The aim of this paper is to construct a tableau decision algorithm for the modal description logic KALC with constant domains. More precisely, we present a tableau procedure that is capable of deciding, given an ALC-formula ' with extra modal operators (which are applied only to concepts and TBox axioms, but not to roles), whether ' is satisfiable in a model with constant domains and arbitrary accessibility relations. Tableau-based

The recent emergence of heavily-optimized modal decision procedures has highlighted the key role of empirical testing in this domain. Unfortunately, the introduction of extensive empirical tests for modal logics is recent, and so far none of the proposed test generators is very satisfactory. To cope with this fact, we present a new random generation method that provides benefits over previous methods for generating empirical tests. It fixes and much generalizes one of the best-known methods, the random CNF test, allowing for generating a much wider variety of problems, covering in principle the whole input space. Our new method produces much more suitable test sets for the current generation of modal decision procedures. We analyze the features of the new method by means of an extensive collection of empirical tests.

We provide an empirical evaluation of one of the main test sets that is currently in use for testing modal satisfiability solvers, viz. the random modal QBF test set. We first discuss some of the background underlying the test set, and then evaluate the test set using criteria set forth by Horrocks, Patel-Schneider, and Sebastiani. We also present some guidelines for the use of the test set.

this paper, we generalise the principles from tableau algorithms for modal logics in order to develop a tableau algorithm for CGF. To the best of our knowledge, this is the rst algorithm for CGF that can be used as the basis for an ecient implementation

. Previous methods for generating random modal formulae (for the multi-modal logic K (m) ) result either in flawed test sets or formulae that are too hard for current modal decision procedures and, also, unnatural. We present here a new system and generation methodology which results in unflawed test sets and more-natural formulae that are better suited for current decision procedures. Most empirical testing of decision procedures for propositional modal logics, usually for the multi-modal logic K (m) , employs randomly generated formulae. This style of testing was initially proposed by Giunchiglia et al [3] and later improved by them and also by Hustadt and Schmidt [6, 1]. Other kinds of randomly generated formulae have been proposed by Massacci [7]. Randomly generated formulae have been used with all the recent, highly optimised modal decision procedures, including DLP [8], FaCT [4], KSatC [1], *SAT [2], and TA [6], and have been used in several comparisons of these systems [7]...

We explore to what extent and how e#ciently constraint programming can be used in the context of automated reasoning for modal logics. We encode modal satisfiability problems as constraint satisfaction problems with non-boolean domains, together with suitable constraints.

The recent emergence of heavily-optimized modal decision procedures has highlighted the key role of empirical testing in this domain. Unfortunately, the introduction of extensive empirical tests for modal logics is recent, and so far none of the proposed test generators is very satisfactory. To cope with this fact, we present a new random generation method that provides benefits over previous methods for generating empirical tests. It fixes and much generalizes one of the best-known methods, the random CNF2m test, allowing for generating a much wider variety of problems, covering in principle the whole input space. Our new method produces much more suitable test sets for the current generation of modal decision procedures. We analyze the features of the new method by means of an extensive collection of empirical tests.

Efficient decision procedures have been conceived in different communities for a very heterogeneous collection of expressive decidable theories. However, despite in the last years we have witnessed an impressive advance in the efficiency of SAT procedures, techniques for efficiently integrating boolean reasoning and theory-specific decision procedures have been deeply investigated only recently, producing impressive performance improvements when applied. The goal of this paper is to analyze, classify and represent within a uniform framework the most effective techniques which have been proposed in various communities in order to maximize the efficiency of boolean reasoning within decision procedures.

Abstract. In the last two decades we have witnessed an impressive advance in the efficiency of propositional satisfiability techniques (SAT), which has brought large and previously-intractable problems at the reach of state-of-the-art SAT solvers. Most of this success is motivated by the impressive level of efficiency reached by current implementations of the DPLL procedure. Plain propositional logic, however, is not the only application domain for DPLL. In fact, DPLL has also been successfully used as a boolean-reasoning kernel for automated reasoning tools in much more expressive logics. In this talk I overview a 12-year experience on integrating DPLL with logic-specific decision procedures in various domains. In particular, I present and discuss three main achievements which have been obtained in this context: the DPLL-based procedures for modal and description logics, the lazy approach to Satisfiability Modulo Theories, and Delayed Theory Combination. 1

We present a novel encoding of modal satisfiability problems as Constraint Satisfaction Problems. We allow the domains of the resulting constraints to contain other values than just the Boolean 0 or 1, and add various constraints to reason about these values. This modelling is pivotal to speeding up the performance of our constraint-based procedure for modal satisfiability in Constraint Logic Programming (CLP). Our encoding results in a correct solver that attempts to minimize the size of the tree model that it is implicitly trying to generate. An important advantage of our modelling is that we do not need to change the underlying CSP algorithms, and can use them almost as “black boxes”.