An extension of
propositional calculus with oper
ATors th
AT express various "modes" of truth. Examples of modes are: necessarily A, possibly A, probably A, it has always been true th
AT A, it is permissible th
AT A, it is believed th
AT A. "It is necessarily true th
AT A" means th
AT things being as they are, A must be true, e.g. "It is necessarily true th
AT x=x" is TRUE while "It is necessarily true th
AT x=y" is FALSE even though "x=y" might be TRUE. Adding modal oper
ATors [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, initi
ATed the modern analysis of modality. He developed the logical systems S1-S5. JCC McKinsey used algebraic methods ({Boolean algebra}s with oper
ATors) to prove the decidability of Lewis' S2 and S4 in 1941. Saul Kripke developed the {rel
ATional semantics} for modal logics (1959, 1963). Vaughan Pr
ATt introduced
dynamic logic in 1976. Amir Pnuelli proposed the use of temporal logic to formalise the behaviour of continually oper
ATing
concurrent programs in 1977. [Robert Goldbl
ATt, "Logics of Time and Comput
ATion", CSLI Lecture Notes No. 7, Centre for the Study of Language and Inform
ATion, Stanford University, Second Edition, 1992, (distributed by University of Chicago Press)]. [Robert Goldbl
ATt, "M
AThem
ATics of Modality", CSLI Lecture Notes No. 43, Centre for the Study of Language and Inform
ATion, 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)
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 ]