Modal logic

математика модальная логика

Англо-русский научно-технический словарь

Modal logic

An extension of propositional calculus with operators that express various "modes" of truth. Examples of modes are: necessarily A, possibly A, probably A, it has always been true that A, it is permissible that A, it is believed that A. "It is necessarily true that A" means that things being as they are, A must be true, e.g. "It is necessarily true that x=x" is TRUE while "It is necessarily true that x=y" is FALSE even though "x=y" might be TRUE. Adding modal operators [F] and [P], meaning, respectively, henceforth and hitherto leads to a "temporal logic". Flavours of modal logics include: Propositional Dynamic Logic (PDL), Propositional Linear Temporal Logic (PLTL), Linear Temporal Logic (LTL), Computational Tree Logic (CTL), Hennessy-Milner Logic, S1-S5, T. C.I. Lewis, "A Survey of Symbolic Logic", 1918, initiated the modern analysis of modality. He developed the logical systems S1-S5. JCC McKinsey used algebraic methods (Boolean algebras with operators) to prove the decidability of Lewis' S2 and S4 in 1941. Saul Kripke developed the relational semantics for modal logics (1959, 1963). Vaughan Pratt introduced dynamic logic in 1976. Amir Pnuelli proposed the use of temporal logic to formalise the behaviour of continually operating concurrent programs in 1977.

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