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Exploring the Jungle of Intuitionistic Temporal Logics

Published online by Cambridge University Press:  22 April 2021

JOSEPH BOUDOU ,
MARTÍN DIÉGUEZ ,
DAVID FERNÁNDEZ-DUQUE Open the ORCID record for DAVID FERNÁNDEZ-DUQUE [Opens in a new window]  and
PHILIP KREMER
JOSEPH BOUDOU
Affiliation:
IRIT, Toulouse University, Toulouse, France (e-mail: joseph.boudou@matabio.fr)
MARTÍN DIÉGUEZ
Affiliation:
LERIA, University of Angers, Angers, France (e-mail: martin.dieguezlodeiro@univ-angers.fr)
DAVID FERNÁNDEZ-DUQUE
Affiliation:
Department of Mathematics WE16, Ghent University, Ghent, Belgium (e-mail: David.FernandezDuque@UGent.be)
PHILIP KREMER
Affiliation:
Department of Philosophy, University of Toronto, Toronto, Canada (e-mail: philip.kremer@utoronto.ca)
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Abstract

The importance of intuitionistic temporal logics in Computer Science and Artificial Intelligence has become increasingly clear in the last few years. From the proof-theory point of view, intuitionistic temporal logics have made it possible to extend functional programming languages with new features via type theory, while from the semantics perspective, several logics for reasoning about dynamical systems and several semantics for logic programming have their roots in this framework. We consider several axiomatic systems for intuitionistic linear temporal logic and show that each of these systems is sound for a class of structures based either on Kripke frames or on dynamic topological systems. We provide two distinct interpretations of “henceforth”, both of which are natural intuitionistic variants of the classical one. We completely establish the order relation between the semantically defined logics based on both interpretations of “henceforth” and, using our soundness results, show that the axiomatically defined logics enjoy the same order relations.

Keywords

TheoryKnowledge Representation and Nonmonotonic Reasoning
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 21 , Issue 4: TPLP Special Issue from the 16th European Conference on Logics in Artificial Intelligence (JELIA 2019) , July 2021 , pp. 459 - 492
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

*

David Fernández-Duque’s research is partially funded by the SNSF-FWO Lead Agency Grant 200021L 196176 (SNSF)/G0E2121N (FWO).

†

Philip Kremer’s research was supported by the Social Sciences and Humanities Research Council of Canada

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