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modal logic : FOLDOC
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


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