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Modal Logic S5 Satisfiability in Answer Set Programming

Published online by Cambridge University Press:  05 November 2021

MARIO ALVIANO Open the ORCID record for MARIO ALVIANO [Opens in a new window] ,
SOTIRIS BATSAKIS  and
GEORGE BARYANNIS Open the ORCID record for GEORGE BARYANNIS [Opens in a new window]
MARIO ALVIANO
Affiliation:
University of Calabria, Italy (e-mail: alviano@mat.unical.it)
SOTIRIS BATSAKIS
Affiliation:
Technical University of Crete, Greece and University of Huddersfield, UK (e-mail: s.batsakis@hud.ac.uk)
GEORGE BARYANNIS
Affiliation:
School of Computing and Engineering, University of Huddersfield, UK (e-mail: g.bargiannis@hud.ac.uk)
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Abstract

Modal logic S5 has attracted significant attention and has led to several practical applications, owing to its simplified approach to dealing with nesting modal operators. Efficient implementations for evaluating satisfiability of S5 formulas commonly rely on Skolemisation to convert them into propositional logic formulas, essentially by introducing copies of propositional atoms for each set of interpretations (possible worlds). This approach is simple, but often results into large formulas that are too difficult to process, and therefore more parsimonious constructions are required. In this work, we propose to use Answer Set Programming for implementing such constructions, and in particular for identifying the propositional atoms that are relevant in every world by means of a reachability relation. The proposed encodings are designed to take advantage of other properties such as entailment relations of subformulas rooted by modal operators. An empirical assessment of the proposed encodings shows that the reachability relation is very effective and leads to comparable performance to a state-of-the-art S5 solver based on SAT, while entailment relations are possibly too expensive to reason about and may result in overhead.

Keywords

modal logicS5Answer Set ProgrammingKripke semantics
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 21 , Issue 5: 37th International Conference on Logic Programming Special Issue I , September 2021 , pp. 527 - 542
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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