Equality-friendly well-founded semantics and applications to description logics

We tackle the problem of defining a well-founded semantics (WFS) for Datalog rules with existentially quantified variables in their heads and nega- tions in their bodies. In particular, we provide a WFS for the recent Datalog± family of ontology languages, which covers several important description logics (DLs). To do so, we generalize Datalog± by non-stratified nonmonotonic nega- tion in rule bodies, and we define a WFS for this generalization via guarded fixed point logic. We refer to this approach as equality-friendly WFS, since it has the advantage that it does not make the unique name assumption (UNA); this brings it close to OWL and its profiles as well as typical DLs, which also do not make the UNA. We prove that for guarded Datalog± with negation under the equality- friendly WFS, conjunctive query answering is decidable, and we provide precise complexity results for this problem. From these results, we obtain precise defi- nitions of the standard WFS extensions of EL and of members of the DL-Lite family, as well as corresponding complexity results for query answering

Reasoning with Forest Logic Programs and f-hybrid Knowledge Bases

Open Answer Set Programming (OASP) is an undecidable framework for integrating ontologies and rules. Although several decidable fragments of OASP have been identified, few reasoning procedures exist. In this article, we provide a sound, complete, and terminating algorithm for satisfiability checking w.r.t. Forest Logic Programs (FoLPs), a fragment of OASP where rules have a tree shape and allow for inequality atoms and constants. The algorithm establishes a decidability result for FoLPs. Although believed to be decidable, so far only the decidability for two small subsets of FoLPs, local FoLPs and acyclic FoLPs, has been shown. We further introduce f-hybrid knowledge bases, a hybrid framework where \SHOQ{} knowledge bases and forest logic programs co-exist, and we show that reasoning with such knowledge bases can be reduced to reasoning with forest logic programs only. We note that f-hybrid knowledge bases do not require the usual (weakly) DL-safety of the rule component, providing thus a genuine alternative approach to current integration approaches of ontologies and rules

Loop Formulas for Description Logic Programs

Description Logic Programs (dl-programs) proposed by Eiter et al. constitute an elegant yet powerful formalism for the integration of answer set programming with description logics, for the Semantic Web. In this paper, we generalize the notions of completion and loop formulas of logic programs to description logic programs and show that the answer sets of a dl-program can be precisely captured by the models of its completion and loop formulas. Furthermore, we propose a new, alternative semantics for dl-programs, called the {\em canonical answer set semantics}, which is defined by the models of completion that satisfy what are called canonical loop formulas. A desirable property of canonical answer sets is that they are free of circular justifications. Some properties of canonical answer sets are also explored.Comment: 29 pages, 1 figures (in pdf), a short version appeared in ICLP'1

Hybrid Rules with Well-Founded Semantics

A general framework is proposed for integration of rules and external first order theories. It is based on the well-founded semantics of normal logic programs and inspired by ideas of Constraint Logic Programming (CLP) and constructive negation for logic programs. Hybrid rules are normal clauses extended with constraints in the bodies; constraints are certain formulae in the language of the external theory. A hybrid program is a pair of a set of hybrid rules and an external theory. Instances of the framework are obtained by specifying the class of external theories, and the class of constraints. An example instance is integration of (non-disjunctive) Datalog with ontologies formalized as description logics. The paper defines a declarative semantics of hybrid programs and a goal-driven formal operational semantics. The latter can be seen as a generalization of SLS-resolution. It provides a basis for hybrid implementations combining Prolog with constraint solvers. Soundness of the operational semantics is proven. Sufficient conditions for decidability of the declarative semantics, and for completeness of the operational semantics are given

Symmetry Breaking for Answer Set Programming

In the context of answer set programming, this work investigates symmetry detection and symmetry breaking to eliminate symmetric parts of the search space and, thereby, simplify the solution process. We contribute a reduction of symmetry detection to a graph automorphism problem which allows to extract symmetries of a logic program from the symmetries of the constructed coloured graph. We also propose an encoding of symmetry-breaking constraints in terms of permutation cycles and use only generators in this process which implicitly represent symmetries and always with exponential compression. These ideas are formulated as preprocessing and implemented in a completely automated flow that first detects symmetries from a given answer set program, adds symmetry-breaking constraints, and can be applied to any existing answer set solver. We demonstrate computational impact on benchmarks versus direct application of the solver. Furthermore, we explore symmetry breaking for answer set programming in two domains: first, constraint answer set programming as a novel approach to represent and solve constraint satisfaction problems, and second, distributed nonmonotonic multi-context systems. In particular, we formulate a translation-based approach to constraint answer set solving which allows for the application of our symmetry detection and symmetry breaking methods. To compare their performance with a-priori symmetry breaking techniques, we also contribute a decomposition of the global value precedence constraint that enforces domain consistency on the original constraint via the unit-propagation of an answer set solver. We evaluate both options in an empirical analysis. In the context of distributed nonmonotonic multi-context system, we develop an algorithm for distributed symmetry detection and also carry over symmetry-breaking constraints for distributed answer set programming.Comment: Diploma thesis. Vienna University of Technology, August 201