Fibring Semantic Tableaux
- 228 Downloads
The methodology of fibring is a successful framework for combining logical systems based on combining their semantics. In this paper, we extend the fibring approach to calculi for logical systems: we describe how to uniformly construct a sound and complete tableau calculus for the combined logic from calculi for the component logics.
We consider semantic tableau calculi that satisfy certain conditions and are therefore known to be “well-behaved”—such that fibring is possible. The identification and formulation of conditions that are neither too weak nor too strong is a main contribution of this paper.
As an example, we fibre tableau calculi for first order predicate logic and for the modal logic K.
KeywordsModal Logic Transition Rule Logical System Predicate Logic Initial Label
Unable to display preview. Download preview PDF.
- 1.W. Ahrendt and B. Beckert. An improved δ-rule for ground first-order tableaux. Unpublished draft available from the authors, 1997.Google Scholar
- 2.B. Beckert and D. Gabbay. A general framework for fibring semantic tableaux. Unpublished draft available from the authors, 1997.Google Scholar
- 3.B. Beckert, R. Hähnle, and P. H. Schmitt. The even more liberalized δ-rule in free variable semantic tableaux. In Proceedings of KGC, LNCS 713. Springer, 1993.Google Scholar
- 4.M. D’Agostino and D. Gabbay. Fibred tableaux for multi-implication logics. In Proceedings of TABLEAUX, LNCS 1071. Springer, 1996.Google Scholar
- 5.M. D’Agostino, D. Gabbay, R. Hähnle, and J. Posegga, editors. Handbook of Tableau Methods. Kluwer, Dordrecht, 1998. To appear.Google Scholar
- 7.D. Gabbay. An overview of fibred semantics and the combination of logics. In Proceedings of FroCoS. Kluwer, Dordrecht, 1996.Google Scholar
- 8.D. Gabbay. Fibring Logic. Oxford University Press, 1998. Forthcoming.Google Scholar
- 9.D. Gabbay and G. Governatori. Fibred modal tableaux. Draft, 1997.Google Scholar