logic
1. <philosophy, mathematics> A branch of philosophy and mathematics that
deals with the formal principles, methods and criteria of validity of inference,
reasoning and knowledge.
Logic is concerned with what is true and how we can know whether something is
true. This involves the formalisation of logical arguments and proofs in terms
of symbols representing propositions and logical connectives. The meanings of
these logical connectives are expressed by a set of rules which are assumed to
be self-evident.
Boolean algebra deals with the basic operations of truth values: AND, OR, NOT
and combinations thereof. Predicate logic extends this with existential and
universal quantifiers and symbols standing for predicates which may depend on
variables. The rules of natural deduction describe how we may proceed from valid
premises to valid conclusions, where the premises and conclusions are
expressions in predicate logic.
Symbolic logic uses a meta-language concerned with truth, which may or may not
have a corresponding expression in the world of objects called existance. In
symbolic logic, arguments and proofs are made in terms of symbols representing
propositions and logical connectives. The meanings of these begin with a set of
rules or primitives which are assumed to be self-evident. Fortunately, even from
vague primitives, functions can be defined with precise meaning.
Boolean logic deals with the basic operations of truth values: AND, OR, NOT and
combinations thereof. Predicate logic extends this with existential quantifiers
and universal quantifiers which introduce bound variables ranging over finite
sets; the predicate itself takes on only the values true and false. Deduction
describes how we may proceed from valid premises to valid conclusions, where
these are expressions in predicate logic.
Carnap used the phrase "rational reconstruction" to describe the logical
analysis of thought. Thus logic is less concerned with how thought does proceed,
which is considered the realm of psychology, and more with how it should proceed
to discover truth. It is the touchstone of the results of thinking, but neither
its regulator nor a motive for its practice.
See also fuzzy logic, logic programming, arithmetic and logic unit, first-order
logic,
See also Boolean logic, fuzzy logic, logic programming, first-order logic, logic
bomb, combinatory logic, higher-order logic, intuitionistic logic, equational
logic, modal logic, linear logic, paradox.
2. <electronics> Boolean logic circuits.
See also arithmetic and logic unit, asynchronous logic, TTL.
(1995-03-17)
Nearby terms:
{log} « logarithmus dualis « LogC « logic »
logical » logical address » Logical Block Addressing
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