A new combination procedure for the word problem that generalizes fusion decidability results in modal logics

Authors:
Franz Baader;Silvio Ghilardi;Cesare Tinelli
Affiliations:
Institut für Theoretische Informatik, TU Dresden, Germany;Dipartimento di Scienze dell' Informazione, Università degli Studi di Milano, Italy;Department of Computer Science, The University of Iowa
Venue:
Information and Computation - Special issue: Combining logical systems
Year:
2006

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Abstract

Previous results for combining decision procedures for the word problem in the non-disjoint case do not apply to equational theories induced by modal logics-which are not disjoint for sharing the theory of Boolean algebras. Conversely, decidability results for the fusion of modal logics are strongly tailored towards the special theories at hand, and thus do not generalize to other types of equational theories. In this paper, we present a new approach for combining decision procedures for the word problem in the non-disjoint case that applies to equational theories induced by modal logics, but is not restricted to them. The known fusion decidability results for modal logics are instances of our approach. However, even for equational theories induced by modal logics our results are more general since they are not restricted to so-called normal modal logics.