logical semantics

PropositionalLogicItisalsoknownasPropositionalCalculus(命题演算)orSententialCalculus(句子演算)Itisthestudyofthetruthconditionsforpropositions（命题的真值条件）:howthetruthofacompositeproposition（复合命题）isdeterminedbythetruthvalueofitsconstituentpropositions（成分命题）andtheconnectionsbetweenthem.PQP&QP∨QP→QP≡QTTTTTTTFFTFFFTFTTFFFFFTTInLogicalSemantics,itmeans“negation”(否定连词)ThisconnectiveConjunctioncorrespondstotheEnglish“and”(合取连词).Itiscalleddisjunction，whichcorrespondstotheEnglish“or”(析取连词)ImplicationcorrespondstotheEnglish“if…then”(蕴涵连词)EquivalencecorrespondstotheEnglish“ifandonlyif…then”(等值连词)thetruthfunctionsofthelogicalconnectivesarenotexactlythesameastheircounterpartsinEnglish.whatarethedifferencebetweenthem？“~”“not”TruthvaluemustbeoppositeIt’shardtosay“&”“and”Theorderoftheconstituentpropositionsisnotimportant.Theorderwillmakeaninfluenceonthetruthvalue.“→”“if···then”IttakesonaccountofthenatureoftherelationbetweenthetwosimplepropositionsTheremustbesomecausalorsimilarrelationshipbetweenthetwo.AllmanarerationalSocratesisamanTherefore,SocratesisrationalPredicatelogic(谓词逻辑),alsocalledpredicatecalculus(谓词演算),studiestheinternalstructureofsimplepropositions.Inthislogicalsystem,propositionswillbeanalyzedintotwoparts:argument(主目)andpredicate(谓词).Anargument(主目)isatermwhichreferstosomeentityaboutwhichastatementisbeingmade.APredicate(谓词)isatermwhichascribessomeproperty，orrelation，totheentity，orentities，referredto.●one-placepredicate（一元谓词）Socratesisaman.●two-placepredicate（二元谓词）JohnlovesMary.●three-placepredicate（三元谓词）JohngaveMaryabook.Casestudy1Socratesisaman.Casestudy2Allmanarerational.Casestudy3•Socratesisrational.•Sheispretty.Universalquantifier（全称量词):all∀Allteachersarefemale.∀x(T(x)F(x))=Forallx,ifxisateacher,thenxisfemaleExistentialquantifier(存在量词):some∃Someteachersarefemale.∃x(T(x)&F(x))=Therearesomex’sthatarebothteachersandfemaleInthesign(在符号表示上):oneusesthequantifier:∀theotherusesthequantifier:∃Inthelogicalconnective(在逻辑连词的选择上)：oneusestheimplicationconnective(蕴含连词)→theotherusestheconjunctionconnective(合取连词)＆Theyarerelatedtoeachotherintermsofnegation.(否定上逆相关)Allmenarerational=Thereisnomanwhoisnotrational∀x(M(x)→R(x))≡～∃x(M(x)＆～R(x))∀x（p（x））≡～∃x（～p（x））～∀x（p（x））≡∃x（～p（x））∃x（p（x））≡～∀x（～p（x））～∃x（p（x））≡∀x（～p（x））“AllmenarerationalSocratesisamanTherefore,Socratesisrational”∀x(M(x)→R(x))M(S)∴R(S)∀x(M(x)→R(x))R(s)∴M(s)∃x(M(x)＆C(x))M(s)∴C(s)●propositionallogic，concernedwiththesemanticrelationbetweenpropositions，treatsasimplepropositionasanunanalyzedwhole.●predicatelogicstudiestheinternalstructureofsimplepropositions.●HowtotreattheCommonNouns●Quantifiers