[loj-ik] /ˈlɒdʒ ɪk/
the science that investigates the principles governing correct or reliable inference.
a particular method of reasoning or argumentation:
We were unable to follow his logic.
the system or principles of reasoning applicable to any branch of knowledge or study.
reason or sound judgment, as in utterances or actions:
There wasn’t much logic in her move.
convincing forcefulness; inexorable truth or persuasiveness:
the irresistible logic of the facts.
a combining form used in the formation of adjectives corresponding to nouns ending in -logy:
the branch of philosophy concerned with analysing the patterns of reasoning by which a conclusion is properly drawn from a set of premises, without reference to meaning or context See also formal logic, deduction (sense 4), induction (sense 4)
any particular formal system in which are defined axioms and rules of inference Compare formal system, formal language
the system and principles of reasoning used in a specific field of study
a particular method of argument or reasoning
force or effectiveness in argument or dispute
reasoned thought or argument, as distinguished from irrationality
the relationship and interdependence of a series of events, facts, etc
chop logic, to use excessively subtle or involved logic or argument
mid-14c., “branch of philosophy that treats of forms of thinking,” from Old French logique (13c.), from Latin (ars) logica, from Greek logike (techne) “reasoning (art),” from fem. of logikos “pertaining to speaking or reasoning,” from logos “reason, idea, word” (see logos). Meaning “logical argumentation” is from c.1600.
The study of the principles of reasoning, especially of the structure of propositions as distinguished from their content and of method and validity in deductive reasoning.
The branch of philosophy dealing with the principles of reasoning. Classical logic, as taught in ancient Greece and Rome, systematized rules for deduction. The modern scientific and philosophical logic of deduction has become closely allied to mathematics, especially in showing how the foundations of mathematics lie in logic.
1. 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. Boolean logic circuits.
See also arithmetic and logic unit, asynchronous logic, TTL.
[loj-i-kuh l] /ˈlɒdʒ ɪ kəl/ adjective 1. according to or agreeing with the principles of : a logical inference. 2. reasoning in accordance with the principles of , as a person or the mind: logical thinking. 3. reasonable; to be expected: War was the logical consequence of such threats. 4. of or relating to . […]
- Logical address
noun 1. a philosophy developed from linguistic analysis asserting that a proposition can be analyzed into simple, independent elements of meaning corresponding to elements making up basic facts about the world and reality. noun 1. the philosophical theory of Bertrand Russell and the early Wittgenstein which held that all meaningful expressions must be analysable into […]
- Logical complement
logic In Boolean algebra, the logical complement or negation of a Boolean value is the opposite value, given by the following truth table: A | -A –+— T | F F | T -A is also written as A with a bar over it or with a small vertical line hanging from the right-hand end […]