Table Of Content

SSeSreeirreiisee ssI SIISSSSNSNN: 1:: 911399233-221--21122282288 MMM G G G EEE NNN &&&CCC MMMooorrrgggaaannn& && CCClllaaayyypppoooooolll PPPuuubbbllliiissshhheeerrrsss EEE SSSYYYNNNTTTHHHEEESSSIIISSS L LLEEECCCTTTUUURRREEESSS O OONNN C CCOOOMMMPPPUUUTTTEEERRR S SSCCCIIIEEENNNCCCEEE SESESE RRR EEE TTT HHH • K • K • K AAA IIInnntttrrroooddduuuccctttiiiooonnn t ttooo L LLooogggiiiccc OOO IIInnntttrrroooddduuuccctttiiiooonnn tttooo LLLooogggiiiccc MMMiciichchhaaaeeel llG GGeeennneeesseseererreethtthh a aannnddd E EErrirciic cK KKaaaooo, ,,S SStattaannnfofforodrrdd U UUnnniviivvereesrrisstiiyttyy TTThhhisii ssb bbooooookk ki sii ssa aag gegneenntlttell eeb bbuuut ttr irrgiigogoororroouuus ssi niinntrttorrooddduuuctccittoiioonnn t ottoo f offoormrrmmalaa lll ollooggigcii.cc .I. tII tti sii ssi niinntettneenndddedeedd p pprirrmiimmaraairrliiylly yf offoor rru uusess eea taa ttt htthheee coccololllellgeegeg eel ellveeevvlee.l l.H. 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TThhheyee yya raaerr eea vaaavviaaliaillbaablbell eea taa tth hhttttpttpp:/::///l//olloogggicii.ccs..tssattanannfoffoordrrdd.e..deedduuu/i//niinntrttorroololloogggicii/cc.//.. III CCC EEErrriiiccc K KKaaaooo AAAbbbooouuuttt M MMooorrrgggaaannn & && C CClllaaayyypppoooooolll P PPuuubbbllliisisshhheeerrrsss MMM TTThhhisii ssv ovvoloullumumme eei sii ssa aap prpirrniintnettdeed dv evvreesrrissoiionon no ofo ffa aaw wwoorokrrk kt htthhataa tta paappppepaeeraasrr ssi niin nS SSynyyntnhtthheseeisssii,ss ,t, htthheee OOO DDDigiigigtiiattala Lll LLibiibrbarrarayrr yyo foo fEf EEnngngigniineneeereeirrniingn gga anandnd dC CComoommppuputuettree rrS ScSicceiineencnecc.ee .. 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FFooro rrm mmooroerr eei n iinfnofforomrrmmataaittoiiononn &&& vivvsiiisstii tts yssnyyntnhtthehseeisssii.ssm..mmoorogrrgagnaancnlccallyaapyypopoooolo.lcl..occomomm CCC LLL MMMooorrrgggaaannn & & & C CClllaaayyypppoooooolll P PPuuubbbllliiissshhheeerrrsss IISISBSBNBN:N: : 9 9797878-8-1-1-1-6-62627270705095-5990-0-00000000005005-050-0-0000 AYAYAY SSSYYYNNNTTTHHHEEESSSIIISSS L LLEEECCCTTTUUURRREEESSS O OONNN C CCOOOMMMPPPUUUTTTEEERRR S SSCCCIIIEEENNNCCCEEE PPP OOO wwwwwwwww..m.mmooorrrgggaaannncccllalaayyypppooooooll.l.c.ccooommm OOO 999778781816162627277005050500005050500 LLL Introduction to Logic Synthesis Lectures on Computer Science IntroductiontoLogic MichaelGeneserethandEricKao 2012 ScienceFictionPrototyping:DesigningtheFuturewithScienceFiction BrianDavidJohnson 2011 StoringClockedProgramsInsideDNA:ASimplifyingFrameworkforNanocomputing JessicaP.ChangandDennisE.Shasha 2011 AnalyticalPerformanceModelingforComputerSystems Y.C.Tay 2010 TheTheoryofTimedI/OAutomata DilsunK.Kaynar,NancyLynch,RobertoSegala,andFritsVaandrager 2006 Copyright© 2012byMorgan&Claypool Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedin anyformorbyanymeans—electronic,mechanical,photocopy,recording,oranyotherexceptforbriefquotationsin printedreviews,withoutthepriorpermissionofthepublisher. IntroductiontoLogic MichaelGeneserethandEricKao www.morganclaypool.com ISBN:9781627050050 paperback ISBN:9781627050067 ebook DOI10.2200/S00432ED1V01Y201207CSL005 APublicationintheMorgan&ClaypoolPublishersseries SYNTHESISLECTURESONCOMPUTERSCIENCE Lecture#5 SeriesISSN SynthesisLecturesonComputerScience Print1932-1228 Electronic1932-1686 Introduction to Logic Michael Genesereth and Eric Kao StanfordUniversity SYNTHESISLECTURESONCOMPUTERSCIENCE#5 M &C Morgan &cLaypool publishers ABSTRACT This book is a gentle but rigorous introduction to formal logic.It is intended primarily for use at thecollegelevel.However,itcanalsobeusedforadvancedsecondaryschoolstudents,anditcanbe usedatthestartofgraduateschoolforthosewhohavenotyetseenthematerial. Theapproachtoteachinglogicusedhereemergedfrommorethan20yearsofteachinglogic tostudentsatStanfordUniversityandfromteachinglogictotensofthousandsofothersviaonline coursesontheWorldWideWeb.Theapproachdiffersfromthattakenbyotherbooksinlogicin twoessentialways,onehavingtodowithcontent,theotherwithform. Likemanyotherbooksonlogic,thisonecoverslogicalsyntaxandsemanticsandprooftheory plusinduction.However,unlikeotherbooks,thisbookbeginswithHerbrandsemanticsratherthan themoretraditionalTarskiansemantics.Thisapproachmakesthematerialconsiderablyeasierfor studentstounderstandandleavesthemwithadeeperunderstandingofwhatlogicisallabout. Theprimarycontentdifferenceconcernsthesemanticsofthelogicthatistaught.Inaddition tothistext,thereareonlineexercises(withautomatedgrading),onlinelogictoolsandapplications, onlinevideosoflectures,andanonlineforumfordiscussion.Theyareavailableat http://logic.stanford.edu/intrologic/. KEYWORDS formallogic,symboliclogic,propositionallogic,Herbrandlogic,first-orderlogic,de- duction,reasoning,artificialintelligence vii Contents Preface .................................................................. xi 1 Introduction ..............................................................1 1.1 Logic ................................................................. 1 1.2 ElementsofLogic ...................................................... 1 1.3 Formalization .......................................................... 6 1.4 Automation............................................................ 9 1.5 ReadingGuide ........................................................ 11 2 PropositionalLogic...................................................... 13 2.1 Introduction .......................................................... 13 2.2 Syntax ............................................................... 13 2.3 Semantics ............................................................ 15 2.4 Satisfaction ........................................................... 18 2.5 LogicalPropertiesofPropositionalSentences.............................. 19 2.6 PropositionalEntailment ............................................... 20 3 PropositionalProofs ..................................................... 23 3.1 Introduction .......................................................... 23 3.2 LinearProofs ......................................................... 23 3.3 StructuredProofs ...................................................... 26 3.4 Fitch................................................................. 28 3.5 SoundnessandCompleteness ........................................... 30 4 PropositionalResolution................................................. 33 4.1 Introduction .......................................................... 33 4.2 ClausalForm.......................................................... 33 4.3 ResolutionPrinciple ................................................... 35 4.4 ResolutionReasoning .................................................. 37 viii 5 Satisfiability ............................................................ 41 5.1 Introduction .......................................................... 41 5.2 TruthTableMethod ................................................... 41 5.3 BasicBacktrackingSearch .............................................. 42 5.4 SimplificationandUnitPropagation...................................... 46 5.5 DPLL ............................................................... 48 5.6 GSAT ............................................................... 49 6 HerbrandLogic ......................................................... 53 6.1 Introduction .......................................................... 53 6.2 Syntax ............................................................... 53 6.3 Semantics ............................................................ 56 6.4 Example:SororityWorld ............................................... 58 6.5 Example:BlocksWorld................................................. 59 6.6 Example:ModularArithmetic........................................... 61 6.7 Example:PeanoArithmetic ............................................. 63 6.8 Example:LinkedLists ................................................. 65 6.9 Example:PseudoEnglish ............................................... 66 6.10 Example:MetalevelLogic .............................................. 67 6.11 PropertiesofSentencesinHerbrandLogic ................................ 69 6.12 LogicalEntailment .................................................... 70 6.13 FiniteHerbrandLogic ................................................. 71 6.14 OmegaHerbrandLogic ................................................ 74 6.15 GeneralHerbrandLogic................................................ 78 7 HerbrandLogicProofs................................................... 81 7.1 Introduction .......................................................... 81 7.2 Proofs................................................................ 81 7.3 Example.............................................................. 84 7.4 Example.............................................................. 85 7.5 Example.............................................................. 87 8 Resolution.............................................................. 89 8.1 Introduction .......................................................... 89 8.2 ClausalForm.......................................................... 89 8.3 Unification ........................................................... 92