Stell, JG, Schmidt, RA and Rydeheard, D (2016) A Bi-Intuitionistic Modal Logic: Foundations and Automation. Journal of Logical and Algebraic Methods in Programming, 85 (4). pp. 500-519. ISSN 2352-2208
Abstract
The paper introduces a bi-intuitionistic modal logic, called BISKT, with two adjoint pairs of tense operators. The semantics of BISKT is defined using Kripke models in which the set of worlds carries a pre-order relation as well as an accessibility relation, and the two relations are linked by a stability condition. A special case of these models arises from graphs in which the worlds are interpreted as nodes and edges of graphs, and formulae represent subgraphs. The pre-order is the incidence structure of the graphs. We present a comprehensive study of the logic, giving decidability, complexity and correspondence results. We also show the logic has the effective finite model property. We present a sound, complete and terminating tableau calculus for the logic and use the MetTeL system to explore implementations of different versions of the calculus. An experimental evaluation gave good results for satisfiable problems using predecessor blocking.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015 Published by Elsevier Inc.This article is available under the terms of the Creative Commons Attribution License (CC BY) (http://creativecommons.org/licenses/by/4.0/). |
Keywords: | intuitionistic logic; modal logic; tableau system; decidability; correspondence theorem |
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: | 24 Nov 2015 11:23 |
Last Modified: | 12 Apr 2017 05:24 |
Published Version: | http://dx.doi.org/10.1016/j.jlamp.2015.11.003 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jlamp.2015.11.003 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:91427 |