Logical Foundations of Computer Science: International Symposium, LFCS 2013, San Diego, CA, USA, January 6-8, 2013. Proceedings

423 Pages·2013·4.32 MB·English

by  Luca Aceto

Lecture Notes in Computer Science 7734
CommencedPublicationin1973
FoundingandFormerSeriesEditors:
GerhardGoos,JurisHartmanis,andJanvanLeeuwen
EditorialBoard
DavidHutchison
LancasterUniversity,UK
TakeoKanade
CarnegieMellonUniversity,Pittsburgh,PA,USA
JosefKittler
UniversityofSurrey,Guildford,UK
JonM.Kleinberg
CornellUniversity,Ithaca,NY,USA
AlfredKobsa
UniversityofCalifornia,Irvine,CA,USA
FriedemannMattern
ETHZurich,Switzerland
JohnC.Mitchell
StanfordUniversity,CA,USA
MoniNaor
WeizmannInstituteofScience,Rehovot,Israel
OscarNierstrasz
UniversityofBern,Switzerland
C.PanduRangan
IndianInstituteofTechnology,Madras,India
BernhardSteffen
TUDortmundUniversity,Germany
MadhuSudan
MicrosoftResearch,Cambridge,MA,USA
DemetriTerzopoulos
UniversityofCalifornia,LosAngeles,CA,USA
DougTygar
UniversityofCalifornia,Berkeley,CA,USA
GerhardWeikum
MaxPlanckInstituteforInformatics,Saarbruecken,Germany
Sergei Artemov Anil Nerode (Eds.)
Logical Foundations
of Computer Science
International Symposium, LFCS 2013
San Diego, CA, USA, January 6-8, 2013
Proceedings
1 3
VolumeEditors
SergeiArtemov
CUNYGraduateCenter
ComputerScience
365FifthAvenue
NewYork,NY10016,USA
E-mail:[email protected]
AnilNerode
CornellUniversity
DepartmentofMathematics
545MalottHall
Ithaca,NY14853,USA
E-mail:[email protected]
ISSN0302-9743 e-ISSN1611-3349
ISBN978-3-642-35721-3 e-ISBN978-3-642-35722-0
DOI10.1007/978-3-642-35722-0
SpringerHeidelbergDordrechtLondonNewYork
LibraryofCongressControlNumber:2012954010
CRSubjectClassification(1998):F.4.1,F.4,F.3,I.2.3,I.2.2,F.2
LNCSSublibrary:SL1–TheoreticalComputerScienceandGeneralIssues
©Springer-VerlagBerlinHeidelberg2013
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
The Symposium on Logical Foundations of Computer Science series provides a
forum for the fast-growing body of work in the logical foundations of computer
science, e.g., those areas of fundamental theoretical logic related to computer
science.The LFCSseriesbeganwith “LogicatBotik,”Pereslavl-Zalessky,1989,
whichwasco-organizedbyAlbert R. Meyer(MIT) andMichaelTaitslin(Tver).
After that, organizationwas taken over by Anil Nerode.
Currently LFCS is governed by a Steering Committee consisting of Anil
Nerode (General Chair), Stephen Cook, Dirk van Dalen, Yuri Matiyasevich,
J. Alan Robinson, Gerald Sacks, and Dana Scott.
The2013SymposiumonLogicalFoundationsofComputerScience(LFCS2013)
tookplaceintheCatamaranResortHotel,SanDiego,California,duringJanuary
6–8.ThisvolumecontainstheextendedabstractsoftalksselectedbytheProgram
CommitteeforpresentationatLFCS2013.
The scope of the symposium is broad and includes constructive mathemat-
ics and type theory; logic, automata and automatic structures; computability
and randomness; logical foundations of programming;logical aspects of compu-
tational complexity; logic programming and constraints; automated deduction
and interactive theorem proving; logical methods in protocol and programveri-
fication;logicalmethodsinprogramspecificationandextraction;domaintheory
logic; logical foundations of database theory; equational logic and term rewrit-
ing;lambdaandcombinatorycalculi;categoricallogicandtopologicalsemantics;
linearlogic;epistemicandtemporallogics;intelligentandmultipleagentsystem
logics; logics of proof and justification; nonmonotonic reasoning; logic in game
theory and social software; logic of hybrid systems; distributed system logics;
mathematical fuzzy logic; system design logics; and other logics in computer
science.
We thank the authorsandreviewersfor theircontributions.We acknowledge
the support of the U.S. National Science Foundation, the Graduate Center of
the City University of New York, and the University of California, San Diego.
We are grateful to Yu Junhua for preparing this volume for Springer.
October 2012 Anil Nerode
Sergei Artemov
LFCS 2013 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-MellonUniversity, USA
Dirk van Dalen Utrecht University, The Netherlands
Program Committee
Sergei Artemov CUNYGraduateCenter,NewYork,USA-Chair
Steve Awodey Carnegie-MellonUniversity, Pittsburgh, USA
Alexandru Baltag University of Amsterdam, The Netherlands
Andreas Blass University of Michigan, Ann Arbor, USA
Samuel Buss University of California, San Diego, USA
Walter Dean University of Warwick, UK
Rod Downey Victoria University of Wellington, New Zealand
Ruy de Queiroz Universidade Federal de Pernambuco, Recife,
Brazil
Antonio Montalban University of Chicago, USA
Rosalie Iemhoff Utrecht University, The Netherlands
Bakhadyr Khoussainov The University of Auckland, New Zealand
Roman Kuznets University of Bern, Switzerland
Robert Lubarsky Florida Atlantic University, Boca Raton, USA
Victor Marek University of Kentucky, Lexington, USA
Franco Montagna Universita` Degli Studi di Siena, Italy
Lawrence Moss Indiana University Bloomington, USA
Anil Nerode Cornell University, Ithaca, USA
Mati Pentus Moscow State University, Russia
Michael Rathjen University of Leeds, UK
Jeffrey Remmel University of California, San Diego, USA
Bryan Renne University of Amsterdam, The Netherlands
Philip Scott University of Ottawa, Canada
Alex Simpson University of Edinburgh, UK
Sonja Smets University of Groningen, The Netherlands
Alasdair Urquhart University of Toronto, Canada
Michael Zakharyaschev Birkbeck College, University of London, UK
VIII LFCS 2013 Organization
Additional Reviewers
Laurent Bienvenu Nicola Gambino Glyn Morrill
Samuel Bucheli William Gasarch Andre Nies
Adam Chlipala Konstantinos Georgatos R. Ramanujam
Alexander Clark Giorgio Ghelli Jan Reimann
Chris Conidis Norihiro Kamide Cody Roux
Giovanni Curi Kohei Kishida Kristina Sojakova
Adam Day Hidenori Kurokawa Mariya Soskova
Eduardo Ferm´e Andrew Lewis Kazushige Terui
Melvin Fitting Dan Licata Sebastiaan Terwijn
Jo¨rg Flum Iris Loeb Jan van Eijck
Table of Contents
Compositional Reasoning for Multi-modal Logics..................... 1
Luca Aceto, Anna Ing´olfsd´ottir, Cristian Prisacariu, and Joshua Sack
Explicit Generic Common Knowledge............................... 16
Evangelia Antonakos
Beyond 2-Safety: Asymmetric Product Programs for Relational
ProgramVerification ............................................. 29
Gilles Barthe, Juan Manuel Crespo, and C´esar Kunz
Assignment Calculus: A Pure Imperative Language................... 44
Marc Bender and Jeffery Zucker
Multiplayer Cost Games with Simple Nash Equilibria................. 59
Thomas Brihaye, Julie De Pril, and Sven Schewe
Forward Chaining for Hybrid ASP ................................. 74
Alex Brik and Jeffrey B. Remmel
Effectivity Questions for Kleene’s Recursion Theorem................. 89
John Case, Sanjay Jain, and Frank Stephan
Sub-computable Bounded Pseudorandomness........................ 104
Douglas Cenzer and Jeffrey B. Remmel
Automated Support for the Investigation of Paraconsistent and Other
Logics .......................................................... 119
Agata Ciabattoni, Ori Lahav, Lara Spendier, and Anna Zamansky
A Modal BI Logic for Dynamic Resource Properties.................. 134
J.R. Courtault and D. Galmiche
Stuttering for Abstract Probabilistic Automata ...................... 149
Benoˆıt Delahaye, Kim G. Larsen, and Axel Legay
Call-by-Value Non-determinism in a Linear Logic Type Discipline...... 164
Alejandro D´ıaz-Caro, Giulio Manzonetto, and Michele Pagani
The Wadge Hierarchy of Petri Nets ω-Languages..................... 179
Jacques Duparc, Olivier Finkel, and Jean-Pierre Ressayre
Iterated Contraction Based on Indistinguishability ................... 194
Konstantinos Georgatos
X Table of Contents
A Note on Extensions: Admissible Rules via Semantics ............... 206
Jeroen Goudsmit
Subset Space vs Relational Semantics of Bimodal Logic: Bringing Out
the Difference ................................................... 219
Bernhard Heinemann
Quantified Differential Temporal Dynamic Logic for Verifying
Properties of Distributed Hybrid Systems ........................... 234
Ping Hou and Hao Zheng
Computational Hardness of Validity in Probability Logic.............. 252
Rutger Kuyper
Update as Evidence: Belief Expansion .............................. 266
Roman Kuznets and Thomas Studer
Separating the Fan Theorem and Its Weakenings..................... 280
Robert S. Lubarsky and Hannes Diener
The Logic of Uncertain Justifications ............................... 296
Bob Milnikel
Justifications, Awareness and Epistemic Dynamics ................... 307
Igor Sedla´r
Normal Forms for Multiple Context-Free Languages and Displacement
Lambek Grammars............................................... 319
Alexey Sorokin
Constructive Polychronous Systems ................................ 335
Jean-Pierre Talpin, Jens Brandt, Mike Gemu¨nde,
Klaus Schneider, and Sandeep Shukla
On Tolerance Analysis of Games with Belief Revision................. 350
C¸a˘gıl Ta¸sdemir
Temporalizing Modal Epistemic Logic .............................. 359
Ren-June Wang
Contextual Natural Deduction..................................... 372
Bruno Woltzenlogel Paleo
Conservatively Approximable Functions............................. 387
Sebastian Wyman
Self-referentiality in the Brouwer–Heyting–Kolmogorov Semantics
of Intuitionistic Logic............................................. 401
Junhua Yu
Author Index.................................................. 415
Compositional Reasoning for Multi-modal
(cid:2)
Logics
Luca Aceto1, Anna Ingo´lfsd´ottir1, Cristian Prisacariu2, and Joshua Sack3
1 ICE-TCS, School of Computer Science, ReykjavikUniversity,Reykjavik,Iceland
luca,[email protected]
2 Dept.of Informatics – Univ.of Oslo, P.O.Box 1080 Blindern, 0316 Oslo, Norway
[email protected]
3 Instituteof Logic, Language, and Computation – University of Amsterdam
[email protected]
Abstract. Weprovidedecompositionandquotientingresultsformulti-
modal logic with respect to a composition operator, traditionally used
for epistemic models, due to van Eijck et al. (Journal of Applied Non-
Classical Logics 21(3–4):397–425, 2011), that involves sets of atomic
propositionsandvaluationfunctionsfromKripkemodels.Whilethecom-
position operator was originally defined only for epistemic S5n models,
our results apply to the composition of any pair of Kripke models. In
particular, our quotienting result extends a specific result in the above
mentioned paper by van Eijck et al. for the composition of epistemic
models with disjoint sets of atomic propositions to compositions of any
twoKripkemodelsregardlessoftheirsetsofatomicpropositions.Wealso
explorethecomplexityoftheformulasweconstructinourdecomposition
result.
1 Introduction
Decompositionandquotientingtechniques[2,9,15,23]havebeenusedforawide
varietyoflogics,suchasHennessy-Milnerlogic[10]ormodalμ-calculus[13],and
much attention has been given to extending and optimizing these [2,14]. Com-
positional reasoning normally involves a parallel-like composition operator over
themodelsofthelogicinquestion.Inthecasesjustcited,themaincomposition
operatorofinterestisusuallysomeformofparallelcompositionfromprocessal-
gebras[4,11,18,19].Inthesecases,oneobserveswhatiscalledthestateexplosion
problem; whenasystemisbuiltupbycomposingseveralprocesses/components,
its state space grows exponentially with the number of components. This is the
main drawback of doing model checking of such systems (even for algorithms
that are linear in the size of the model and the formula). Compositional reason-
ing has proved useful in tackling the state space explosion problem in several
applications.
(cid:2) LucaAcetoandAnnaIngo´lfsdo´ttirwerepartiallysupportedbytheproject‘Processes
and Modal Logics’ (project nr. 100048021) of the Icelandic Research Fund. Joshua
SackwaspartiallysupportedbytheVIDIresearchprogrammenumber639.072.904,
which is financed bythe NetherlandsOrganisation for ScientificResearch.
S.ArtemovandA.Nerode(Eds.): LFCS2013,LNCS7734,pp. 1–15,2013.
(cid:2)c Springer-VerlagBerlinHeidelberg2013
2 L. Aceto et al.
Intuitively, considering some form of composition of models M ||M and a
1 2
formula ϕ to check on this composed model, the technique of compositional
reasoning provides an alternative to checking M ||M |=ϕ, by instead checking
1 2
two potentially simpler problems: M |= φ and M |= φ . When the two new
1 1 2 2
formulas are not much larger than the original, this method can be very useful.
There are also heuristic techniques that aim at keeping the new formulas small
[2].
The aim of this paper is to develop a theory of compositionality and quo-
tienting for multi-modal logic with respect to a composition operator that has
been recently introduced in [22] for S5n (epistemic) models. This composition
behaves similarly to the well-known synchronous composition; however, while
the set of states in a parallel composition is generally the Cartesian product,
the composition between epistemic models introduced in [22] eliminates states
whose atomic valuations on the components are not, so to speak, compatible.
Arguably,the compositionof[22] is the mostnaturalthatone wouldwanton
S5n models. This composition behaves similarly to the well-known synchronous
compositionoflabelledtransitionsystems.Itiseasytoseethatthestandardasyn-
chronouscompositionthatisnormallystudiedinprocessalgebrasandconcurrency
theorydoesnotpreserveS5nmodels(seee.g.[1]),whereasthesynchronouscompo-
sitiondoes.Anotherobservationisthatunlikeothertypesofframes(i.e.,transition
systemswithoutavaluationofpropositionalconstants),theS5nframesaretrivial
withoutpropositionalconstantsandavaluationattachedtotheirstates(i.e.,they
arebisimilarto asinglereflexivepoint). Therefore,acompositionofS5n models
shouldtakevaluationsandpropositionalconstantsintoconsideration.
Although originally defined for S5n models, the composition of [22] is also
well-defined onother classesof models. For example, the class of Kripke models
isclosedunderit.Anexampleofaclassofmodelsthatisnotclosedwithrespect
to the composition of [22] is that of KD45 models, often used to model belief.
(See Remark 2.6.)
The involvementofvaluationsandpropositionalconstantsincompositionsin
generalhasreceivedrelativelylittleattention,anddistinguishestheresultsinthis
paperfrommainstreamcompositionresults[6,9,15,23].Thereare,however,other
compositions that use valuations and propositionalconstants, andthere is work
thatemploysrelatedtechniques.Onecompositionthatusesvaluationsisthecon-
currentprogramof[16],wheretwonon-epistemicmodelsarecomposedinsuchaway
thatthestatesofthecompositionmaydisagreewiththecomponentsonthevalu-
ation.Thecompositionweemployinthispapereliminatesanystatewherethere
maybesuchdisagreementbetweenacompositestateanditscomponents.Another
relatedcompositionistheupdateproductfrom[5],thoughthatcompositionisnot
betweentwoKripkemodels,butbetweenaKripke(orepistemic)modelandanac-
tionmodel,asyntacticstructurethatdiffersfromaKripkemodelinthattheval-
uationisreplacedbyafunctionassigningaformulatoeachpointofthemodel.A
compositionresultinthesettingoftransitionsystemsthatalsoinvolvespruning
theglobalstatespaceisthatof[20];howeverthisresultdoesnotinvolvelogicaswe
do.Furthermore,giventhatmodalformulascharacterizefinitetransitionsystems