We present a sound and complete tableau calculus for a class BReg of extended regular grammar logics which contains useful epistemic logics for reasoning about agent beliefs. Our calculus is cut-free and has the analytic superformula property so it gives a decision procedure. Applying sound global caching to the calculus, we obtain the first optimal (EXPTime) tableau decision procedure for BReg...

A generic tableau algorithm, which is the basis for a general customizable method for producing test oracles from temporal logic speciications, is described in 8]. The algorithm accepts semantic rules as parameters for building the semantic tableau for a speciication. Parameterizing the tableau algorithm by semantic rules permits it to easily accommodate a variety of temporal operators and prov...

A logic for specifying probabilistic transition systems is presented. Our perspective is that of agents performing actions. A procedure for deciding whether sentences in this logic are valid is provided. One of the main contributions of the paper is the formulation of the decision procedure: a tableau system which appeals to solving systems of linear equations. The tableau rules eliminate propo...

This paper presents an abstract tableau calculus for the description logic SHOI. SHOI is the extension of ALC with singleton concepts, role inverse, transitive roles and role inclusion axioms. The presented tableau calculus is inspired by a recently introduced tableau synthesis framework. Termination is achieved by a variation of the unrestricted blocking mechanism that immediately rewrites ter...

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...

We show how to combine the standard tableau system for the basic description logic ALC with Wolper's tableau calculus for propositional temporal logic PTL in order to design a terminating sound and complete tableau-based satissability-checking algorithm for the temporal description logic PTL ALC of 19] interpreted in models with constant domains. We use the method of quasimodels 16, 14] to repr...

The existing pure tableau technique for satisfiability checking BCTL* [7] begins by constructing all possible colours. Traditional tableaux begin with a single root node, and only construct formulae that are derived from that root. These rooted tableaux provide much better performance on most real world formulae, as they only need to construct a fraction of the possible nodes. We present a root...

In this paper, we present a case study that illustrates the utility of pattern tableau discovery for data quality analysis. Given a usersupplied integrity constraint, such as a boolean predicate expected to be satisfied by every tuple, a functional dependency, or an inclusion dependency, a pattern tableau is a concise summary of subsets of the data that satisfy or fail the constraint. We descri...

The methodology of fibring is a successful framework for combining logical systems based on combining their semantics. In this paper, we extend the fibring approach to calculi for logical systems: we describe how to uniformly construct a sound and complete tableau calculus for the combined logic from calculi for the component logics. We consider semantic tableau calculi that satisfy certain con...