Abstract not found

Both OWL-DL and function-free Horn rules are decidable fragments of first-order logic with interesting, yet orthogonal expressive power. A combination of OWL-DL and rules is desirable for the Semantic Web; however, it might easily lead to the undecidability of interesting reasoning problems. Here, we present a decidable such combination where rules are required to be DL-safe: each variable in the rule is required to occur in a non-DL-atom in the rule body. We discuss the expressive power of such a combination and present an algorithm for query answering in the related logic SHIQ extended with DL-safe rules, based on a reduction to disjunctive programs.

As applications of description logics proliferate, efficient reasoning with large ABoxes (sets of individuals with descriptions) becomes ever more important. Motivated by the prospects of reusing optimization techniques from deductive databases, in this paper, we present a novel approach to checking consistency of ABoxes, instance checking and query answering, w.r.t. ontologies formulated using a slight restriction of the description logic SHIQ. Our approach proceeds in three steps: (i) the ontology is translated into firstorder clauses, (ii) TBox and RBox clauses are saturated using a resolution-based decision procedure, and (iii) the saturated set of clauses is translated into a disjunctive datalog program. Thus, query answering can be performed using the resulting program, while applying all existing optimization techniques, such as join-order optimizations or magic sets. Equally important, the resolution-based decision procedure we present is for unary coding of numbers worst-case optimal, i.e. it runs in EXPTIME.

UML is the de-facto standard formalism for software design and analysis. To support the design of large-scale industrial applications, sophisticated CASE tools are available on the market, that provide a user-friendly environment for editing, storing, and accessing multiple UML diagrams. It would be highly desirable to equip such CASE tools with automated reasoning capabilities in order to detect relevant formal properties of UML diagrams, such as inconsistencies or redundancies. With regard to this issue, we consider UML class diagrams, which are one of the most important components of UML, and we address the problem of reasoning on such diagrams. We resort to several results developed in the eld of Description Logics (DLs), a family of logics that admit decidable reasoning procedures.

The Davis-Putnam-Logemann-Loveland procedure (DPLL) was introduced in the early

Although the OWL Web Ontology Language adds considerable expressive power to the Semantic Web it does have expressive limitations, particularly with respect to what can be said about properties. We present SWRL (the Semantic Web Rules Language), a Horn clause rules extension to OWL that overcomes many of these limitations. SWRL extends OWL in a syntactically and semantically coherent manner: the basic syntax for SWRL rules is an extension of the abstract syntax for OWL DL and OWL Lite; SWRL rules are given formal meaning via an extension of the OWL DL model-theoretic semantics; SWRL rules are given an XML syntax based on the OWL XML presentation syntax; and a mapping from SWRL rules to RDF graphs is given based on the OWL RDF/XML exchange syntax. We discuss the expressive power of SWRL, showing that the ontology consistency problem is undecidable, provide several examples of SWRL usage, and discuss a prototype implementation of reasoning support for SWRL. 1

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.

We consider a new extension of the Skolem class for first-order logic and prove its decidability by resolution techniques. We then extend this class including the built-in equational theory of exclusive or. Again, we prove the decidability of the class by resolution techniques.

Abstract not found

This dissertation describes an approach for automatically verifying data structures, focusing on techniques for automatically proving formulas that arise in such verification. I have implemented this approach with my colleagues in a verification system called Jahob. Jahob verifies properties of Java programs with dynamically allocated data structures. Developers write Jahob specifications in classical higher-order logic (HOL); Jahob reduces the verification problem to deciding the validity of HOL formulas. I present a new method for proving HOL formulas by combining automated reasoning techniques. My method consists of 1) splitting formulas into individual HOL conjuncts, 2) soundly approximating each HOL conjunct with a formula in a more tractable fragment and 3) proving the resulting approximation using a decision procedure or a theorem prover. I present three concrete logics; for each logic I show how to use it to approximate HOL formulas, and how to decide the validity of formulas in this logic. First, I present an approximation of HOL based on a translation to first-order logic, which enables the use of existing resolution-based theorem provers. Second, I present an approximation of HOL based on field constraint analysis, a new technique that enables