The Collaborative International Dictionary of English v.0.48:

modal logic \mo"dal log"ic\, n.
   A system of logic which studies how to combine propositions
   which include the concepts of necessity, possibility, and
   obligation.
   [PJC]

WordNet (r) 3.0 (2006):

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

The Free On-line Dictionary of Computing (30 December 2018):

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.

   [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)