Table Of ContentOutstanding Contributions to Logic 15
Sergei Odintsov Editor
Larisa Maksimova
on Implication,
Interpolation, and
Definability
Outstanding Contributions to Logic
Volume 15
Editor-in-chief
Sven Ove Hansson, Royal Institute of Technology, Stockholm, Sweden
Editorial Board
Marcus Kracht, Universität Bielefeld
Lawrence Moss, Indiana University
Sonja Smets, Universiteit van Amsterdam
Heinrich Wansing, Ruhr-Universität Bochum
More information about this series at http://www.springer.com/series/10033
Sergei Odintsov
Editor
Larisa Maksimova
on Implication, Interpolation,
fi
and De nability
123
Editor
SergeiOdintsov
SobolevInstitute ofMathematics
Novosibirsk
Russia
ISSN 2211-2758 ISSN 2211-2766 (electronic)
Outstanding Contributions to Logic
ISBN978-3-319-69916-5 ISBN978-3-319-69917-2 (eBook)
https://doi.org/10.1007/978-3-319-69917-2
LibraryofCongressControlNumber:2017956323
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Preface
Several scientific affairs in 2012 and 2013 were dedicated to Prof. Larisa
Maksimova who celebrated her anniversary in November 2013. Among them are
the special session on the conference Advances in Modal Logic 2012 (22–25
August 2012, Copenhagen, Denmark) and the conference Mal’tsev Meeting 2013
(12–15 August 2013, Novosibirsk, Russia). Mal’tsev Meeting is an annual con-
ferenceofNovosibirkalgebraicandlogicalschool,anoutstandingrepresentativeof
whichisLarisaMaksimova.ProfessorHeinrichWansing,amemberoftheeditorial
board of the series Outstanding Contributions to Logic, participated Mal’tsev
Meeting2013,wherehepresentedaninvitedtalk.Theideatopublishavolumeof
thisseriesdevotedtoLarisaMaksimovabelongsnamelytoHeinrichWansing.The
field of interests of Larisa Maksimova can be characterized as applied algebraic
logic. She intensively used in her investigations various algebraic methods;
establishedalgebraicanalogsofnumerouslogicalpropertiessuchasdifferentkinds
of interpolation and definability properties, disjunction property; and carefully
studied the relationship between relational and algebraic semantics for various
kinds of logics. However, her investigations were aimed all the time at obtaining
concrete logical results. In many cases, it was an exhaustive description of logics
with one or another remarkable property ina big class of logics. The present book
collects original contributions written by colleagues, collaborators, and former Ph.
D.studentsofMaksimovathatarerelatedtooneoranothertopicofherresearch.It
contains a “historical” part (Chaps. 1–3) including a scientific autobiography of
ProfessorMaksimova,asurveyofherworksonrelevantlogics,andasurveyofher
first famous results on classes of superintuitionistic logics and of normal modal
logics extending S4. The rest of the book constitutes research papers as well as a
few surveys.
Novosibirsk, Russia Sergei Odintsov
September 2017
v
Acknowledgements
I would like to thank Prof. Maksimova for her kind attention to my work on this
book. As a customer of the seminar “Non-standard logics” in Novosibirsk State
University,IamgratefultoProf.Maksimovaforcreatingandsupportingthisform
of intellectual communication, which caused, in particular, the change of my field
ofscientificinterestsfromtheclassicalcomputabilitytheorytonon-classicallogics.
I would like to thank all authors of this volume for valuable contributions and all
anonymous referees for useful reviews. My special thanks to Veta Yun for com-
prisingthelistofpublicationsbyLarisaMaksimovaandtoSergeiDrobyshevichfor
hisessentialhelpintheworkonthecamera-readycopyonthebook.Finally,Iam
grateful to Heinrich Wansing for the suggestion to edit this volume.
vii
Contents
1 Maksimova,RelevanceandtheStudyofLatticesofNon-classical
Logics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Sergei Odintsov
2 A Short Scientific Autobiography . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Larisa Maksimova
3 Larisa Maksimova’s Early Contributions to Relevance Logic. . . . . 33
Katalin Bimbó and J. Michael Dunn
4 A Note on Strictly Positive Logics and Word Rewriting
Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Lev Beklemishev
5 Characteristic Formulas Over Intermediate Logics. . . . . . . . . . . . . 71
Alex Citkin
6 A Generalization of Maksimova’s Criterion for the Disjunction
Property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Alex Citkin
7 Rasiowa–Sikorski Sets and Forcing. . . . . . . . . . . . . . . . . . . . . . . . . 117
Janusz Czelakowski
8 l-Levels of Interpolation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Giovanna D’Agostino
9 Decidability of Some Interpolation Properties for Weakly
Transitive Modal Logics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
Anastasia Karpenko
10 Lattice NExtS4 from the Embedding Theorem Viewpoint . . . . . . . 185
Alexei Muravitsky
ix
x Contents
11 LinearTemporalLogicwithNon-transitiveTime,Algorithmsfor
Decidability and Verification of Admissibility . . . . . . . . . . . . . . . . . 219
Vladimir V. Rybakov
12 Segerberg Squares of Modal Logics and Theories of Relation
Algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
Valentin Shehtman
13 On Algebraisation of Superintuitionistic Predicate Logics. . . . . . . . 297
Dmitry Tishkovsky
14 Dummett Logic, Irreflexive Modality and Novikov
Completeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
Alexander Yashin
15 On Linear Logic of Knowledge and Time. . . . . . . . . . . . . . . . . . . . 339
Veta F. Yun
Appendix A: Larisa Maksimova. List of Publications .. .... ..... .... 351
Index .... .... .... .... .... ..... .... .... .... .... .... ..... .... 367
Contributors
Lev Beklemishev Steklov Mathematical Institute, RAS, Moscow, Russia;
Moscow M.V. Lomonosov State University, Moscow, Russia; National Research
University Higher School of Economics, Moscow, Russia
KatalinBimbó DepartmentofPhilosophy,UniversityofAlberta,Edmonton,AB,
Canada
Alex Citkin Metropolitan Telecommunications, Warren, NJ, USA; Metropolitan
Telecommunications, New York, NY, USA
Janusz Czelakowski Insitute of Mathematics and Informatics, Opole University,
Opole, Poland
GiovannaD’Agostino DepartmentofMathematicsandComputerScience,Udine,
Italy
J. Michael Dunn School of Informatics, Computing, and Engineering and
Department of Philosophy, Indiana University, Bloomington, IN, USA
Anastasia Karpenko Novosibirsk State University, Novosibirsk, Russia
Larisa Maksimova Sobolev Institute of Mathematics, Novosibirsk, Russia
Alexei Muravitsky Louisiana Scholars’ College, Northwestern State University,
Natchitoches, LA, USA
Sergei Odintsov Sobolev Institute of Mathematics, Novosibirsk, Russia
VladimirV.Rybakov Institute ofMathematicsandInformatics, Siberian Federal
University Krasnoyarsk, and (part time) Institute of Informatics Systems (Siberian
Division RAS), Krasnoyarsk, Russia
ValentinShehtman KharkevichInstituteforInformationTransmissionProblems,
RAS,Moscow,Russia;NationalResearchUniversityHigherSchoolofEconomics,
Moscow, Russia; Moscow State University, Moscow, Russia
xi
