1. the logical study of necessity and possibility
2. a system of logic whose formal properties resemble certain moral and epistemological concepts
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
WordNet (r) 3.0 (2006):
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):
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
"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,