modal logic

3 definitions found

modal logic - 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]

modal logic - WordNet (r) 2.1 (2005) :

  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

modal logic - Free On-line Dictionary of Computing (26 May 2007) :

  modal logic
  
     <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)