Optimal Tableaux for Conditional Logics with Cautious Monotonicity

Lutz Schröder, Dirk Pattinson, Daniel Hausmann

In: Michael Wooldridge (Hrsg.). Proceedings of the 19th European Conference on Artificial Intelligence. European Conference on Artificial Intelligence (ECAI-2010) 19th August 16-20 Lisbon Portugal Frontiers in Artificial Intelligence and Applications IOS Press 8/2010.


Conditional logics capture default entailment in a modal framework in which non-monotonic implication becomes a first-class citizen, and in particular can be negated and nested. There is a wide range of axiomatizations of conditionals in the literature, from weak systems such as the basic conditional logic CK, which allows only for equivalent exchange of conditional antecedents, to strong systems such as Burgess' system S, which imposes the full Kraus-Lehmann-Magidor properties of preferential logic. While tableaux systems implementing the actual complexity of the logic at hand have recently been developed for several weak systems, strong systems including in particular disjunction elimination or cautious monotonicity have so far eluded such efforts; previous results for strong systems are limited to semantics-based decision procedures and completeness proofs for Hilbert-style axiomatizations. Here, we present tableaux systems of optimal complexity PSpace for several strong axiom systems in conditional logic, including system S; the arising decision procedure for system S is implemented in the generic reasoning tool CoLoSS.


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ECAI-453.pdf (pdf, 166 KB )

Deutsches Forschungszentrum für Künstliche Intelligenz
German Research Center for Artificial Intelligence