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KRIPKE COMPLETENESS OF STRICTLY POSITIVE MODAL LOGICS OVER MEET-SEMILATTICES WITH OPERATORS

Published online by Cambridge University Press:  03 April 2019

STANISLAV KIKOT ,
AGI KURUCZ ,
YOSHIHITO TANAKA ,
FRANK WOLTER  and
MICHAEL ZAKHARYASCHEV
STANISLAV KIKOT
Affiliation:
DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF OXFORD WOLFSON BUILDING, PARKS ROAD, OXFORD OX1 3QD, UK and DEPARTMENT OF COMPUTER SCIENCE AND INFORMATION SYSTEMS BIRKBECK, UNIVERSITY OF LONDON MALET STREET, LONDON WC1E 7HX, UK and INSTITUTE FOR INFORMATION TRANSMISSION PROBLEMS 19 BOLSHOY KARETNY PEREULOK, MOSCOW 127051, RUSSIA and MOSCOW INSTITUTE OF PHYSICS AND TECHNOLOGY 9 INSTITUTSKIY PEREULOK, DOLGOPRUDNY, MOSCOW REGION141701, RUSSIAE-mail: [email protected]
AGI KURUCZ
Affiliation:
DEPARTMENT OF INFORMATICS KING’S COLLEGE LONDON STRAND CAMPUS, BUSH HOUSE, 30 ALDWYCH, LONDON WC2B 4BG, UK E-mail: [email protected]
YOSHIHITO TANAKA
Affiliation:
FACULTY OF ECONOMICS KYUSHU SANGYO UNIVERSITY 2-3-1 MATSUKADAI, HIGASHI-KU, FUKUOKA813-8503, JAPANE-mail: [email protected]
FRANK WOLTER
Affiliation:
DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF LIVERPOOL ASHTON BUILDING, ASHTON STREET, LIVERPOOL L69 3BX, UK E-mail: [email protected]
MICHAEL ZAKHARYASCHEV
Affiliation:
DEPARTMENT OF COMPUTER SCIENCE AND INFORMATION SYSTEMS BIRKBECK, UNIVERSITY OF LONDON MALET STREET, LONDON WC1E 7HX, UK E-mail: [email protected]
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Abstract

Our concern is the completeness problem for spi-logics, that is, sets of implications between strictly positive formulas built from propositional variables, conjunction and modal diamond operators. Originated in logic, algebra and computer science, spi-logics have two natural semantics: meet-semilattices with monotone operators providing Birkhoff-style calculi and first-order relational structures (aka Kripke frames) often used as the intended structures in applications. Here we lay foundations for a completeness theory that aims to answer the question whether the two semantics define the same consequence relations for a given spi-logic.

Keywords

03B4503G25semilattices with operatorsmodal logicKripke completeness
Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 2 , June 2019 , pp. 533 - 588
Copyright
Copyright © The Association for Symbolic Logic 2019 

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