Optimal Tableaux for Conditional Logics with Cautious Monotonicity

Conditional logics capture default entailment in a modal framework in which non-monotonic implication is 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-LehmannMagidor 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 system...

• Type: Conference
• Year: 2010
• Where: ECAI
• Authors: Lutz Schröder, Dirk Pattinson, Daniel Hausmann
• Keywords: Artificial Intelligence, Conditional Logic, Conditional Logic Ck, ECAI 2010, Strong Systems