Publication
Generic Modal Cut Elimination Applied to Conditional Logics
Dirk Pattinson; Lutz Schröder
In: Martin Giese; Arild Waaler (Hrsg.). Automated Reasoning with Analytic Tableaux and Related Methods. International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX-09), July 6-10, Oslo, Norway, Lecture Notes in Computer Science, Vol. 5607, Springer, 2009.
Abstract
We develop a general criterion for cut elimination in sequent
calculi for propositional modal logics, which rests on absorption of
cut, contraction, weakening and inversion by the purely
modal part of the rule system. Our criterion applies also
to a wide variety of logics outside the realm of normal modal
logic. We give extensive example instantiations of our framework to
various conditional logics. For these, we obtain fully internalised
calculi
which are substantially simpler than those known in the literature,
along with
leaner proofs of cut elimination and complexity.
In one case, conditional logic with modus ponens and conditional
excluded middle,
cut elimination and complexity are explicitly stated as open in the
literature.