Computational Logic PDF
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ISBN: 978-0-444-51624-4 ISSN: 1874-5857 For information on all North Holland publications visit our web site at http://store.elsevier.com/ EDITORIAL NOTE J¨org Siekmann and Dov Gabbay Becauseofspaceandtimeconsiderations, notalltopicscouldbecoveredbychap- ters in this Handbook. They will appear in a separate publication soon. CONTRIBUTORS AUTHORS Klaus Ambos-Spies Heidelberg University, Germany. [email protected] Jos Baeten CWI Amsterdam, The Netherlands. [email protected] Henk Barendregt Radboud University Nijmegen, The Netherlands. [email protected] Christoph Benzmu¨ller Freie Universit¨at Berlin, Gemany. [email protected] Martin Davis New York University, USA. [email protected] Didier Dubois IRIT, France. [email protected] Peter A. Fejer University of Massachusetts Boston, USA. [email protected] Lance Fortnow Georgia Institute of Technology, USA. [email protected] Dov Gabbay BarIlanUniversity,Israel;King’sCollegeLondon,UK;UniversityofLuxembourg, Luxembourg; University of Manchester, UK. [email protected] John R. Harrison Intel Corporation, USA. [email protected] Contributors ix Pascal Hitzler Wright State University, USA. [email protected] Steven Homer Boston University, USA. [email protected] Fairouz Kamareddine Herriot Watt University, UK. [email protected] Matthias Knorr Universidade Nova de Lisboa, Portugal. [email protected] Robert Kowalski Imperial College London, UK [email protected] Claude Kirchner Inria, France. [email protected] H´el`ene Kirchner Inria, France. [email protected] Jens Lehmann University of Leipzig, Germany [email protected] John-Jules Meyer Universiteit Utrecht, The Netherlands. [email protected] Dale Miller Inria, France. [email protected] Jack Minker University of Maryland, USA. [email protected] Henri Prade IRIT, France. [email protected] Davide Sangiorgi University of Bologna, Italy. [email protected] x Contributors Axel Polleres Vienna University of Economics and Business, Austria. [email protected] Dietmar Seipel University of Wu¨rzburg, Germany. [email protected] J¨org Siekmann Saarland University, DFKI, Germany. [email protected] Josef Urban Radboud University Nijmegen, The Netherlands. [email protected] Joe Wells Herriot Watt University, UK. [email protected] Freek Wiedijk Radboud University Nijmegen, The Netherlands. [email protected] Carlo Zaniolo University of California, Los Angeles, USA. [email protected] Christoph Zengler University of Tuebingen, Germany. [email protected] Readers xi READERS Luca Aceto Reykjavik University, Iceland. [email protected] Peter B. Andrews Carnegie Mellon University, USA. [email protected] Serge Autexier DFKI, Germany. [email protected] Franz Baader Dresden University, Germany. [email protected] Johan van Benthem Universiteit Amsterdam, The Netherlands [email protected] Jasmin Blanchette Technical Univesity of Munich, Germany. [email protected] Maarten H. van Emden University of Victoria, Canada. [email protected] William Farmer McMaster University, Canada. [email protected] Peter Fejer University of Massachusetts Boston, USA. [email protected] Herman Geuvers Radboud University Nijmegen, The Netherlands. [email protected] Robert van Glabbeek Nicta, Australia. [email protected] Lluis Godo Lacasa Universitat Autonoma de Varcelona, Spain. [email protected] xii Contributors Georg Gottlob Univesity of Oxford, UK. [email protected] Patrick Hayes Florida Institute for Human and Machine Cognition, USA. [email protected] Ian Horrocks Oxford University, UK. [email protected] Deepak Kapur University of New Mexico, USA. [email protected] Kurt Mehlhorn Max-Planck-Institut fu¨r Informatik, Germany. [email protected] Lawrence C. Paulson Cambridge University, UK. [email protected] Lu´ıs Moniz Pereira University of Lisbon, Portugal. [email protected] Richard Shore Cornell University, USA. [email protected] J¨org Siekmann DFKI, Germany. [email protected] Bruno Woltzenlogel Paleo Vienna University of Technology, Austria. [email protected] Michael Wooldridge Liverpool University, UK. [email protected] COMPUTATIONAL LOGIC J¨org Siekmann Computationallogicwasborninthetwentiethcenturyandevolvedinclosesym- biosiswiththefirstelectroniccomputersandthegrowingimportanceofcomputer science, informaticsandartificialintelligence(AI).Thefieldhasnowoutgrownits humble beginnings and early expectations by far: with more than ten thousand people working in research and development of logic and logic-related methods, withseveraldozeninternationalconferencesandseveraltimesasmanyworkshops addressing the growing richness and diversity of the field, and with the founda- tional role and importance these methods now assume in mathematics, computer science, artificial intelligence, cognitive science, linguistics, law, mechatronics and many other engineering fields where logic-related techniques are used inter alia to state and settle correctness issues, the field has diversified in ways that the pure logicians working in the early decades of the twenties century could have hardly anticipated - let alone those researchersof the previous centuries presented in this eleven volume account of the history of logic. Dating back to its roots in Greek, Indian, Chinese and Arabic philosophy the field has grown in richness and diversity over the centuries to finally reach the modern methodological approach first expressed in the work of Gottlob Frege.1 Logical calculi, which not only capture formal reasoning, but also an important aspect of human thought, are now amenable to investigation with mathemati- cal rigour and computational support and fertilized the early Leibniz’ dream of mechanized reasoning: “Calculemus”. The beginning of the last century saw the influence of these developments in the foundations of mathematics in the works of David Hilbert and Paul Bernays, Bertrand Russell and Alfred North Whitehead2 and others, in the foundations of syntax and semantics of language, and in ana- lytic philosophy most vividly expressed in the previous century by the logicians and philosophers in the Vienna Circle. The Dartmouth Conference in 1956 generally considered the birthplace of ar- tificial intelligence — raised explicitly the hopes for the new possibilities that the adventofelectroniccomputingmachineryoffered: logicalstatementscouldnowbe executed on a machine with all the far-reaching consequences that ultimately led to logic programming,3 question answering systems, deduction systems for math- 1See volume 3, “The Rise of modern Logic : from Leibnitz to Frege” in this eleven volume handbookonthehistoryoflogic. 2See volume 4 “British Logic in the 19th Century” and volume 5 “Logic from Russell to Church”ofthishandbookonthehistoryoflogic. 3SeethechapterbyRobertKowalski. Handbook of the History of Logic. Volume 9: Computational Logic. Volume editor: Jörg Siekmann Series editors: Dov M. Gabbay and John Woods Copyright © 2014 Elsevier BV. All rights reserved. 16 J¨orgSiekmann ematicsandengineering,4 logicaldesignandverificationofcomputersoftwareand hardware,deductivedatabases5andsoftwaresynthesisaswellaslogicaltechniques fortheanalysisandverificationinthefieldsofmechanicalengineering. Inthisway thegrowingrichnessoffoundationalandpurelylogicalinvestigationsthathadled to such developments as: first order calculi • type theory and higher order logic • nonclassical logics • semantics • constructivism • andothers, wasextendedbynewquestionsandproblems, inparticularfromcom- puter science and artificial intelligence, leading to: denotational semantics for programming languages • first- and higher-order logical calculi for automated reasoning • non-monotonic reasoning • logical foundations for computing machinery such as CSP, π-Calculus and • others for program verification knowledge representation formalisms such as description logics • logics for the semantic web • logical foundations for cognitive robotics • syntax and semantics for natural language processing • logical foundations of databases • linear logics, probabilistic reasoning and uncertainty management • logicalfoundationsanditsrelationshiptothephilosophyofmind,andmany • others. 4SeethechapterbyJohnHarrison,FreekWiedijkandJosefUrban;thechapterbyChristoph Benzmu¨llerandDaleMiller;thechapterbyGillesDowekandHermanGeuvers;thechapterby ClaudeandH´el`enKirchnerandthechapterbyFairouzKamareddine,J.B.Wells,C.Zenglerand HenkBarendregt. 5SeethechapterbyJackMinker,DietmarSeipelandCarloZaniolo. ComputationalLogic 17 In many respects, logic provides computer science with both a unifying founda- tional framework and a tool for modeling.6 In fact, logic has been called the cal- culus of computer science, most prominently represented at the LICS conference (Logic in Computer Science), playing a crucial role in diverse areas such as com- putationalcomplexity,7 unsolvability,8 distributedcomputing,concurrency,9 multi agent systems,10 database systems, hardware design, programming languages, knowledge representation,11 the semantic web,12 and software engineering. As John McCarthy succinctly coined it: “Newtonian physics is to mechanical engi- neering as logic is to computer science”. But the demands from artificial intel- ligence, computational linguistics and philosophy have spawned even more new ideas and developments as we shall argue below.13 This growing diversity is reflected in the numerous conferences and workshops that address particular aspects of the fields mentioned above. For example, only forty years ago, there was just one international conference on Automated De- duction (later to be called CADE). Today there is not only the annual CADE but also the biannual IJCAR, the International Joint Conference on Automated Deduction, which unites every two years CADE, FroCos (the International Sym- posium on Frontiers of Combining Systems), FTP ( International Worshop on First-order Theorem Proving), the TABLEAUX conference (Automated Reason- ing with Analytic Tableaux and Related Methods) and sometimes other smaller conferences as well. There is also the RTA conference (Rewriting Techniques and Applications), the LPAR (Logic Programming and Automated Reasoning), TPHOL (Theorem Proving in Higher Order Logic), and UNIF (the Unification Workshop). Several conferences on mathematical theorem proving have recently unitedintoCICM(ConferenceonIntelligentComputerMathematics),amongoth- ers CALCULEMUS, MKM (Mathematical Knowledge Management), DML (Dig- ital Mathematical Libraries) and the OpenMath workshops. CICM has usually half a dozen workshops colocated such as MathUI (Mathematical User Interfaces) and ThEdu (Theorem Prover Components for Educational Software) and others. Each of these conferences is held regularly on its own or back to back with a re- lated conference, but with its own set of proceedings and supported by a mature scientific community. Frequently, these conferences spawn dozens of national and international workshops, that drive the development and represent the creative innovation, but may not be ready yet for archival presentation. Some of these that united the young rebels of the field are CALCULEMUS, MKM (Mathemat- ical Knowledge Management), CIAO the Workshop that started with induction but soon became an event of its own, the Proof Presentation workshop, UITP 6SeethechapterbyMartinDavis. 7SeethechapterbyLanceFortnowandStevenHomer. 8SeethechapterbyKlausAmbos-SpiesandPeterFejer. 9SeethechapterbyJosBaetenandDavideSangiorgi. 10SeethechapterbyJohn-JulesMeyer 11SeethechapterbyMatthiasKnorrandPascalHitzler. 12SeethechapterbyPascalHitzler,JensLehmannandAxelPolleres 13SeethechapterbyDovGabbayandthechapterbyDidierDuboisandHenriPrade.
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