From The Collaborative International Dictionary of English v.0.48:

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; the
      science of correct reasoning.
      [1913 Webster]

            Logic is the science of the laws of thought, as
            thought; that is, of the necessary conditions to
            which thought, considered in itself, is subject.
                                                  --Sir W.
                                                  Hamilton.
      [1913 Webster]

   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.
         [1913 Webster]

   2. A treatise on logic; as, Mill's Logic.
      [1913 Webster]

   3. correct reasoning; as, I can't see any logic in his
      argument; also, sound judgment; as, the logic of surrender
      was uncontestable.
      [PJC]

   4. The path of reasoning used in any specific argument; as,
      his logic was irrefutable.
      [PJC]

   5. (Electronics, Computers) A function of an electrical
      circuit (called a gate) that mimics certain elementary
      binary logical operations on electrical signals, such as
      AND, OR, or NOT; as, a logic circuit; the arithmetic and
      logic unit.
      [PJC]

From WordNet (r) 2.0:

logic
     n 1: the branch of philosophy that analyzes inference
     2: reasoned and reasonable judgment; "it made a certain kind of
        logic"
     3: the principles that guide reasoning within a given field or
        situation; "economic logic requires it"; "by the logic of
        war"
     4: a system of reasoning [syn: logical system, system of
        logic]

From Moby Thesaurus II by Grady Ward, 1.0:

72 Moby Thesaurus words for "logic":
   Aristotelian logic, Boolean algebra, Ramistic logic, admissibility,
   aesthetics, algebra of classes, algebra of relations, axiology,
   casuistry, common sense, cosmology, deduction, dialectic,
   dialectics, doctrine of inference, doctrine of terms,
   epistemological logic, epistemology, ethics, experimental logic,
   first philosophy, formal logic, gnosiology, good sense,
   intelligence, judiciousness, justifiability, justness, logicality,
   logicalness, logics, logistic, material logic, mathematical logic,
   mental philosophy, metaphysics, moral philosophy, ontology,
   phenomenology, philosophastry, philosophic doctrine,
   philosophic system, philosophic theory, philosophical inquiry,
   philosophical speculation, philosophy, plausibility, practicality,
   presence of mind, propositional calculus, psychological logic,
   psychologism, ratiocination, rationality, reason, reasonability,
   reasonableness, reasoning, school of philosophy, school of thought,
   science of being, sense, sensibleness, set theory, sophistry,
   sound sense, soundness, sweet reason, theory of beauty,
   theory of knowledge, value theory, wisdom

From The Free On-line Dictionary of Computing (27 SEP 03):

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.
     
        (1995-03-17)
     
     

From THE DEVIL'S DICTIONARY ((C)1911 Released April 15 1993):

LOGIC, n.  The art of thinking and reasoning in strict accordance with
the limitations and incapacities of the human misunderstanding.  The
basic of logic is the syllogism, consisting of a major and a minor
premise and a conclusion -- thus:
    _Major Premise_:  Sixty men can do a piece of work sixty times as
quickly as one man.
    _Minor Premise_:  One man can dig a posthole in sixty seconds;
therefore --
    _Conclusion_:  Sixty men can dig a posthole in one second.
    This may be called the syllogism arithmetical, in which, by
combining logic and mathematics, we obtain a double certainty and are
twice blessed.