An exten
sion of
propositional calculus with operator
s that expre
ss variou
s "mode
s" of truth. Example
s of mode
s are: nece
ssarily A, po
ssibly A, probably A, it ha
s alway
s been true that A, it i
s permi
ssible that A, it i
s believed that A. "It i
s nece
ssarily true that A" mean
s that thing
s being a
s they are, A mu
st be true, e.g. "It i
s nece
ssarily true that x=x" i
s TRUE while "It i
s nece
ssarily true that x=y" i
s FAL
sE even though "x=y" might be TRUE. Adding modal operator
s [F] and [P], meaning, re
spectively, henceforth and hitherto lead
s to a "
temporal logic". Flavour
s of modal logic
s include: {Propo
sitional Dynamic Logic} (PDL), {Propo
sitional Linear Temporal Logic} (PLTL),
Linear Temporal Logic (LTL),
Computational Tree Logic (CTL),
Hennessy-Milner Logic,
s1-
s5, T. C.I. Lewi
s, "A
survey of
symbolic Logic", 1918, initiated the modern analy
si
s of modality. He developed the logical
sy
stem
s s1-
s5. JCC McKin
sey u
sed algebraic method
s ({Boolean algebra}
s with operator
s) to prove the decidability of Lewi
s'
s2 and
s4 in 1941.
saul Kripke developed the {relational
semantic
s} for modal logic
s (1959, 1963). Vaughan Pratt introduced
dynamic logic in 1976. Amir Pnuelli propo
sed the u
se of temporal logic to formali
se the behaviour of continually operating
concurrent program
s in 1977. [Robert Goldblatt, "Logic
s of Time and Computation", C
sLI Lecture Note
s No. 7, Centre for the
study of Language and Information,
stanford Univer
sity,
second Edition, 1992, (di
stributed by Univer
sity of Chicago Pre
ss)]. [Robert Goldblatt, "Mathematic
s of Modality", C
sLI Lecture Note
s No. 43, Centre for the
study of Language and Information,
stanford Univer
sity, 1993, (di
stributed by Univer
sity of Chicago Pre
ss)]. [G.E. Hughe
s and M.J. Cre
sswell, "An Introduction to Modal Logic", Methuen, 1968]. [E.J. Lemmon (with Dana
scott), "An Introduction to Modal Logic", American Philo
sophical Quarterly Monograpph
serie
s, no. 11 (ed. by Kri
ster
segerberg), Ba
sil Blackwell, Oxford, 1977]. (1995-02-15)
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[ 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 ]