This paper tries to identify the basic problems encountered in handling equality in the semantic tableau framework, and to describe the state of the art in solving these problems. The two main paradigms for handling equality are compared: adding new tableau expansion rules and using E-unification algorithms.

This paper is concerned with the possibilities of refining and improving calculi generated in the tableau synthesis framework [10]. A general method in the tableau synthesis framework allows to reduce the branching factor of tableau rules and preserves completeness if a general rule refinement condition holds. In this paper we consider two approaches to satisfy this general rule refinement cond...

We give the first formal formalisation of global caching for abstract modal tableaux. Our global caching method is sound and applicable to different tableau calculi of (EXPTime-complete) modal or description logics to produce optimal (EXPTime) decision procedures.

We present a dynamic description logic D-ALCO@ for representing knowledge about dynamic application domains. D-ALCO@ is a combination of a typical action theory and the description logic ALCO@, in such a way that actions are treated as citizens of the logic. Actions of D-ALCO@ are explicitly specified with the help of formulas, and are then used in the construction of concepts and formulas. Bas...

In this paper we demonstrate how general purpose automated theorem proving techniques can be used to solve realistic model-based diagnosis problems. For this we modify a model generating tableau calculus such that a model of a correctly behaving device can be used to guide the search for minimal n-fault diagnoses. Our experiments show that our general approach is competitive with specialized di...

• Real-time systems must adhere to quantitative timing constraints

Tableau systems are very popular in AI for their simplicity and versatility. In recent papers we showed that tableau-based procedures are intrinsically ineecient, and proposed an alternative approach of building decision procedures on top of SAT decision procedure. We called this approach \SAT-based". In extensive empirical tests on the case study of modal K, a SAT-based procedure drastically o...

In this paper we demonstrate how general purpose automated theorem proving techniques can be used to solve realistic model-based diagnosis problems. For this we modify a model generating tableau calculus such that a model of a correctly behaving device can be used to guide the search for minimal diagnoses. Our experiments show that our general approach is competitive with specialized diagnosis ...

Given a positive integer n, and partitions λ and μ of n, let Kλμ denote the Kostka number, which is the number of semistandard Young tableaux of shape λ and weight μ. Let J(λ) denote the number of μ such that Kλμ = 1. By applying a result of Berenshtein and Zelevinskii, we obtain a formula for J(λ) in terms of restricted partition functions, which is recursive in the number of distinct part siz...