Ullrich Hustadt

Reasoning in Description Logics by a Reduction to Disjunctive Datalog

As applications of description logics proliferate, efficient reasoning with knowledge bases containing many assertions becomes ever more important. For such cases, we developed a novel reasoning algorithm that reduces a

Resolution-Based Methods for Modal Logics

\mathcal{SHIQ}

MSPASS: Modal Reasoning by Translation and First-Order Resolution

knowledge base to a disjunctive datalog program while preserving the set of ground consequences. Queries can then be answered in the resulting program while reusing existing and practically proven optimization techniques of deductive databases, such as join-order optimizations or magic sets. Moreover, we use our algorithm to derive precise data complexity bounds: we show that

Issues of Decidability for Description Logics in the Framework of Resolution

\mathcal{SHIQ}

A Decomposition Rule for Decision Procedures by Resolution-Based Calculi

is data complete for NP, and we identify an expressive fragment of

TRP++ 2.0: A Temporal Resolution Prover

\mathcal{SHIQ}

An empirical analysis of modal theorem provers

with polynomial data complexity.

4 Computational modal logic

In this paper we give an overview of resolution methods for extended propositional modal logics. We adopt the standard translation approach and consider different resolution refinements which provide decision procedures for the resulting clause sets. Our procedures are based on ordered resolution and selection-based resolution. The logics that we cover are multi-modal logics defined over relations closed under intersection, union, converse and possibly complementation.

Combinations of Modal Logics

mspass is an extension of the first-order theorem prover spass, which can be used as a modal logic theorem prover, a theorem prover for description logics and a theorem prover for the relational calculus.

Using Resolution for Testing Modal Satisfiability and Building Models

We describe two methods on the basis of which efficient resolution decision procedures can be developed for a range of description logics. The first method uses an ordering restriction and applies to the description logic ALB, which extends ALC with the top role, full role negation, role intersection, role disjunction, role converse, domain restriction, range restriction, and role hierarchies. The second method is based solely on a selection restriction and applies to reducts of ALB without the top role and role negation. The latter method can be viewed as a polynomial simulation of familiar tableaux-based decision procedures. It can also be employed for automated model generation.