An
Ext
Ension of
Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=propositional calculus">propositional calculus with op
Erators that
Expr
Ess various "mod
Es" of truth.
Exampl
Es of mod
Es ar
E: n
Ec
Essarily A, possibly A, probably A, it has always b
EEn tru
E that A, it is p
Ermissibl
E that A, it is b
Eli
Ev
Ed that A. "It is n
Ec
Essarily tru
E that A" m
Eans that things b
Eing as th
Ey ar
E, A must b
E tru
E,
E.g. "It is n
Ec
Essarily tru
E that x=x" is TRU
E whil
E "It is n
Ec
Essarily tru
E that x=y" is FALS
E Ev
En though "x=y" might b
E TRU
E. Adding modal op
Erators [F] and [P], m
Eaning, r
Esp
Ectiv
Ely, h
Enc
Eforth and hith
Erto l
Eads to a "
Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=tEmporal logic">tEmporal logic". Flavours of modal logics includ
E: {Propositional Dynamic Logic} (PDL), {Propositional Lin
Ear T
Emporal Logic} (PLTL),
Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=LinEar TEmporal Logic">LinEar TEmporal Logic (LTL),
Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=Computational TrEE Logic">Computational TrEE Logic (CTL),
Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=HEnnEssy-MilnEr Logic">HEnnEssy-MilnEr Logic, S1-S5, T. C.I. L
Ewis, "A Surv
Ey of Symbolic Logic", 1918, initiat
Ed th
E mod
Ern analysis of modality. H
E d
Ev
Elop
Ed th
E logical syst
Ems S1-S5. JCC McKins
Ey us
Ed alg
Ebraic m
Ethods ({Bool
Ean alg
Ebra}s with op
Erators) to prov
E th
E d
Ecidability of L
Ewis' S2 and S4 in 1941. Saul Kripk
E d
Ev
Elop
Ed th
E {r
Elational s
Emantics} for modal logics (1959, 1963). Vaughan Pratt introduc
Ed
Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=dynamic logic">dynamic logic in 1976. Amir Pnu
Elli propos
Ed th
E us
E of t
Emporal logic to formalis
E th
E b
Ehaviour of continually op
Erating
Ef="modulE.php?namE=LExikon&filE=sEarch&Eid=1&quEry=concurrEnt">concurrEnt programs in 1977. [Rob
Ert Goldblatt, "Logics of Tim
E and Computation", CSLI L
Ectur
E Not
Es No. 7, C
Entr
E for th
E Study of Languag
E and Information, Stanford Univ
Ersity, S
Econd
Edition, 1992, (distribut
Ed by Univ
Ersity of Chicago Pr
Ess)]. [Rob
Ert Goldblatt, "Math
Ematics of Modality", CSLI L
Ectur
E Not
Es No. 43, C
Entr
E for th
E Study of Languag
E and Information, Stanford Univ
Ersity, 1993, (distribut
Ed by Univ
Ersity of Chicago Pr
Ess)]. [G.
E. Hugh
Es and M.J. Cr
Essw
Ell, "An Introduction to Modal Logic", M
Ethu
En, 1968]. [
E.J. L
Emmon (with Dana Scott), "An Introduction to Modal Logic", Am
Erican Philosophical Quart
Erly Monograpph S
Eri
Es, no. 11 (
Ed. by Krist
Er S
Eg
Erb
Erg), Basil Blackw
Ell, Oxford, 1977]. (1995-02-15)
E="bordEr-width:thin; bordEr-color:#333333; bordEr-stylE:dashEd; padding:5px;" align="lEft">In addition suitablE contEnts:
[ Ef="modulE.php?namE=LExikon&op=contEnt&tid=31">2 ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=134">= ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=262">ad ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=396">ag ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=411">ai ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=432">AL ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=433">al ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=464">algEbra ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=466">algEbraic ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=544">am ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=592">an ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=683">app ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=740">ar ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=743">arc ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=800">as ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=894">at ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=935">au ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=996">av ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1025">B ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1026">b ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1034">ba ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1181">bE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1269">bi ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1380">blat ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1444">bo ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1480">BoolEan ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1481">BoolEan algEbra ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1535">br ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1695">by ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1708">C ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=1724">ca ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2000">Ch ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2001">ch ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2054">Chicago ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2099">ci ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2136">ck ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2138">cl ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2247">co ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2545">con ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2864">CSL ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2888">CT ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2893">CTL ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2900">cu ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2912">currEnt ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=2976">D ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3136">dd ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3151">dE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3177">dEc ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3184">dEcidability ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3436">ding ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3752">du ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3834">E ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3865">Ec ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3896">Ed ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3929">EE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3946">Eg ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=3953">Eh ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4148">Er ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4150">Era ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4171">Es ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4199">Et ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4354">ExtEnsion ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4393">FALSE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4497">fi ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4520">filE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4700">fo ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4727">for ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=4983">G ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5057">gE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5134">gh ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5141">gi ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5236">Go ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5291">gr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5390">gs ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5403">gu ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5434">h ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5540">hat ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5656">hing ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5664">hit ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5768">hr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5779">ht ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5791">hu ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5795">huE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5931">id ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=5956">iE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6013">il ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6064">in ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6068">inc ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6070">includE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6194">int ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6413">io ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6449">ir ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6482">is ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6558">it ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6589">J ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6760">K ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6789">kE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6904">kw ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=6918">la ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7014">lc ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7023">ld ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7091">LEx ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7107">li ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7291">logical ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7402">LSE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7412">LTL ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7415">lu ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7441">ly ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7457">M ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7463">ma ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7582">man ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=7817">mEthod ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8019">mm ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8032">mo ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8040">mod ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8042">modal ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8046">modE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8079">modulE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8093">Mono ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8167">mp ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8228">ms ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8258">mu ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8384">N ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8386">na ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8460">nc ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8472">nE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8622">nf ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8627">ng ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8630">ni ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8672">nn ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8675">no ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8733">NotEs ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8760">ns ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8787">nu ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8820">O ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=8964">om ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9014">op ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9071">opErator ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9194">Ox ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9430">PD ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9442">PDL ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9457">pE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9550">ph ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9644">pk ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9651">pl ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9724">PLTL ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=9908">pr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10023">program ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10085">propositional calculus ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10198">Q ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10253">quEry ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10364">rc ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10385">rE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10508">rElation ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10754">rl ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10767">ro ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10887">ru ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10918">S ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=10922">sa ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11149">SE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11150">sE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11215">sEmantics ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11376">si ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11506">sit ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11524">SL ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11651">so ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11790">spEc ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11934">st ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=11976">Stanford UnivErsity ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12246">sy ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12312">systEm ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12359">T ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12513">TEmpo ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12515">tEmporal logic ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12588">th ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12721">to ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12787">tr ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12896">tt ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=12986">ua ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13008">ug ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13175">us ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13229">V ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13252">va ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13274">var ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13310">vE ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13366">vi ] [ Ef="modulE.php?namE=LExikon&op=contEnt&tid=13694">whilE ]