Automated Reasoning with Analytic Tableaux and Related Methods: 20th International Conference, TABLEAUX 2011, Bern, Switzerland, July 4-8, 2011. Proceedings PDF
Preview Automated Reasoning with Analytic Tableaux and Related Methods: 20th International Conference, TABLEAUX 2011, Bern, Switzerland, July 4-8, 2011. Proceedings
Lecture Notes in Artificial Intelligence 6793 EditedbyR.Goebel,J.Siekmann,andW.Wahlster Subseries of Lecture Notes in Computer Science Kai Brünnler George Metcalfe (Eds.) Automated Reasoning with Analytic Tableaux and Related Methods 20th International Conference, TABLEAUX 2011 Bern, Switzerland, July 4-8, 2011 Proceedings 1 3 SeriesEditors RandyGoebel,UniversityofAlberta,Edmonton,Canada JörgSiekmann,UniversityofSaarland,Saarbrücken,Germany WolfgangWahlster,DFKIandUniversityofSaarland,Saarbrücken,Germany VolumeEditors KaiBrünnler UniversitätBern InstitutfürInformatikundAngewandteMathematik Neubrückstr.10,3012Bern,Switzerland E-mail:[email protected] GeorgeMetcalfe UniversitätBern MathematischesInstitut Sidlerstr.5,3012Bern,Switzerland E-mail:[email protected] ISSN0302-9743 e-ISSN1611-3349 ISBN978-3-642-22118-7 e-ISBN978-3-642-22119-4 DOI10.1007/978-3-642-22119-4 SpringerHeidelbergDordrechtLondonNewYork LibraryofCongressControlNumber:2011930102 CRSubjectClassification(1998):I.2.3,F.4.1-2,I.2,D.1.6,D.2.4 LNCSSublibrary:SL7–ArtificialIntelligence ©Springer-VerlagBerlinHeidelberg2011 Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,re-useofillustrations,recitation,broadcasting, reproductiononmicrofilmsorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965, initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violationsareliable toprosecutionundertheGermanCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply, evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelaws andregulationsandthereforefreeforgeneraluse. Typesetting:Camera-readybyauthor,dataconversionbyScientificPublishingServices,Chennai,India Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface This volume contains the research papers presented at the 20th International ConferenceonAutomatedReasoningwithAnalyticTableauxandRelatedMeth- ods (TABLEAUX 2011) held July 4-8, 2011 in Bern, Switzerland. TheProgramCommitteeofTABLEAUX2011received34submissions.Each paper was reviewed by at least three referees and, following a thorough and livelyonlinediscussionphase,16researchpapersand2systemdescriptionswere accepted based on their originality, technical soundness, presentation, and rel- evance to the conference. We would like to sincerely thank both the authors for their contributions and the members of the Program Committee and addi- tional referees for their much appreciated time, energy, and professionalism in the review and selection process. In addition to the contributed papers, the program of TABLEAUX 2011 included three keynote talks by distinguished researchers in the field of au- tomated reasoning and proof theory: Maria Paola Bonacina (Universita` degli Studi di Verona, Italy), Ulrich Furbach (University of Koblenz-Landau, Ger- many), and Kazushige Terui (Kyoto University, Japan). There were also two tutorials: “Tableaux(-like) Methods for the Satisfiability Problems of Temporal Logics”byMartinLange(UniversityofKassel,Germany),and“Introductionto Proof Nets” by Lutz Strassburger (INRIA Saclay, France). Two workshopsare held in conjunctionwith TABLEAUX 2011:“FTP 2011, the 8th International Workshop on First-Order Theorem Proving” chaired by Martin Giese (University of Oslo, Norway),and the second edition of “Gentzen SystemsandBeyond”organizedbyRomanKuznetsandRichardMcKinley(Uni- versity of Bern, Switzerland). We would like to thank the members of the Organizing Committee for their much appreciated support and expertise: Samuel Bucheli, Roman Kuznets, Richard McKinley, and Nia Stephens-Metcalfe. Finally, we would like to thank our sponsors for their generous and very welcome support: the Bu¨rgergemeinde Bern, the Kurt G¨odel Society, the Swiss AcademyofSciences,theSwissMathematicalSociety,theSwissNationalScience Foundation, the Hasler Foundation, and the University of Bern. We would also liketo acknowledgethe Easychairconferencemanagementsystemwhichgreatly facilitated the smooth running of the review process and compilation of these proceedings. May 1, 2011 George Metcalfe Kai Bru¨nnler Organization Program Committee Arnon Avron Tel Aviv University, Israel Peter Baumgartner National ICT, Australia Bernhard Beckert Karlsruhe Institute of Technology, Germany Torben Brau¨ner Roskilde University, Denmark Kai Bru¨nnler University of Bern, Switzerland Agata Ciabattoni TU Vienna, Austria Marta Cialdea Mayer University of Rome 3, Italy Roy Dyckhoff University of St. Andrews, UK Martin Giese University of Oslo, Norway Valentin Goranko Technical University of Denmark Rajeev Gore The Australian National University Ullrich Hustadt University of Liverpool, UK Reiner H¨ahnle Chalmers University of Technology, Sweden Martin Lange University of Kassel, Germany George Metcalfe University of Bern, Switzerland Dale Miller INRIA Saclay, France Neil Murray University at Albany SUNY, USA Nicola Olivetti Paul C´ezanne University, France Jens Otten Potsdam University, Germany Dirk Pattinson Imperial College London, UK Andre Platzer Carnegie Mellon University, USA Renate Schmidt University of Manchester, UK Viorica Sofronie- Stokkermans MPI, Saarbru¨cken,Germany Ulrich Ultes-Nitsche University of Fribourg, Switzerland Luca Vigan`o University of Verona, Italy Arild Waaler University of Oslo, Norway Additional Reviewers Antonsen, Roger Egly, Uwe B´ılkova´,Marta Facchini, Alessandro Cerrito, Serenella Fermu¨ller, Christian Chapman, Peter Garg, Deepak Dawson, Jeremy Giese, Martin Deyoung, Henry Gladisch, Christoph VIII Organization Gliozzi, Valentina Roschger, Christoph Hetzl, Stefan Sauro, Luigi Hodkinson, Ian Schneider, Thomas Jia, Limin Serre, Olivier Khodadadi, Mohammad Shapirovsky, Ilya Klebanov, Vladimir Son, Tran Cao Kontchakov,Roman Stolpe, Audun Kuznets, Roman Straccia, Umberto Lian, Espen H. Strassburger, Lutz Martins, Joao Terui, Kazushige Matusiewicz, Andrew Tishkovsky, Dmitry Pozzato,Gian Luca Tiu, Alwen Qi, Guilin Wischnewski, Patrick Ramanayake,Revantha Zeilberger, Noam Renshaw, David Previous Meetings 1992Lautenbach, Germany 1993Marseille, France 1994Abingdon, UK 1995St. Goar, Germany 1996Terrasini, Italy 1997Pont-`a-Mousson,France 1998Oisterwijk, The Netherlands 1999Saratoga Springs, USA 2000St. Andrews, UK 2001Siena, Italy (part of IJCAR) 2002Copenhagen, Denmark 2003Rome, Italy 2004Cork, Ireland (part of IJCAR) 2005Koblenz, Germany 2006Seattle, USA (part of IJCAR) 2007Aix-en-Provence,France 2008Sydney, Australia (part of IJCAR) 2009Oslo, Norway 2010Edinburgh, UK (part of IJCAR) TABLEAUX Steering Committee Rajeev Gor´e (President) Australian National University, Australia Kai Bru¨nnler University of Bern, Switzerland Martin Giese University of Oslo, Norway Valentin Goranko Technical University of Denmark Organization IX Reiner H¨ahnle Chalmers University of Technology, Sweden George Metcalfe University of Bern, Switzerland Angelo Montanari University of Udine, Italy Neil Murray University at Albany - SUNY, USA Sponsors Bu¨rgergemeinde Bern Haslerstiftung Kurt Go¨del Society Swiss Academy of Sciences Swiss Mathematical Society Swiss National Science Foundation University of Bern Table of Contents On Interpolation in Decision Procedures ............................ 1 Maria Paola Bonacina and Moa Johansson First-Order Tableaux in Applications (Extended Abstract) ............ 17 Ulrich Furbach Proof Theory and Algebra in Substructural Logics ................... 20 Kazushige Terui CSymLean: A Theorem Prover for the Logic CSL over Symmetric Minspaces....................................................... 21 R´egis Alenda and Nicola Olivetti Schemata of SMT-Problems ....................................... 27 Vincent Aravantinos and Nicolas Peltier Kripke Semantics for Basic Sequent Systems......................... 43 Arnon Avron and Ori Lahav Hybrid and First-Order Complete Extensions of CaRet ............... 58 Laura Bozzelli and Ruggero Lanotte Optimal Tableau Systems for Propositional Neighborhood Logic over All, Dense, and Discrete Linear Orders ............................. 73 Davide Bresolin, Angelo Montanari, Pietro Sala, and Guido Sciavicco Craig Interpolation in Displayable Logics ........................... 88 James Brotherston and Rajeev Gor´e A Tableaux Based Decision Procedure for a Broad Class of Hybrid Formulae with Binders............................................ 104 Serenella Cerrito and Marta Cialdea Mayer Basic Constructive Connectives, Determinism and Matrix-Based Semantics....................................................... 119 Agata Ciabattoni, Ori Lahav, and Anna Zamansky On the Proof Complexity of Cut-Free Bounded Deep Inference ........ 134 Anupam Das The Modal µ-Calculus Caught Off Guard ........................... 149 Oliver Friedmann and Martin Lange XII Table of Contents A Conditional Constructive Logic for Access Control and Its Sequent Calculus ........................................................ 164 Valerio Genovese, Laura Giordano, Valentina Gliozzi, and Gian Luca Pozzato A Tableau Calculus for a Nonmonotonic Extension of EL⊥ ............ 180 Laura Giordano, Valentina Gliozzi, Nicola Olivetti, and Gian Luca Pozzato Correctness and Worst-Case Optimality of Pratt-Style Decision Procedures for Modal and Hybrid Logics............................ 196 Mark Kaminski, Thomas Schneider, and Gert Smolka Cut Elimination for Shallow Modal Logics .......................... 211 Bjo¨rn Lellmann and Dirk Pattinson A Non-clausal Connection Calculus ................................ 226 Jens Otten MetTeL: A Tableau Prover with Logic-Independent Inference Engine ......................................................... 242 Dmitry Tishkovsky, Renate A. Schmidt, and Mohammad Khodadadi A Hypersequent System for Go¨del-Dummett Logic with Non-constant Domains........................................................ 248 Alwen Tiu MaLeCoP: Machine Learning Connection Prover ..................... 263 Josef Urban, Jiˇr´ı Vyskoˇcil, and Petr Sˇtˇep´anek Author Index.................................................. 279 (cid:2) On Interpolation in Decision Procedures Maria Paola Bonacina and Moa Johansson Dipartimento diInformatica, Universit`adegli Studidi Verona Strada LeGrazie 15, I-37134 Verona, Italy [email protected], [email protected] Abstract. Interpolation means finding intermediate formulae between givenformulae.Whenformulaedecorateprogramlocations,anddescribe sets of program states, interpolation may enable a program analyzer to discoverinformationaboutintermediatelocationsandstates.Thismech- anismhasanincreasingnumberofapplications,thatarerelevanttopro- gram analysisandsynthesis.Westudyinterpolation intheorem proving decisionproceduresbasedontheDPLL(T)paradigm.Wesurveyinterpo- lationsystemsforDPLL,equalitysharingandDPLL(T),reconstructing from theliteraturetheircompletenessproofs, andclarifying therequire- mentsforinterpolationinthepresenceofequality. 1 Introduction Automated deduction and program verification have always been connected, as described, for instance, in [34] and [1]. A theorem proving technique that has recently found application in verification is interpolation. Informally, inter- polants are formula ‘in between’ other formulæ in a proof,containing only their shared symbols. Interpolation was proposed for abstraction refinement in soft- ware model checking,first for propositionallogic and propositionalsatisfiability [25],andthenforquantifier-freefragmentsoffirst-ordertheories,theircombina- tions, and satisfiability modulo theories [18,26,35,21,11,12,17,6,7,9]. Considered theories include equality [26,16], linear rational arithmetic [26,21], Presburger or linear integer arithmetic [21,6], or fragments thereof [12], and arrayswithout extensionality[21,7,8].Inthesepapersthetheoryreasoningisdoneeitherbyspe- cializedsequent-styleinferencesystems[18,26,6,7]orbysatisfiabilityprocedures, suchascongruenceclosureforequality[16],integratedinaDPLL(T)framework [35,11,12,17].Subsequently,interpolationwassuggestedforinvariantgeneration, and in the context of inference systems for first-order logic with equality, based onresolutionandsuperposition[27,23,19].Anearlyleadtowardsthisapplication can be traced back to [10]. More recently, interpolation was related to abstract interpretation [14] and applied to improve the quality of annotations [28]. The aim of this paper is to present the core of the state of the art in inter- polation for the proofs generated by theorem provers for satisfiability modulo (cid:2) ResearchsupportedinpartbyMIURgrantno.2007-9E5KM8andEUCOSTAction IC0901. K.Bru¨nnlerandG.Metcalfe(Eds.):TABLEAUX2011,LNAI6793,pp.1–16,2011. (cid:2)c Springer-VerlagBerlinHeidelberg2011
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