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.
