log⋅ic
[loj-ik] 
ɪk
| 1. | the science that investigates the principles governing correct or reliable inference. |
| 2. | a particular method of reasoning or argumentation: We were unable to follow his logic. |
| 3. | the system or principles of reasoning applicable to any branch of knowledge or study. |
| 4. | reason or sound judgment, as in utterances or actions: There wasn't much logic in her move. |
| 5. | convincing forcefulness; inexorable truth or persuasiveness: the irresistible logic of the facts. |
| 6. | Computers. logic circuit. |
-logic
| a combining form used in the formation of adjectives corresponding to nouns ending in -logy: analogic. |
logic circuit
| a circuit designed to perform complex functions defined in terms of elementary functions of mathematical logic. |
Based on the Random House Dictionary, © Random House, Inc. 2009.
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| log·ic (lŏj'ĭk) n.
[Middle English, from Old French logique, from Latin logica, from Greek logikē (tekhnē), (art) of reasoning, logic, feminine of logikos, of reasoning, from logos, reason; see leg- in Indo-European roots.] |
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Logic
Log"ic\, n. [OE. logike, F. logique, L. logica, logice, Gr. logikh` (sc. te`chnh), fr. logiko`s belonging to speaking or reason, fr. lo`gos speech, reason, le`gein to say, speak. See Legend.]1. The science or art of exact reasoning, or of pure and formal thought, or of the laws according to which the processes of pure thinking should be conducted; the science of the formation and application of general notions; the science of generalization, judgment, classification, reasoning, and systematic arrangement; correct reasoning. Logic is science of the laws of thought, as that is, of the necessary conditions to which thought, considered in itself, is subject. --Sir W. Hamilton. Note: Logic is distinguished as pure and applied. "Pure logic is a science of the form, or of the formal laws, of thinking, and not of the matter. Applied logic teaches the application of the forms of thinking to those objects about which men do think." --Abp. Thomson. 2. A treatise on logic; as, Mill's Logic.Cite This Source
logic
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.
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logic
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| 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. |
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logic
1.
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.
See also arithmetic and logic unit, asynchronous logic, TTL.
(1995-03-17)
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