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1、CausalTheoriesasLogicProgramsPaoloFerrarisUniversityofTexasatAustin,AustinTX78712,USAotto@cs.utexas.edu∗∗∗UNPUBLISHEDDRAFT∗∗∗Abstract.Weshowhowwecanrewriteanycausaltheory—underthesemanticsofcausallogicduetoMcCainandTurner—asalogicprogramintheanswersetsemantics.Usingthistranslationthemodelsofanycausa
2、ltheorycanbecomputedusinganswersetsolvers.1IntroductionCausallogic[McCainandTurner,1997]isaformalismforknowledgerepresen-tation,especiallysuitedforrepresentingeffectsofactions.Causaltheoriesaresyntacticallysimplebutalsoverygeneral:theyconsistofcausalrulesoftheformF⇐G(1)whereFandGarepropositionalformu
3、las.Intuitively,rule(1)saysthatthereisacauseforFtobetrueifGistrue.Forinstance,thecausalrulept+1⇐at(2)canbeusedtodescribetheeffectofanactionaonaBooleanfluentp:ifaisexecutedattimetthenthereisacauseforptoholdattimet+1.Otherimportantconceptsincommonsensereasoningcanbeeasilyexpressedbyrulesofthiskindtoo.Fo
4、rinstance,aruleoftheformF⇐F(“ifFistruethenthereisacauseforthis”)expresses,intuitively,thatFistruebydefault.Inparticular,thecausalrulept⇐pt(3)saysthatBooleanfluentpisnormallytrue.Theframeproblem[McCarthyandHayes,1969]issolvedincausallogicusingtherulespt+1⇐pt∧pt+1(4)¬pt+1⇐¬pt∧¬pt+1.Theserulessay:ifaflue
5、ntpistrue(false)attimetthennormallyitremainstrue(false)attimet+1.Inmanyusefulcausalrules,suchas(2)–(4),theformulabeforethe“⇐”isaliteralor⊥.Rulesofthiskindsarecalleddefinite.Otherimportantrulesarenotdefinite:forinstance,theequivalenceoftwofluentspandqatsometimetisexpressedbypt↔qt⇐>.Searchformodelsofacau
6、saltheoryisanimportantcomputationalproblem.Infact,thesemanticsofcausallogicdefineswhenaninterpretationisamodelofacausaltheorywithoutofferinganysearchmethodbetterthantheexaustiveone.Twosearchtechniquesexistinthespecialcasewhenthetheoryisdefinite,i.e.,allitsrulesaredefinite.Inthiscase,thecausaltheorycanbe
7、convertedintoapropositionaltheory,calledits“literalcompletion”[McCainandTurner,1997],thathasthesamemodels.Turningacausaltheoryintoitsliteralcompletiondoesn’tleadtoanincreaseinsize.Wecanthenuseasatisfia
