accepted
definitions, of such a sort that it can yield a shared framework
of knowledge-representation on
the part of different information systems communities.
INTELLIGENCE
Historically, intelligence has been viewed as the capacity
or ability to learn. When that ability
or capacity is evaluated in relation to one's chronological
age by employing standardized
tests, the result is a numerical value known as IQ. The
problem that has plagued IQ tests is
that IQ must be something more than merely an IQ test score
or else it would not be worth
measuring. There are those who suggest that the term "intelligence"
carries with it an
evaluative connotation, where its meaning presupposes mentality
and it indicates a high level
of mentality. Alternatively, its use in the context of the
phrase "artificial intelligence" raises the
possibility that, even if machines are incapable of possessing
"ordinary intelligence," they
might still be described as "intelligence machines"
by virtue of their capacity to perform
various complex tasks successfully and reliably, especially
ones that have required human
beings in the past.
INTENTIONAL
About something. Things that are about other things (e.g.,
mental states, words) are said to
have intentional properties. Not to be confused with a different,
ordinary usage of "intentional"
to mean on purpose.
INTERACTIVE NETWORKS
Connectionist networks (or artificial neural networks) in
which two units (or nodes) can
mutually influence each other's state of activation.
INTERNALISM
The view that the conditions that confer knowledge or justification
must, in principle, be
accessible to the would-be knower.
INTERPRETATION
An interpretation for a language L specifies a non-empty
domain D of individuals and assigns
objects from D to the names of the language and sets of
n-tuples from D to the n-place
predicates of L .
INTROSPECTION
A faculty or capacity for deriving knowledge, especially
about one's own mental states, by
internal observation. Two kinds of knowledge by introspection
can be distinguished, those
which attend to mental states at the time of their occurrence
and those which attend to mental
states that have been acquired in the past. When past mental
states are the object of
contemplation through a process of recollection or remembering,
the introspective faculty is
also known as that of memory.
IRC (Internet Relay Chat) see CHAT
ISOMORPHISM
A structure preserving one-to-one mapping from one structure
to another structure, also
holding in the inverse relation.
J
K
KNOWLEDGE REPRESENTATION
Different schemes for representing knowledge have been advanced,
including predicate
calculus, scripts and frames, and production systems. The
theory of knowledge
representation, when adequately elaborated, ought to provide
a foundation for understanding
when one or another mode of knowledge representation is
most appropriate and the
strengths and limitations thereof.
KNOWLEDGE VS. BELIEF
The tradition theory of knowledge holds that x knows that
p if and only if (i) x believes that p,
(ii) x is justified in believing that p, and (iii) p is
true. Hence, knowledge is envisioned as
justified true belief. Some alternative conceptions of knowledge
have viewed knowledge as
true belief, in which case the possession of knowledge can
be merely accidental, or as
justified belief, in which case persons can know things
that are not true. Belief itself, however,
is never viewed as sufficient for knowledge, where the importance
of beliefs in practical
contexts stems from the guidance that they provide in the
conduct of behavior and in
theoretical contexts from the foundation they provide for
systematically explaining and
predicting events.
KNOWLEDGE, EMPIRICAL
Knowledge about the external world, especially knowledge
that is justified on the basis of
direct perception or inductive or deductive inferences based
upon direct perception.
Alternatively, any knowledge that is synthetic rather than
analytic and a posteriori rather than
a priori. A distinction may be drawn between empirical and
scientific knowledge, where the
objects of empirical knowledge are singular sentences that
describe the contents of relatively
isolated regions of space/time and the objects of scientific
knowledge are generalizations
(hypotheses and theories) about laws of nature that define
the world's structure. Scientific
knowledge can then be said to be based on empirical knowledge,
yet not be reducible to it.
KNOWLEDGE, STANDARD DEFINITION OF
The definition of "knowledge" as true belief supported
by evidence. Beginning with Plato's
Theaetetus, "knowledge" is viewed as true belief
plus something which has the function of
preventing knowledge from being merely a matter of accident
or hunch, superstition or a lucky
guess. This conception assumes that knowledge requires satisfying
a suitable condition of
evidential justification that goes beyond having a belief
that happens to be true. See also
KNOWLEDGE VS. BELIEF.
L
LAMBDA CALCULUS
A logical calculus developed by Alonzo Church based on the
idea of the application of
functions to their arguments.
LANGUAGE
A system of signs used for communication between human beings.
Natural or ordinary
languages include English, French, German, and any other
used by a community of humans.
Artificial languages can be constructed for special purposes,
such as the development of
formal systems, the programming of computers, and the like.
See also ARTIFICIAL
LANGUAGE; NATURAL LANGUAGE; SEMANTICS;
and SYNTAX.
LANGUAGE, ARTIFICAL
Any system of notation and its rules of correct use (syntax)
which has been constructed for
special purposes other than ordinary communication between
the members of a languageusing
community. Good examples include formal systems in logic
and pure mathematics (as
uninterpreted systems) or programming languages in computer
science (as interpreted
systems). According to this definition, certain special
cases (such as Morse code) can be
viewed as falling in between natural and artificial language.
See also LANGUAGE;
SEMANTICS; SYNTAX.
LANGUAGE, NATURAL
Any system of notation and its rules of use which has been
developed for the general purpose
of facilitating communication between the members of a language-using
community.
Examples include English, Spanish, German, Russian, Japanese,
and Chinese. They are
often viewed as conventional. Though the basic unit of meaning
for a language appears to be
the habits, tendencies, and dispositions of individual language
users, communities (usually
typified by the populations of specific geographical regions,
with their traditions and practices)
promote the use of the same linguistic habits, tendencies,
and dispositions between different
language users to promote communication and cooperation
between them. See also
ARTIFICIAL LANGUAGE; LANGUAGE.
LANGUAGE-OF-THOUGHT HYPOTHESIS
The thesis that there is a system of mental representation
with a compositional syntax and
semantics. This language is often called Mentalese. Perhaps
the leading theory of thinking in
the computational theory of mind appeals to the language-of-thought
hypothesis, maintaining
that thinking consists in the manipulation of mental symbols
in virtue of their syntactic
properties. These syntactic operations are supposed to be
such that the mental symbol
transitions can be interpreted as processes of reasoning
(deductive, inductive, or analogical)
given the meanings of the mental symbols. The theory of
meaning for mental symbols is
called psychosemantics. (See SYMBOLS [2], on the
meanings of mental symbols.) Jerry
Fodor, the leading proponent of the language-of-thought
hypothesis, has argued that
concepts are words in the language of thought, and that
having a propositional attitude in a
certain intentional mode (e.g., belief, desire, intention,
etc.) with the content that P consists in
bearing a computational relation constitutive of the intentional
mode to a mentalese sentence
that means that P. Thus, for instance, to believe that P
is to bear a certain computational
relation R constitutive of the belief relation to a mentalese
sentence that means that P, to
desire that P is to bear a certain computational relation
R* constitutive of desire to a
mentalese sentence that means that P, and so on. This theory
of propositional attitudes, he
contends, offers the best explanation of the systematicity
of capacities to have propositional
attitudes and of the productivity of propositional attitudes.
Fodor has also maintained that
every (neurologically normal) human being has an innate
stock of primitive mental symbols
(concepts) that are sufficient, in principle, to draw every
distinction that may ever be drawn in
any human language. This innateness hypothesis is, however,
logically independent of the
language-of-thought account of thinking, concepts, and propositional
attitudes.
LIGHT AI
The alternative to GOFAI (Good Old-Fashioned Artificial
Intelligence), see AI, STRONG.
LIMIT CYCLE
In a phase space, closed orbit that is attractor of all
trajectories of a dynamical system.
LINEAR DYNAMICS
Dynamics determined by a linear equation: the rate of dynamical
effects is proportional to its
cause.
LISP
Historically the first functional programming language.
LISTSERV
An e-mail system that distributes messages to and from a
list of subscribers. While most
listservs automatically redistribute messages to members
as they are sent, some listservs are
moderated: messages first go to the moderator/editor who
then determines whether they are
appropriate for further distribution and discussion by the
list members.
LOGIC
The study of arguments, which are usually separated into
the categories of deductive and
inductive. The first system of logic was that of classical
term logic, formalized by Aristotle,
which studied the validity of arguments that can be formulated
by means of a restricted class
of sentences having specific kinds of logical form. Classical
term logic characterizes the
conclusions that follow from one premise (called immediate
inference) and the conclusions
that follow from two premises (called syllogistic inference),
when premises and conclusions
are restricted to so-called categorical sentences. Until
around the mid-nineteenth century,
Aristotelian logic was widely viewed as exhaustive of the
subject. But the introduction of the
sentential function by Gottlob Frege revolutionized the
subject, and today Aristotelian logic is
recognized to be only a special and relatively modest fragment
of modern logic, which
includes sentential logic (or the study of arguments when
whole sentences are the basic units
of analysis) and predicate logic (or the study of arguments
when sentences are analyzed on
the basis of their internal structure). Although elementary
logic is exclusively extensional (or
"truth functional"), advanced logic pursues the
formalization of intensional relations that are
not merely truth-functional, including the nature of subjunctive,
causal, and probabilistic
conditionals, but also set theory, recursive function theory,
and the theory of models.
LOGIC, AUTOEPISTEMIC
The modal logic of the operator "the agent knows that
p." The agent can reach (defeasible)
conclusions about the world based on its own epistemic state.
LOGIC, CLASSICAL TERM
A system of logic studied by Aristotle that is restricted
to the validity of arguments that are
composed of sentences of four basic kinds called "categorical
sentences," namely: (A)
universal affirmative: All S are P; (E) universal negative:
No S are P; (I) particular affirmative:
Some S are P; and (O) particular negative: Some S are non-P.
There are two principal
branches, know as immediate inference (which studies arguments
having one categorical
premise and one categorical conclusion) and syllogistic
inference (which studies arguments
having two categorical premises and one categorical conclusion).
Medieval logicians
discovered that two sets of logical relations are involved
here, depending upon whether the
subject (S-term) and predicate (P-term) classes are assumed
to have at least one member,
which is known as the existential presupposition. On the
existential presupposition, for
example, (I) sentences follow from (A) sentences, but not
when that presupposition is not
made. Hence, even with respect to immediate inference, there
are two sets of logical
relations, known as the strong and as the weak squares of
opposition, whose respective
differences depend upon whether the existential presupposition
is adopted.
LOGIC, DEFAULT
A particularly flexible, nonmonotonic formalism introduced
by R. Reiter, based on the notion
of a defeasible inference rule called a "default."
LOGIC, EXTENSIONAL
Any system of logic that restricts its attention to truth-functional
operators and truth-functional
properties of and relations between sentences. Operators,
properties, and relations of this
kind are exclusively ones for which semantically relevant
features of language and logic are
limited to functions of truth-values (true/false) exclusively.
LOGIC, INTENSIONAL
Any system of logic that goes beyond merely truth-functional
operators and truth-functional
properties of and relations between sentences. Among the
kinds of sentences that are
studied within intensional logics are subjunctive conditionals,
counterfactual conditionals,
nomological conditionals, deontological conditionals, and
others unnamed.
LOGIC, INTUITIONIST
A logic, invented by Brouwer and based on the idea of mental
constructions, which rejects the
principle of excluded middle.
LOGIC, MODAL
A logic designed to represent state transitions: the logic
associates a modality c with each
state transition ® , where semantically a sentence c
A is true at a state s if and only if A is
true at every state s¢ such that s ® s¢. More
informally, the logic of necessity and possibility.
LOGIC, PREDICATE
Any system of logic that analyzes the validity of arguments
on the basis of the internal
structure of sentences rather than treating them as basic
units of analysis. Even the traditional
argument, "All men are mortal; Socrates is a man; therefore,
Socrates is mortal," cannot be
successfully analyzed within sentential logic, since it
has the form, "p; q; therefore, r," where
"p," "q," and "r" are variables
standing for unspecified sentences, which is not a valid
form.
Within predicate logic, however, it can be analyzed as having
the form, "(x)(Hx ® Mx); Hs;
therefore, Ms," where (x) means "for all,"
"Hx" means "x is a man (human)," "Mx"
means "x is
mortal," and "s" stands for "Socrates."
When predicate logic is restricted to properties of and
relations between individuals with no quantification over
properties, it is known as "first order";
when quantification over properties is allowed, it is "second
order" instead. Almost all
investigations within contemporary logic go beyond predicate
logic.
LOGIC, SENTENTIAL
Any system of logic that restricts it attention to entire
sentences, while ignoring the internal
structure of the sentences themselves.
LOGICAL CONSEQUENCE
A relation between sets G of sentences and single sentences
f. Logical consequence for
classical first-order logic (denoted by |= ) requires that
f be true on every interpretation on
which all sentences in G are true. Other formalisms, most
notably defeasible ones, employ
alternative definitions.
LOGICAL POSITIVISM/LOGICAL EMPIRICISM
Closely related, influential philosophical movements that
emerged between the First and
Second World Wars. Logical positivism accepted the analytic/synthetic
distinction, the
observational/theoretical distinction, and a methodological
commitment to the use of
extensional logic for philosophical explications. Sometimes
it embraced the thesis that every
meaningful non-analytic sentence is either an observation
sentence or a deductive
consequence of observation sentences, as in A. J. Ayer's
Language, Truth and Logic. Logical
empiricism succeeded logical positivism by abandoning this
overly stringent conception of
cognitive significance and, in some cases, by abandoning
the analytic/synthetic distinction or,
in other cases, by abandoning the observational/theoretical
distinction. Rudolf Carnap, one of
the most important members of these movements, later abandoned
even the methodological
commitment to extentional languages as indispensable for
philosophical explications.
LOGICISM
The view that all of mathematics can be reduced to logic.
LOGICS, DEFEASIBLE
Logics in which the implications of a given piece of information
can be overridden by later
additions. A piece of information P may be taken to warrant
a conclusion Q, though later
additional information R "defeats" that conclusion.
LOGICS, INFINITE-VALUED
In classical logics, sentences or propositions are thought
as taking only one of two values:
True or False. In infinite-valued logics, including "fuzzy
logics," sentences or propositions are
allowed to take intermediate truth-values: 1/3 true or 1/2
false, for example.
LOGICS, MONOTONIC
Logics that allow "strengthening of the antecedent":
if P entails Q, then P conjoined with any
other R also entails Q. Contrasted with nonmonotonic or
defeasible logics.
LOOPING
The process of repeatedly executing a section of a program
until some condition is met.
LÖWENHEIM-SKOLEM THEOREM
A feature of classical first-order logic, according to which
if a set G of sentences has arbitrarily
large finite models then it has an infinite model. Together
with Compactness, this property
characterizes first-order logic.
M
MACROSCOPIC STATE
Global state of a dynamical system determined by the collective
interactions of its microscopic
elements.
MATHEMATICS, PURE VS. APPLIED
Mathematics may be pursued as the study of formal systems,
where applications of those
formal systems are restricted to abstract domains. This
is the area of pure mathematics.
Mathematics may also be pursued as the study of formal systems
where those systems are
subject to empirical interpretations. This is the area of
applied mathematics, which also
qualifies as a branch of empirical science. Alternatively,
the domain of mathematics can be
restricted to comparative (or topological) relations and
to quantitative (or metrical) relations
exclusively.
MEANING
The problem of meaning, sometimes also referred to as the
problem of representation or the
problem of content, is among the central issues confronting
cognitive science. Since different
signs (words, sentences) can have the same meaning, the
meaning of a sign (word,
sentence) cannot be properly identified with its linguistic
(or other) formulation. In the case of
defined signs (words, sentences), there exist equivalence
classes of signs (words, sentences)
that have the same meaning, but that two or more signs (words,
sentences) have the same
meaning does not explain what it means for any of them to
have any meaning at all. Among
the various theories of meaning that have been proposed,
the language-of-thought hypothesis
maintains that every (neurologically normal) human being
has an innate mental language,
where learning an ordinary language simply involves pairing
up the words in that ordinary
language with innate concepts in the language of thought.
The inferential network model
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