KT and S4 Satisfiability in a Constraint Logic Environment

Authors:
Lynn Stevenson;Katarina Britz;Tertia Hörne
Affiliations:
Meraka Institute, CSIR, South Africa and School of Computing, University of South Africa,;Meraka Institute, CSIR, South Africa and School of Computing, University of South Africa,;School of Computing, University of South Africa,
Venue:
PRICAI '08 Proceedings of the 10th Pacific Rim International Conference on Artificial Intelligence: Trends in Artificial Intelligence
Year:
2008

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Abstract

The modal satisfiability problem is solved either by using a specifically designed algorithm, or by translating the modal logic formula into an instance of a different class of problem, such as a first-order logic problem, a propositional satisfiability problem, or, more recently, a constraint satisfaction problem. In the latter approach, the modal formula is translated into layered propositional formulae. Each layer is translated into a constraint satisfaction problem which is solved using a constraint solver. We extend this approach to the modal logics KT and S4 and introduce a range of optimizations of the basic prototype. The results compare favorably with those of other solvers, and support the adoption of constraint programming as implementation platform for modal and other related satisfiability solvers.