Table Of ContentLecture 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
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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
