An extension of
proposITional calculus w
ITh 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 h
ITherto leads to a "
temporal logic". Flavours of modal logics include: {Propos
ITional Dynamic Logic} (PDL), {Propos
ITional 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, in
ITiated the modern analysis of modal
ITy. He developed the logical systems S1-S5. JCC McKinsey used algebraic methods ({Boolean algebra}s w
ITh operators) to prove the decidabil
ITy 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 Univers
ITy, Second Ed
ITion, 1992, (distributed by Univers
ITy of Chicago Press)]. [Robert Goldblatt, "Mathematics of Modal
ITy", CSLI Lecture Notes No. 43, Centre for the Study of Language and Information, Stanford Univers
ITy, 1993, (distributed by Univers
ITy of Chicago Press)]. [G.E. Hughes and M.J. Cresswell, "An Introduction to Modal Logic", Methuen, 1968]. [E.J. Lemmon (w
ITh 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)
In addITion suITable contents:
[ 2 ] [ = ] [ ad ] [ ag ] [ ai ] [ AL ] [ al ] [ algebra ] [ algebraic ] [ am ] [ an ] [ app ] [ ar ] [ arc ] [ as ] [ at ] [ au ] [ av ] [ B ] [ b ] [ ba ] [ be ] [ bi ] [ blat ] [ bo ] [ Boolean ] [ Boolean algebra ] [ br ] [ by ] [ C ] [ ca ] [ Ch ] [ ch ] [ Chicago ] [ ci ] [ ck ] [ cl ] [ co ] [ con ] [ CSL ] [ CT ] [ CTL ] [ cu ] [ current ] [ D ] [ dd ] [ de ] [ dec ] [ decidabilITy ] [ ding ] [ du ] [ E ] [ ec ] [ ed ] [ ee ] [ eg ] [ eh ] [ er ] [ era ] [ es ] [ et ] [ extension ] [ FALSE ] [ fi ] [ file ] [ fo ] [ for ] [ G ] [ ge ] [ gh ] [ gi ] [ Go ] [ gr ] [ gs ] [ gu ] [ h ] [ hat ] [ hing ] [ hIT ] [ hr ] [ ht ] [ hu ] [ hue ] [ id ] [ ie ] [ il ] [ in ] [ inc ] [ include ] [ int ] [ io ] [ ir ] [ is ] [ IT ] [ J ] [ K ] [ ke ] [ kw ] [ la ] [ lc ] [ ld ] [ Lex ] [ li ] [ logical ] [ LSE ] [ LTL ] [ lu ] [ ly ] [ M ] [ ma ] [ man ] [ method ] [ mm ] [ mo ] [ mod ] [ modal ] [ mode ] [ module ] [ Mono ] [ mp ] [ ms ] [ mu ] [ N ] [ na ] [ nc ] [ ne ] [ nf ] [ ng ] [ ni ] [ nn ] [ no ] [ Notes ] [ ns ] [ nu ] [ O ] [ om ] [ op ] [ operator ] [ Ox ] [ PD ] [ PDL ] [ pe ] [ ph ] [ pk ] [ pl ] [ PLTL ] [ pr ] [ program ] [ proposITional calculus ] [ Q ] [ query ] [ rc ] [ re ] [ relation ] [ rl ] [ ro ] [ ru ] [ S ] [ sa ] [ SE ] [ se ] [ semantics ] [ si ] [ sIT ] [ SL ] [ so ] [ spec ] [ st ] [ Stanford UniversITy ] [ sy ] [ system ] [ T ] [ Tempo ] [ temporal logic ] [ th ] [ to ] [ tr ] [ tt ] [ ua ] [ ug ] [ us ] [ V ] [ va ] [ var ] [ ve ] [ vi ] [ while ]