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|whose combination is not disjoint since they share 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 equational theories. In this paper, we present a new approach for combining decision proce- dures for the word problem in the non-disjoint case that applies to equa- tional 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: Automated Reasoning : Second International Joint Conference, IJCAR 2004, Cork, Ireland, July 4-8, 2004 : Proceedings / David Basin, Michael Rusinowitch. - Berlin : Springer, 2004. - ISBN 3540223452. - pp. 183-197 (( Intervento presentato al 2. convegno International Joint Conference on Automated Reasoning (IJCAR 04) tenutosi a Cork nel 2004.
A New Combination Procedure for the Word Problem that generalizes Fusion Decidability in Modal Logic
S. Ghilardi;
2004
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|whose combination is not disjoint since they share 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 equational theories. In this paper, we present a new approach for combining decision proce- dures for the word problem in the non-disjoint case that applies to equa- tional 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.
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