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COMPLETE INTUITIONISTIC TEMPORAL LOGICS FOR TOPOLOGICAL DYNAMICS

Part of: Proof theory and constructive mathematics General logic

Published online by Cambridge University Press:  04 February 2022

JOSEPH BOUDOU ,
MARTÍN DIÉGUEZ  and
DAVID FERNÁNDEZ-DUQUE Open the ORCID record for DAVID FERNÁNDEZ-DUQUE [Opens in a new window]
JOSEPH BOUDOU
Affiliation:
INSTITUT DE RECHERCHE EN INFORMATIQUE DE TOULOUSE TOULOUSE UNIVERSITYTOULOUSE, FRANCEE-mail:[email protected]
MARTÍN DIÉGUEZ
Affiliation:
LABORATOIRE D’ETUDE ET DE RECHERCHE EN INFORMATIQUE D’ANGERS UNIVERSITÉ D’ANGERSANGERS, FRANCEE-mail:[email protected]
DAVID FERNÁNDEZ-DUQUE
Affiliation:
DEPARTMENT OF MATHEMATICS GHENT UNIVERSITYGHENT, BELGIUME-mail:[email protected]
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Abstract

The language of linear temporal logic can be interpreted on the class of dynamic topological systems, giving rise to the intuitionistic temporal logic ${\sf ITL}^{\sf c}_{\Diamond \forall }$ , recently shown to be decidable by Fernández-Duque. In this article we axiomatize this logic, some fragments, and prove completeness for several familiar spaces.

Keywords

topologial semanticstemporal logicintuitionistic logic

MSC classification

Primary: 03B44: Temporal logic
Secondary: 03F55: Intuitionistic mathematics
Type
Article
Information
The Journal of Symbolic Logic , Volume 87 , Issue 3 , September 2022 , pp. 995 - 1022
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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