An extension of
href="module.php?name=Lexikon&file=search&eid=1&query=propositional calculus">propositional calculus wit
h operators t
hat express various "modes" of trut
h. Examples of modes are: necessarily A, possibly A, probably A, it
has always been true t
hat A, it is permissible t
hat A, it is believed t
hat A. "It is necessarily true t
hat A" means t
hat t
hings being as t
hey are, A must be true, e.g. "It is necessarily true t
hat x=x" is TRUE w
hile "It is necessarily true t
hat x=y" is FALSE even t
houg
h "x=y" mig
ht be TRUE. Adding modal operators [F] and [P], meaning, respectively,
hencefort
h and
hit
herto leads to a "
href="module.php?name=Lexikon&file=search&eid=1&query=temporal logic">temporal logic". Flavours of modal logics include: {Propositional Dynamic Logic} (PDL), {Propositional Linear Temporal Logic} (PLTL),
href="module.php?name=Lexikon&file=search&eid=1&query=Linear Temporal Logic">Linear Temporal Logic (LTL),
href="module.php?name=Lexikon&file=search&eid=1&query=Computational Tree Logic">Computational Tree Logic (CTL),
href="module.php?name=Lexikon&file=search&eid=1&query=hennessy-Milner Logic">hennessy-Milner Logic, S1-S5, T. C.I. Lewis, "A Survey of Symbolic Logic", 1918, initiated t
he modern analysis of modality.
he developed t
he logical systems S1-S5. JCC McKinsey used algebraic met
hods ({Boolean algebra}s wit
h operators) to prove t
he decidability of Lewis' S2 and S4 in 1941. Saul Kripke developed t
he {relational semantics} for modal logics (1959, 1963). Vaug
han Pratt introduced
href="module.php?name=Lexikon&file=search&eid=1&query=dynamic logic">dynamic logic in 1976. Amir Pnuelli proposed t
he use of temporal logic to formalise t
he be
haviour of continually operating
href="module.php?name=Lexikon&file=search&eid=1&query=concurrent">concurrent programs in 1977. [Robert Goldblatt, "Logics of Time and Computation", CSLI Lecture Notes No. 7, Centre for t
he Study of Language and Information, Stanford University, Second Edition, 1992, (distributed by University of C
hicago Press)]. [Robert Goldblatt, "Mat
hematics of Modality", CSLI Lecture Notes No. 43, Centre for t
he Study of Language and Information, Stanford University, 1993, (distributed by University of C
hicago Press)]. [G.E.
hug
hes and M.J. Cresswell, "An Introduction to Modal Logic", Met
huen, 1968]. [E.J. Lemmon (wit
h Dana Scott), "An Introduction to Modal Logic", American P
hilosop
hical Quarterly Monograpp
h Series, no. 11 (ed. by Krister Segerberg), Basil Blackwell, Oxford, 1977]. (1995-02-15)
In addition suitable contents:
[ href="module.php?name=Lexikon&op=content&tid=31">2 ] [ href="module.php?name=Lexikon&op=content&tid=134">= ] [ href="module.php?name=Lexikon&op=content&tid=262">ad ] [ href="module.php?name=Lexikon&op=content&tid=396">ag ] [ href="module.php?name=Lexikon&op=content&tid=411">ai ] [ href="module.php?name=Lexikon&op=content&tid=432">AL ] [ href="module.php?name=Lexikon&op=content&tid=433">al ] [ href="module.php?name=Lexikon&op=content&tid=464">algebra ] [ href="module.php?name=Lexikon&op=content&tid=466">algebraic ] [ href="module.php?name=Lexikon&op=content&tid=544">am ] [ href="module.php?name=Lexikon&op=content&tid=592">an ] [ href="module.php?name=Lexikon&op=content&tid=683">app ] [ href="module.php?name=Lexikon&op=content&tid=740">ar ] [ href="module.php?name=Lexikon&op=content&tid=743">arc ] [ href="module.php?name=Lexikon&op=content&tid=800">as ] [ href="module.php?name=Lexikon&op=content&tid=894">at ] [ href="module.php?name=Lexikon&op=content&tid=935">au ] [ href="module.php?name=Lexikon&op=content&tid=996">av ] [ href="module.php?name=Lexikon&op=content&tid=1025">B ] [ href="module.php?name=Lexikon&op=content&tid=1026">b ] [ href="module.php?name=Lexikon&op=content&tid=1034">ba ] [ href="module.php?name=Lexikon&op=content&tid=1181">be ] [ href="module.php?name=Lexikon&op=content&tid=1269">bi ] [ href="module.php?name=Lexikon&op=content&tid=1380">blat ] [ href="module.php?name=Lexikon&op=content&tid=1444">bo ] [ href="module.php?name=Lexikon&op=content&tid=1480">Boolean ] [ href="module.php?name=Lexikon&op=content&tid=1481">Boolean algebra ] [ href="module.php?name=Lexikon&op=content&tid=1535">br ] [ href="module.php?name=Lexikon&op=content&tid=1695">by ] [ href="module.php?name=Lexikon&op=content&tid=1708">C ] [ href="module.php?name=Lexikon&op=content&tid=1724">ca ] [ href="module.php?name=Lexikon&op=content&tid=2000">Ch ] [ href="module.php?name=Lexikon&op=content&tid=2001">ch ] [ href="module.php?name=Lexikon&op=content&tid=2054">Chicago ] [ href="module.php?name=Lexikon&op=content&tid=2099">ci ] [ href="module.php?name=Lexikon&op=content&tid=2136">ck ] [ href="module.php?name=Lexikon&op=content&tid=2138">cl ] [ href="module.php?name=Lexikon&op=content&tid=2247">co ] [ href="module.php?name=Lexikon&op=content&tid=2545">con ] [ href="module.php?name=Lexikon&op=content&tid=2864">CSL ] [ href="module.php?name=Lexikon&op=content&tid=2888">CT ] [ href="module.php?name=Lexikon&op=content&tid=2893">CTL ] [ href="module.php?name=Lexikon&op=content&tid=2900">cu ] [ href="module.php?name=Lexikon&op=content&tid=2912">current ] [ href="module.php?name=Lexikon&op=content&tid=2976">D ] [ href="module.php?name=Lexikon&op=content&tid=3136">dd ] [ href="module.php?name=Lexikon&op=content&tid=3151">de ] [ href="module.php?name=Lexikon&op=content&tid=3177">dec ] [ href="module.php?name=Lexikon&op=content&tid=3184">decidability ] [ href="module.php?name=Lexikon&op=content&tid=3436">ding ] [ href="module.php?name=Lexikon&op=content&tid=3752">du ] [ href="module.php?name=Lexikon&op=content&tid=3834">E ] [ href="module.php?name=Lexikon&op=content&tid=3865">ec ] [ href="module.php?name=Lexikon&op=content&tid=3896">ed ] [ href="module.php?name=Lexikon&op=content&tid=3929">ee ] [ href="module.php?name=Lexikon&op=content&tid=3946">eg ] [ href="module.php?name=Lexikon&op=content&tid=3953">eh ] [ href="module.php?name=Lexikon&op=content&tid=4148">er ] [ href="module.php?name=Lexikon&op=content&tid=4150">era ] [ href="module.php?name=Lexikon&op=content&tid=4171">es ] [ href="module.php?name=Lexikon&op=content&tid=4199">et ] [ href="module.php?name=Lexikon&op=content&tid=4354">extension ] [ href="module.php?name=Lexikon&op=content&tid=4393">FALSE ] [ href="module.php?name=Lexikon&op=content&tid=4497">fi ] [ href="module.php?name=Lexikon&op=content&tid=4520">file ] [ href="module.php?name=Lexikon&op=content&tid=4700">fo ] [ href="module.php?name=Lexikon&op=content&tid=4727">for ] [ href="module.php?name=Lexikon&op=content&tid=4983">G ] [ href="module.php?name=Lexikon&op=content&tid=5057">ge ] [ href="module.php?name=Lexikon&op=content&tid=5134">gh ] [ href="module.php?name=Lexikon&op=content&tid=5141">gi ] [ href="module.php?name=Lexikon&op=content&tid=5236">Go ] [ href="module.php?name=Lexikon&op=content&tid=5291">gr ] [ href="module.php?name=Lexikon&op=content&tid=5390">gs ] [ href="module.php?name=Lexikon&op=content&tid=5403">gu ] [ href="module.php?name=Lexikon&op=content&tid=5434">h ] [ href="module.php?name=Lexikon&op=content&tid=5540">hat ] [ href="module.php?name=Lexikon&op=content&tid=5656">hing ] [ href="module.php?name=Lexikon&op=content&tid=5664">hit ] [ href="module.php?name=Lexikon&op=content&tid=5768">hr ] [ href="module.php?name=Lexikon&op=content&tid=5779">ht ] [ href="module.php?name=Lexikon&op=content&tid=5791">hu ] [ href="module.php?name=Lexikon&op=content&tid=5795">hue ] [ href="module.php?name=Lexikon&op=content&tid=5931">id ] [ href="module.php?name=Lexikon&op=content&tid=5956">ie ] [ href="module.php?name=Lexikon&op=content&tid=6013">il ] [ href="module.php?name=Lexikon&op=content&tid=6064">in ] [ href="module.php?name=Lexikon&op=content&tid=6068">inc ] [ href="module.php?name=Lexikon&op=content&tid=6070">include ] [ href="module.php?name=Lexikon&op=content&tid=6194">int ] [ href="module.php?name=Lexikon&op=content&tid=6413">io ] [ href="module.php?name=Lexikon&op=content&tid=6449">ir ] [ href="module.php?name=Lexikon&op=content&tid=6482">is ] [ href="module.php?name=Lexikon&op=content&tid=6558">it ] [ href="module.php?name=Lexikon&op=content&tid=6589">J ] [ href="module.php?name=Lexikon&op=content&tid=6760">K ] [ href="module.php?name=Lexikon&op=content&tid=6789">ke ] [ href="module.php?name=Lexikon&op=content&tid=6904">kw ] [ href="module.php?name=Lexikon&op=content&tid=6918">la ] [ href="module.php?name=Lexikon&op=content&tid=7014">lc ] [ href="module.php?name=Lexikon&op=content&tid=7023">ld ] [ href="module.php?name=Lexikon&op=content&tid=7091">Lex ] [ href="module.php?name=Lexikon&op=content&tid=7107">li ] [ href="module.php?name=Lexikon&op=content&tid=7291">logical ] [ href="module.php?name=Lexikon&op=content&tid=7402">LSE ] [ href="module.php?name=Lexikon&op=content&tid=7412">LTL ] [ href="module.php?name=Lexikon&op=content&tid=7415">lu ] [ href="module.php?name=Lexikon&op=content&tid=7441">ly ] [ href="module.php?name=Lexikon&op=content&tid=7457">M ] [ href="module.php?name=Lexikon&op=content&tid=7463">ma ] [ href="module.php?name=Lexikon&op=content&tid=7582">man ] [ href="module.php?name=Lexikon&op=content&tid=7817">method ] [ href="module.php?name=Lexikon&op=content&tid=8019">mm ] [ href="module.php?name=Lexikon&op=content&tid=8032">mo ] [ href="module.php?name=Lexikon&op=content&tid=8040">mod ] [ href="module.php?name=Lexikon&op=content&tid=8042">modal ] [ href="module.php?name=Lexikon&op=content&tid=8046">mode ] [ href="module.php?name=Lexikon&op=content&tid=8079">module ] [ href="module.php?name=Lexikon&op=content&tid=8093">Mono ] [ href="module.php?name=Lexikon&op=content&tid=8167">mp ] [ href="module.php?name=Lexikon&op=content&tid=8228">ms ] [ href="module.php?name=Lexikon&op=content&tid=8258">mu ] [ href="module.php?name=Lexikon&op=content&tid=8384">N ] [ href="module.php?name=Lexikon&op=content&tid=8386">na ] [ href="module.php?name=Lexikon&op=content&tid=8460">nc ] [ href="module.php?name=Lexikon&op=content&tid=8472">ne ] [ href="module.php?name=Lexikon&op=content&tid=8622">nf ] [ href="module.php?name=Lexikon&op=content&tid=8627">ng ] [ href="module.php?name=Lexikon&op=content&tid=8630">ni ] [ href="module.php?name=Lexikon&op=content&tid=8672">nn ] [ href="module.php?name=Lexikon&op=content&tid=8675">no ] [ href="module.php?name=Lexikon&op=content&tid=8733">Notes ] [ href="module.php?name=Lexikon&op=content&tid=8760">ns ] [ href="module.php?name=Lexikon&op=content&tid=8787">nu ] [ href="module.php?name=Lexikon&op=content&tid=8820">O ] [ href="module.php?name=Lexikon&op=content&tid=8964">om ] [ href="module.php?name=Lexikon&op=content&tid=9014">op ] [ href="module.php?name=Lexikon&op=content&tid=9071">operator ] [ href="module.php?name=Lexikon&op=content&tid=9194">Ox ] [ href="module.php?name=Lexikon&op=content&tid=9430">PD ] [ href="module.php?name=Lexikon&op=content&tid=9442">PDL ] [ href="module.php?name=Lexikon&op=content&tid=9457">pe ] [ href="module.php?name=Lexikon&op=content&tid=9550">ph ] [ href="module.php?name=Lexikon&op=content&tid=9644">pk ] [ href="module.php?name=Lexikon&op=content&tid=9651">pl ] [ href="module.php?name=Lexikon&op=content&tid=9724">PLTL ] [ href="module.php?name=Lexikon&op=content&tid=9908">pr ] [ href="module.php?name=Lexikon&op=content&tid=10023">program ] [ href="module.php?name=Lexikon&op=content&tid=10085">propositional calculus ] [ href="module.php?name=Lexikon&op=content&tid=10198">Q ] [ href="module.php?name=Lexikon&op=content&tid=10253">query ] [ href="module.php?name=Lexikon&op=content&tid=10364">rc ] [ href="module.php?name=Lexikon&op=content&tid=10385">re ] [ href="module.php?name=Lexikon&op=content&tid=10508">relation ] [ href="module.php?name=Lexikon&op=content&tid=10754">rl ] [ href="module.php?name=Lexikon&op=content&tid=10767">ro ] [ href="module.php?name=Lexikon&op=content&tid=10887">ru ] [ href="module.php?name=Lexikon&op=content&tid=10918">S ] [ href="module.php?name=Lexikon&op=content&tid=10922">sa ] [ href="module.php?name=Lexikon&op=content&tid=11149">SE ] [ href="module.php?name=Lexikon&op=content&tid=11150">se ] [ href="module.php?name=Lexikon&op=content&tid=11215">semantics ] [ href="module.php?name=Lexikon&op=content&tid=11376">si ] [ href="module.php?name=Lexikon&op=content&tid=11506">sit ] [ href="module.php?name=Lexikon&op=content&tid=11524">SL ] [ href="module.php?name=Lexikon&op=content&tid=11651">so ] [ href="module.php?name=Lexikon&op=content&tid=11790">spec ] [ href="module.php?name=Lexikon&op=content&tid=11934">st ] [ href="module.php?name=Lexikon&op=content&tid=11976">Stanford University ] [ href="module.php?name=Lexikon&op=content&tid=12246">sy ] [ href="module.php?name=Lexikon&op=content&tid=12312">system ] [ href="module.php?name=Lexikon&op=content&tid=12359">T ] [ href="module.php?name=Lexikon&op=content&tid=12513">Tempo ] [ href="module.php?name=Lexikon&op=content&tid=12515">temporal logic ] [ href="module.php?name=Lexikon&op=content&tid=12588">th ] [ href="module.php?name=Lexikon&op=content&tid=12721">to ] [ href="module.php?name=Lexikon&op=content&tid=12787">tr ] [ href="module.php?name=Lexikon&op=content&tid=12896">tt ] [ href="module.php?name=Lexikon&op=content&tid=12986">ua ] [ href="module.php?name=Lexikon&op=content&tid=13008">ug ] [ href="module.php?name=Lexikon&op=content&tid=13175">us ] [ href="module.php?name=Lexikon&op=content&tid=13229">V ] [ href="module.php?name=Lexikon&op=content&tid=13252">va ] [ href="module.php?name=Lexikon&op=content&tid=13274">var ] [ href="module.php?name=Lexikon&op=content&tid=13310">ve ] [ href="module.php?name=Lexikon&op=content&tid=13366">vi ] [ href="module.php?name=Lexikon&op=content&tid=13694">while ]