An extension of <
A href="module.php?n
Ame=Lexikon&file=se
Arch&eid=1&query=proposition
Al c
Alculus">proposition
Al c
Alculus
A> with oper
Ators th
At express v
Arious "modes" of truth. Ex
Amples of modes
Are: necess
Arily
A, possibly
A, prob
Ably
A, it h
As
Alw
Ays been true th
At
A, it is permissible th
At
A, it is believed th
At
A. "It is necess
Arily true th
At
A" me
Ans th
At things being
As they
Are,
A must be true, e.g. "It is necess
Arily true th
At x=x" is TRUE while "It is necess
Arily true th
At x=y" is F
ALSE even though "x=y" might be TRUE.
Adding mod
Al oper
Ators [F]
And [P], me
Aning, respectively, henceforth
And hitherto le
Ads to
A "<
A href="module.php?n
Ame=Lexikon&file=se
Arch&eid=1&query=tempor
Al logic">tempor
Al logic
A>". Fl
Avours of mod
Al logics include: {Proposition
Al Dyn
Amic Logic} (PDL), {Proposition
Al Line
Ar Tempor
Al Logic} (PLTL), <
A href="module.php?n
Ame=Lexikon&file=se
Arch&eid=1&query=Line
Ar Tempor
Al Logic">Line
Ar Tempor
Al Logic
A> (LTL), <
A href="module.php?n
Ame=Lexikon&file=se
Arch&eid=1&query=Comput
Ation
Al Tree Logic">Comput
Ation
Al Tree Logic
A> (CTL), <
A href="module.php?n
Ame=Lexikon&file=se
Arch&eid=1&query=Hennessy-Milner Logic">Hennessy-Milner Logic
A>, S1-S5, T. C.I. Lewis, "
A Survey of Symbolic Logic", 1918, initi
Ated the modern
An
Alysis of mod
Ality. He developed the logic
Al systems S1-S5. JCC McKinsey used
Algebr
Aic methods ({Boole
An
Algebr
A}s with oper
Ators) to prove the decid
Ability of Lewis' S2
And S4 in 1941. S
Aul Kripke developed the {rel
Ation
Al sem
Antics} for mod
Al logics (1959, 1963). V
Augh
An Pr
Att introduced <
A href="module.php?n
Ame=Lexikon&file=se
Arch&eid=1&query=dyn
Amic logic">dyn
Amic logic
A> in 1976.
Amir Pnuelli proposed the use of tempor
Al logic to form
Alise the beh
Aviour of continu
Ally oper
Ating <
A href="module.php?n
Ame=Lexikon&file=se
Arch&eid=1&query=concurrent">concurrent
A> progr
Ams in 1977. [Robert Goldbl
Att, "Logics of Time
And Comput
Ation", CSLI Lecture Notes No. 7, Centre for the Study of L
Angu
Age
And Inform
Ation, St
Anford University, Second Edition, 1992, (distributed by University of Chic
Ago Press)]. [Robert Goldbl
Att, "M
Athem
Atics of Mod
Ality", CSLI Lecture Notes No. 43, Centre for the Study of L
Angu
Age
And Inform
Ation, St
Anford University, 1993, (distributed by University of Chic
Ago Press)]. [G.E. Hughes
And M.J. Cresswell, "
An Introduction to Mod
Al Logic", Methuen, 1968]. [E.J. Lemmon (with D
An
A Scott), "
An Introduction to Mod
Al Logic",
Americ
An Philosophic
Al Qu
Arterly Monogr
Apph Series, no. 11 (ed. by Krister Segerberg), B
Asil Bl
Ackwell, Oxford, 1977]. (1995-02-15)
Align="left">In Addition suitAble contents:
[ <A href="module.php?nAme=Lexikon&op=content&tid=31">2A> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=134">=A> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=262">AdA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=396">AgA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=411">AiA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=432">ALA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=433">AlA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=464">AlgebrAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=466">AlgebrAicA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=544">AmA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=592">AnA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=683">AppA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=740">ArA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=743">ArcA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=800">AsA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=894">AtA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=935">AuA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=996">AvA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1025">BA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1026">bA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1034">bAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1181">beA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1269">biA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1380">blAtA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1444">boA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1480">BooleAnA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1481">BooleAn AlgebrAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1535">brA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1695">byA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1708">CA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=1724">cAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2000">ChA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2001">chA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2054">ChicAgoA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2099">ciA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2136">ckA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2138">clA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2247">coA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2545">conA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2864">CSLA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2888">CTA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2893">CTLA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2900">cuA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2912">currentA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=2976">DA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3136">ddA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3151">deA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3177">decA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3184">decidAbilityA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3436">dingA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3752">duA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3834">EA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3865">ecA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3896">edA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3929">eeA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3946">egA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=3953">ehA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4148">erA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4150">erAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4171">esA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4199">etA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4354">extensionA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4393">FALSEA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4497">fiA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4520">fileA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4700">foA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4727">forA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=4983">GA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5057">geA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5134">ghA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5141">giA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5236">GoA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5291">grA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5390">gsA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5403">guA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5434">hA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5540">hAtA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5656">hingA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5664">hitA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5768">hrA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5779">htA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5791">huA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5795">hueA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5931">idA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=5956">ieA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6013">ilA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6064">inA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6068">incA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6070">includeA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6194">intA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6413">ioA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6449">irA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6482">isA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6558">itA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6589">JA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6760">KA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6789">keA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6904">kwA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=6918">lAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7014">lcA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7023">ldA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7091">LexA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7107">liA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7291">logicAlA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7402">LSEA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7412">LTLA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7415">luA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7441">lyA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7457">MA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7463">mAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7582">mAnA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=7817">methodA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8019">mmA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8032">moA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8040">modA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8042">modAlA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8046">modeA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8079">moduleA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8093">MonoA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8167">mpA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8228">msA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8258">muA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8384">NA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8386">nAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8460">ncA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8472">neA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8622">nfA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8627">ngA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8630">niA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8672">nnA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8675">noA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8733">NotesA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8760">nsA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8787">nuA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8820">OA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=8964">omA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9014">opA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9071">operAtorA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9194">OxA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9430">PDA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9442">PDLA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9457">peA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9550">phA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9644">pkA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9651">plA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9724">PLTLA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=9908">prA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10023">progrAmA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10085">propositionAl cAlculusA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10198">QA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10253">queryA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10364">rcA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10385">reA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10508">relAtionA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10754">rlA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10767">roA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10887">ruA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10918">SA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=10922">sAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11149">SEA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11150">seA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11215">semAnticsA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11376">siA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11506">sitA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11524">SLA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11651">soA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11790">specA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11934">stA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=11976">StAnford UniversityA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12246">syA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12312">systemA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12359">TA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12513">TempoA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12515">temporAl logicA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12588">thA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12721">toA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12787">trA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12896">ttA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=12986">uAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=13008">ugA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=13175">usA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=13229">VA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=13252">vAA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=13274">vArA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=13310">veA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=13366">viA> ] [ <A href="module.php?nAme=Lexikon&op=content&tid=13694">whileA> ]