abstract. This paper explores the development of calculi using different proof methods for propositional dynamic modal logics. Dynamic modal logics are PDL-like extended modal logics which are closely related to description logics. We show how tableau systems, modal resolution systems and Rasiowa-Sikorski systems, which are dual tableau systems, can be developed and studied by using standard principles and methods of first-order theorem proving. We translate modal logic reasoning problems to first-order clausal form and then use a suitable refinement of resolution to construct and mimic derivations using the desired proof method. The inference rules of the calculus can then be read off from the clausal form used.

Abstract. This paper presents a tableau approach for deciding description logics outside the scope of OWL DL and current state-of-the-art tableau-based description logic systems. In particular, we de ne a sound and complete tableau calculus for the description logic ALBO and show that it provides a basis for decision procedures for this logic and numerous other description logics. ALBO is the extension of ALC with the Boolean role operators, inverse of roles, domain and range restriction operators and it includes full support for objects (nominals). ALBO is a very expressive description logic which is NExpTime complete and subsumes Boolean modal logic and the two-variable fragment of rstorder logic. An important novelty is the use of a versatile, unrestricted blocking rule as a replacement for standard loop checking mechanisms implemented in description logic systems. Our decision procedure is implemented in the MetTeL system. 1