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Provability logic is a modal logic, in which the box (or "necessity") operator is interpreted as 'it is provable that'. The point is to capture the notion of a proof predicate of a reasonably rich formal theory, such as Peano arithmetic. ==Examples== There are a number of provability logics, some of which are covered in the literature mentioned in the References section. The basic system is generally referred to as GL (for Gödel-Löb) or L or K4W. It can be obtained by adding the modal version of Löb's theorem to the logic K (or K4). Namely, the axioms of GL are all tautologies of classical propositional logic plus all formulas of one of the following forms: * Distribution Axiom: * Löb's Axiom: And the rules of inference are: * Modus Ponens: From ''p'' → ''q'' and ''p'' conclude ''q''; * Necessitation: From ''p'' conclude . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「provability logic」の詳細全文を読む スポンサード リンク
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