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.

A New Combination Procedure for the Word Problem that generalizes Fusion Decidability in Modal Logic / F. Baader, S. Ghilardi, C. Tinelli. - In: INFORMATION AND COMPUTATION. - ISSN 0890-5401. - 204:10(2006), pp. 1413-1452.

A New Combination Procedure for the Word Problem that generalizes Fusion Decidability in Modal Logic

S. Ghilardi
Secondo
;
2006

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.
word problems, combination, fusion of modal logics
Settore M-FIL/02 - Logica e Filosofia della Scienza
2006
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/23396
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