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. Predicatelogic 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 truthvalues: AND, OR, NOT and combinations thereof. Predicatelogic 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, equationallogic, modal logic, linear logic, paradox.

2. electronics Boolean logic circuits.

See also arithmetic and logic unit, asynchronous logic,

TTL.

(1995-03-17)