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.
Computers. logic circuit.

1325–75; Middle English logik < Latin logica, noun use of neuter plural (in ML taken as feminine singular) of Greek logikós of speech or reason. See logo-, -ic

logicless, adjective
nonlogic, noun

4. sense, cogency.
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a combining form used in the formation of adjectives corresponding to nouns ending in -logy:, analogic.

< Greek -logikós. See logic

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Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
logic (ˈlɒdʒɪk)
1.  formal logic deduction See also induction 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
2.  formal system Compare formal language any particular formal system in which are defined axioms and rules of inference
3.  the system and principles of reasoning used in a specific field of study
4.  a particular method of argument or reasoning
5.  force or effectiveness in argument or dispute
6.  reasoned thought or argument, as distinguished from irrationality
7.  the relationship and interdependence of a series of events, facts, etc
8.  chop logic to use excessively subtle or involved logic or argument
9.  electronics, computing
 a.  See also logic circuit the principles underlying the units in a computer system that perform arithmetical and logical operations
 b.  (as modifier): a logic element
[C14: from Old French logique from Medieval Latin logica (neuter plural, treated in Medieval Latin as feminine singular), from Greek logikos concerning speech or reasoning]

Collins English Dictionary - Complete & Unabridged 10th Edition
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Word Origin & History

mid-14c., "branch of philosophy that treats of forms of thinking," from O.Fr. logique, from L. (ars) logica, from Gk. 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.
Online Etymology Dictionary, © 2010 Douglas Harper
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American Heritage
Science Dictionary
logic   (lŏj'ĭk)  Pronunciation Key 
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 American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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American Heritage
Cultural Dictionary

logic definition

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.

The American Heritage® New Dictionary of Cultural Literacy, Third Edition
Copyright © 2005 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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Computing Dictionary

logic definition

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.
The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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Example sentences
We dealt with him by systematically tearing his comments apart using logic and
These issues are too important, many appear to believe, for logic and science
  to play a part.
Not to mention the brains ability to perform fuzzy logic, and many other lines
  of reasoning.
While addressing a problem in the arcane field of mathematical logic, he
  imagined a machine that could mimic human reasoning.
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