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On the Beth properties of some intuitionistic modal logics

On the Beth properties of some intuitionistic modal logics  Let L be one of the intuitionistic modal logics considered in [4]. As in the classical modal case (see [7]), we define two different forms of the Beth property for L, which are denoted by B 1 and B 2 ; in this paper we study the relation among B 1 ,B 2 and the interpolation properties C 1 and C 2 , introduced in [4]. It turns out that C 1 implies B 1 , but contrary to the boolean case, is not equivalent to B 1 . It is shown that B 2 and C 2 are independent, and moreover it comes out that, in contrast to classical case, there exists an extension of the intuitionistic modal logic of S 4 -type, that has not the property B 2 . Finally we give two algebraic properties, that characterize respectively B 1 and B 2 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

On the Beth properties of some intuitionistic modal logics

Luppi, C.
Archive for Mathematical Logic , Volume 41 (5) – Jul 1, 2002
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References (10)

Publisher
Springer Journals
Copyright
Copyright © 2002 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/s001530100120
Publisher site
See Article on Publisher Site

Abstract

 Let L be one of the intuitionistic modal logics considered in [4]. As in the classical modal case (see [7]), we define two different forms of the Beth property for L, which are denoted by B 1 and B 2 ; in this paper we study the relation among B 1 ,B 2 and the interpolation properties C 1 and C 2 , introduced in [4]. It turns out that C 1 implies B 1 , but contrary to the boolean case, is not equivalent to B 1 . It is shown that B 2 and C 2 are independent, and moreover it comes out that, in contrast to classical case, there exists an extension of the intuitionistic modal logic of S 4 -type, that has not the property B 2 . Finally we give two algebraic properties, that characterize respectively B 1 and B 2 .

Journal

Archive for Mathematical Logic – Springer Journals

Published: Jul 1, 2002

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