Sergei Artemov · Anil Nerode (Eds.) 7 Logical Foundations 3 5 9 S of Computer Science C N L International Symposium, LFCS 2016 Deerfield Beach, FL, USA, January 4–7, 2016 Proceedings 123 Lecture Notes in Computer Science 9537 Commenced Publication in 1973 Founding and Former Series Editors: Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen Editorial Board David Hutchison Lancaster University, Lancaster, UK Takeo Kanade Carnegie Mellon University, Pittsburgh, PA, USA Josef Kittler University of Surrey, Guildford, UK Jon M. Kleinberg Cornell University, Ithaca, NY, USA Friedemann Mattern ETH Zurich, Zürich, Switzerland John C. Mitchell Stanford University, Stanford, CA, USA Moni Naor Weizmann Institute of Science, Rehovot, Israel C. Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen TU Dortmund University, Dortmund, Germany Demetri Terzopoulos University of California, Los Angeles, CA, USA Doug Tygar University of California, Berkeley, CA, USA Gerhard Weikum Max Planck Institute for Informatics, Saarbrücken, Germany More information about this series at http://www.springer.com/series/7407 Sergei Artemov Anil Nerode (Eds.) (cid:129) Logical Foundations of Computer Science International Symposium, LFCS 2016 fi – Deer eld Beach, FL, USA, January 4 7, 2016 Proceedings 123 Editors SergeiArtemov Anil Nerode City University of NewYork Cornell University NewYork,NY Ithaca, NY USA USA ISSN 0302-9743 ISSN 1611-3349 (electronic) Lecture Notesin Computer Science ISBN 978-3-319-27682-3 ISBN978-3-319-27683-0 (eBook) DOI 10.1007/978-3-319-27683-0 LibraryofCongressControlNumber:2015957091 LNCSSublibrary:SL1–TheoreticalComputerScienceandGeneralIssues ©SpringerInternationalPublishingSwitzerland2016 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartofthe material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynow knownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbookare believedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsortheeditors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissionsthatmayhavebeenmade. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAGSwitzerland Preface TheSymposiumonLogicalFoundationsofComputerScienceseriesprovidesaforum forthefast-growingbodyofworkinthelogicalfoundationsofcomputerscience,e.g., those areas of fundamental theoretical logic related to computer science. The LFCS seriesbeganwith“LogicatBotik,”Pereslavl-Zalessky,1989,whichwasco-organized by Albert R. Meyer (MIT) and Michael Taitslin (Tver). After that, the organization passedtoAnilNerode.CurrentlyLFCSisgovernedbyaSteeringCommitteeconsisting of Anil Nerode (General Chair), Stephen Cook, Dirk van Dalen, Yuri Matiyasevich, J. Alan Robinson, Gerald Sacks, and Dana Scott. The 2016 Symposium on Logical FoundationsofComputerScience(LFCS2016)tookplaceintheWyndhamDeerfield Beach Resort, Deerfield Beach, Florida, USA, during January 4–7. This volume con- tainstheextendedabstractsoftalksselectedbytheProgramCommitteeforpresentation atLFCS 2016. Thescopeofthesymposiumisbroadandincludesconstructivemathematicsandtype theory;homotopytypetheory;logic,automata,andautomaticstructures;computability andrandomness;logicalfoundationsofprogramming;logicalaspectsofcomputational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive theorem proving; logical methods in protocol and program verification; logical methods in program specification and extraction; domain theory logics; logical foundations of database theory; equational logic and term rewriting; lambda and combinatory calculi; categorical logic and topological semantics; linear logic;epistemicandtemporallogics;intelligentandmultiple-agentsystemlogics;logics of proof and justification; non-monotonic reasoning; logic in game theory and social software;logicofhybridsystems;distributedsystemlogics;mathematicalfuzzylogic; system designlogics; other logicsin computer science. We thank the authors and reviewers for their contributions. We acknowledge the support of the US National Science Foundation, Cornell University, the Graduate Center of the City University of New York, and Florida Atlantic University. October 2015 Anil Nerode Sergei Artemov Organization Steering Committee Stephen Cook University of Toronto, Canada Yuri Matiyasevich Steklov Mathematical Institute, St. Petersburg, Russia Anil Nerode Cornell University, USA - General Chair J. Alan Robinson Syracuse University, USA Gerald Sacks Harvard University, USA Dana Scott Carnegie-Mellon University, USA Dirk van Dalen Utrecht University, The Netherlands Program Committee Sergei Artemov CUNY Graduate Center, New York, USA - Chair Eugene Asarin Université Paris Diderot – Paris 7, France Steve Awodey Carnegie Mellon University, USA Matthias Baaz The Vienna University of Technology, Austria Alexandru Baltag University of Amsterdam, The Netherlands Lev Beklemishev Steklov Mathematical Institute, Moscow, Russia Andreas Blass University of Michigan, Ann Arbor, USA Samuel Buss University of California, San Diego, USA Robert Constable Cornell University, USA Thierry Coquand University of Gothenburg, Sweden Ruy de Queiroz The Federal University of Pernambuco, Recife, Brazil Nachum Dershowitz Tel Aviv University, Israel Melvin Fitting CUNY Graduate Center, New York, USA Sergey Goncharov Sobolev Institute of Mathematics, Novosibirsk, Russia Denis Hirschfeldt University of Chicago, USA Martin Hyland University of Cambridge, UK Rosalie Iemhoff Utrecht University, The Netherlands Hajime Ishihara Japan Advanced Institute of Science and Technology, Kanazawa, Japan Bakhadyr Khoussainov The University of Auckland, New Zealand Roman Kuznets The Vienna University of Technology, Austria Daniel Leivant Indiana University Bloomington, USA Robert Lubarsky Florida Atlantic University, Boca Raton, USA Victor Marek University of Kentucky, Lexington, USA Lawrence Moss Indiana University Bloomington, USA Anil Nerode Cornell University, USA VIII Organization Hiroakira Ono Japan Advanced Institute of Science and Technology, Kanazawa, Japan Ramaswamy The Institute of Mathematical Sciences, Chennai, India Ramanujam Michael Rathjen University of Leeds, UK Jeffrey Remmel University of California, San Diego, USA Helmut Schwichtenberg University of Munich, Germany Philip Scott University of Ottawa, Canada Alex Simpson University of Ljubljana, Slovenia Sonja Smets University of Amsterdam, The Netherlands Sebastiaan Terwijn Radboud University Nijmegen, The Netherlands Alasdair Urquhart University of Toronto, Canada Additional Reviewers Marc Bagnol Peter Lefanu Lumsdaine Pablo Barenbaum Bob Milnikel Can Baskent Joshua Moerman Gianluigi Bellin Edward Morehouse Marta Bilkova Rafael Peñaloza Spencer Breiner Andrew Polonsky Merlin Carl Damien Pous Thomas Colcombet Revantha Ramanayake Pilar Dellunde Arnaud Sangnier Eric Finster Katsuhiko Sano Jose Gil-Ferez Mirek Truszczynski Stefan Göller Benno van den Berg Makoto Kanazawa Michael Warren Ryo Kashima Pascal Weil Bjoern Lellmann Fan Yang Contents Modal Logics with Hard Diamond-Free Fragments . . . . . . . . . . . . . . . . . . . 1 Antonis Achilleos Pairing Traditional and Generic Common Knowledge . . . . . . . . . . . . . . . . . 14 Evangelia Antonakos On Aggregating Probabilistic Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Sergei Artemov Classical Logic with Mendler Induction: A Dual Calculus and Its Strong Normalization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Marco Devesas Campos and Marcelo Fiore Index Sets for Finite Normal Predicate Logic Programs with Function Symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Douglas Cenzer, Victor W. Marek, and Jeffrey B. Remmel Multiple Conclusion Rules in Logics with the Disjunction Property. . . . . . . . 76 Alex Citkin Multiple Conclusion Linear Logic: Cut Elimination and More . . . . . . . . . . . 90 Harley Eades III and Valeria de Paiva The Online Space Complexity of Probabilistic Languages . . . . . . . . . . . . . . 106 Nathanaël Fijalkow Type Theoretical Databases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Henrik Forssell, Håkon Robbestad Gylterud, and David I. Spivak Augmenting Subset Spaces to Cope with Multi-agent Knowledge. . . . . . . . . 130 Bernhard Heinemann On Lambek’s Restriction in the Presence of Exponential Modalities . . . . . . . 146 Max Kanovich, Stepan Kuznetsov, and Andre Scedrov A Quest for Algorithmically Random Infinite Structures, II . . . . . . . . . . . . . 159 Bakhadyr Khoussainov Probabilistic Justification Logic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 Ioannis Kokkinis, Zoran Ognjanović, and Thomas Studer Sequent Calculus for Intuitionistic Epistemic Logic IEL. . . . . . . . . . . . . . . . 187 Vladimir N. Krupski and Alexey Yatmanov X Contents Interpolation Method for Multicomponent Sequent Calculi. . . . . . . . . . . . . . 202 Roman Kuznets Adjoint Logic with a 2-Category of Modes . . . . . . . . . . . . . . . . . . . . . . . . 219 Daniel R. Licata and Michael Shulman Parallel Feedback Turing Computability. . . . . . . . . . . . . . . . . . . . . . . . . . . 236 Robert S. Lubarsky Compactness in the Theory of Continuous Automata. . . . . . . . . . . . . . . . . . 251 Scott Messick Measure Quantifier in Monadic Second Order Logic. . . . . . . . . . . . . . . . . . 267 Henryk Michalewski and Matteo Mio A Cut-Free Labelled Sequent Calculus for Dynamic Epistemic Logic . . . . . . 283 Shoshin Nomura, Hiroakira Ono, and Katsuhiko Sano The Urysohn Extension Theorem for Bishop Spaces . . . . . . . . . . . . . . . . . . 299 Iosif Petrakis AnArithmeticalInterpretationofVerificationandIntuitionisticKnowledge ... 317 Tudor Protopopescu Definability in First Order Theories of Graph Orderings. . . . . . . . . . . . . . . . 331 R. Ramanujam and R.S. Thinniyam The Complexity of Disjunction in Intuitionistic Logic . . . . . . . . . . . . . . . . . 349 R. Ramanujam, Vaishnavi Sundararajan, and S.P. Suresh Intransitive Temporal Multi-agent’s Logic, Knowledge and Uncertainty, Plausibility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364 Vladimir Rybakov Ogden Property for Linear Displacement Context-Free Grammars. . . . . . . . . 376 Alexey Sorokin Levy Labels and Recursive Types. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392 Rick Statman Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
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