Source : WordNet®

modal logic
     n 1: the logical study of necessity and possibility
     2: a system of logic whose formal properties resemble certain
        moral and epistemological concepts

Source : Free On-Line Dictionary of Computing

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
        algebra}s 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.
     
        [Robert Goldblatt, "Logics of Time and Computation", CSLI
        Lecture Notes No. 7, Centre for the Study of Language and
        Information, Stanford University, Second Edition, 1992,
        (distributed by University of Chicago Press)].
     
        [Robert Goldblatt, "Mathematics of Modality", CSLI Lecture
        Notes No. 43, Centre for the Study of Language and
        Information, Stanford University, 1993, (distributed by
        University of Chicago Press)].
     
        [G.E. Hughes and M.J. Cresswell, "An Introduction to Modal
        Logic", Methuen, 1968].
     
        [E.J. Lemmon (with Dana Scott), "An Introduction to Modal
        Logic", American Philosophical Quarterly Monograpph Series,
        no. 11 (ed. by Krister Segerberg), Basil Blackwell, Oxford,
        1977].
     
        (1995-02-15)