Classical logic

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Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. They are characterised by a number of properties:[1]

Classical logic is bivalent, i.e. it uses only Boolean-valued functions. And while not entailed by the preceding conditions, contemporary discussions of classical logic normally only include propositional and first-order logics.[2][3]

Contents

Examples of classical logics

  • Aristotle's Organon introduces his theory of syllogisms, which is a logic with a restricted form of judgments: assertions take one of four forms, All Ps are Q, Some Ps are Q, No Ps are Q, and Some Ps are not Q. These judgments find themselves if two pairs of two dual operators, and each operator is the negation of another, relationships that Aristotle summarised with his square of oppositions. Aristotle explicitly formulated the law of the excluded middle and law of non-contradiction in justifying his system, although these laws cannot be expressed as judgments within the syllogistic framework.
  • Nagarjuna's tetralemma;
  • Avicenna's temporal modal logic;
  • George Boole's algebraic reformulation of logic, his system of Boolean logic;
  • The first-order logic found in Gottlob Frege's Begriffsschrift.

Non-classical logics

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