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Simulating polyadic modal logics by monadic ones

Published online by Cambridge University Press:  12 March 2014

George Goguadze ,
Carla Piazza  and
Yde Venema
George Goguadze
Affiliation:
Faculty of Computer Science, University of Saarland, IM Stadwald/36.1, Saarbrücken, Germany, E-mail: george@ags.uni-sb.de
Carla Piazza
Affiliation:
Dipartimento di Matematica e Infomatica, Università Degli Studi di Udine, Via Delle Scienze 206, I-33100 Udine, Italy Dipartimento di Informatica, Università ca' Foscari di Venezia, Via Torino 155, I-30172 Mestre, Italy, E-mail: piazza@dimi.uniud.it
Yde Venema
Affiliation:
Institute of Logic, Language and Computation, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands, E-mail: yde@science.uva.nl
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Abstract

We define an interpretation of modal languages with polyadic operators in modal languages that use monadic operators (diamonds) only. We also define a simulation operator which associates a logic Λsim in the diamond language with each logic Λ in the language with polyadic modal connectives. We prove that this simulation operator transfers several useful properties of modal logics, such as finite/recursive axiomatizability, frame completeness and the finite model property, canonicity and first-order definability.

Keywords

Modal logicpolyadic operatorsinterpretationsimulationtransfer results
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 68 , Issue 2 , June 2003 , pp. 419 - 462
Copyright
Copyright © Association for Symbolic Logic 2003

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