Schmidt, RA, Stell, JG and Rydeheard, DE (2014) Axiomatic and tableau-based reasoning for Kt(H,R). In: Goré, R, Kooi, B and Kurucz, A, (eds.) Advances in Modal Logic. Advances In Modal Logic, 05-08 Aug 2014, Groningen, Netherlands. College Publications , 478 - 497. ISBN 978-1-84890-151-3
Abstract
We introduce a tense logic, called Kt(H, R), arising from logics for spatial reasoning. Kt(H, R) is a multi-modal logic with two modalities and their converses defined with respect to a pre-order and a relation stable over this pre-order. We show Kt(H,R) is decidable, it has the effective finite model property and reasoning in Kt(H,R) is PSPACE-complete. Two complete Hilbert-style axiomatisations are given. The main focus of the paper is tableau-based reasoning. Our aim is to gain insight into the numerous possibilities of defining tableau calculi and their properties. We present several labelled tableau calculi for Kt(H,R) in which the theory rules range from accommodating correspondence properties closely, to accommodating Hilbert axioms closely. The calculi provide the basis for decision procedures that have been imple- mented and tested on modal and intuitionistic problems.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © 2014, Author(s). This is an author produced version of a paper published in Advances in Modal Logic. Uploaded with permission from the publisher. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) > Artificial Intelligence & Biological Systems (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 22 Jan 2015 10:47 |
Last Modified: | 19 Dec 2022 13:30 |
Published Version: | http://www.aiml.net/volumes/volume10/ |
Status: | Published |
Publisher: | College Publications |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:82608 |