Practical Reasoning for Very Expressive Description Logics

Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical. We present an algorithm that decides satisfiability of the DL ALC extended with transitive and inverse roles and functional restrictions with respect to general concept inclusion axioms and role hierarchies; early experiments indicate that this algorithm is well-suited for implementation. Additionally, we show that ALC extended with just transitive and inverse roles is still in PSPACE. We investigate the limits of decidability for this family of DLs, showing that relaxing the constraints placed on the kinds of roles used in number restrictions leads to the undecidability of all inference problems. Finally, we describe a number of optimisation techniques that are crucial in obtaining implementations of the decision procedures, which, despite the worst-case complexity of the problem, exhibit good performance with real-life problems

Reasoning with Individuals for the Description Logic SHIQ

While there has been a great deal of work on the development of reasoning algorithms for expressive description logics, in most cases only Tbox reasoning is considered. In this paper we present an algorithm for combined Tbox and Abox reasoning in the SHIQ description logic. This algorithm is of particular interest as it can be used to decide the problem of (database) conjunctive query containment w.r.t. a schema. Moreover, the realisation of an efficient implementation should be relatively straightforward as it can be based on an existing highly optimised implementation of the Tbox algorithm in the FaCT system.Comment: To appear at CADE-1

A Goal-Directed Decision Procedure for Hybrid PDL

We present the first goal-directed decision procedure for hybrid PDL. The procedure is based on a modular approach that scales from basic modal logic with eventualities to hybrid PDL. The approach is designed so that nominals and eventualities are treated orthogonally. To deal with the complex programs of PDL, the approach employs a novel disjunctive program decomposition. In arguing the correctness of our approach, we employ the novel notion of support generalizing the standard notion of Hintikka sets

An On-the-fly Tableau-based Decision Procedure for PDL-Satisfiability

We present a tableau-based algorithm for deciding satisfiability for propositional dynamic logic (PDL) which builds a finite rooted tree with ancestor loops and passes extra information from children to parents to separate good loops from bad loops during backtracking. It is easy to implement, with potential for parallelisation, because it constructs a pseudo-model ``on the fly'' by exploring each tableau branch independently. But its worst-case behaviour is 2EXPTIME rather than EXPTIME. A prototype implementation in the TWB (http://twb.rsise.anu.edu.au) is available.Comment: 26 pages, longer version of article in Methods for Modalities 2007; improved readability of proof