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The well-founded semantics (WFS) for logic programs is one of the few major paradigms for closed-world reasoning. With the advent of the Semantic Web, it is being used as part of rule systems for ontology reasoning, and also investigated as to its usefulness as a semantics for hybrid systems featuring combined open- and closed-world reasoning. Even in its most basic form, however, the WFS is undecidable. In fact, it is not even semi-decidable, which means that it is a theoretical impossibility that sound and complete reasoners for the WFS exist. Surprisingly, however, this matter has received next to no attention in research, although it has already been shown in 1995 by John Schlipf [1]. In this paper, we present several conditions under which query-answering under the well-founded semantics is decidable or semi-decidable. To the best of our knowledge, these are the very first results on such conditions. [ABSTRACT FROM AUTHOR]

In Artificial Intelligence, knowledge representation studies the formalisation of knowledge and its processing within machines. Techniques of automated reasoning allow a computer system to draw conclusions from knowledge represented in a machine-interpretable form. Recently, ontologies have evolved in computer science as computational artefacts to provide computer systems with a conceptual yet computational model of a particular domain of interest. In this way, computer systems can base decisions on reasoning about domain knowledge, similar to humans. This chapter gives an overview on basic knowledge representation aspects and on ontologies as used within computer systems. After introducing ontologies in terms of their appearance, usage and classification, it addresses concrete ontology languages that are particularly important in the context of the Semantic Web. The most recent and predominant ontology languages and formalisms are presented in relation to each other and a selection of them is discussed in more detail. [ABSTRACT FROM AUTHOR]

In this paper we present a MOF compliant metamodel and UML profile for the Semantic Web Rule Language (SWRL) that integrates with our previous work on a metamodel and UML profile for OWL DL. Based on this metamodel and profile, UML tools can be used for visual modeling of rule-extended ontologies. [ABSTRACT FROM AUTHOR]

Morphisms constitute a general tool for modelling complex relationships between mathematical objects in a disciplined fashion. In Formal Concept Analysis (FCA), morphisms can be used for the study of structural properties of knowledge represented in formal contexts, with applications to data transformation and merging. In this paper we present a comprehensive treatment of some of the most important morphisms in FCA and their relationships, including dual bonds, scale measures, infomorphisms, and their respective relations to Galois connections. We summarize our results in a concept lattice that cumulates the relationships among the considered morphisms. The purpose of this work is to lay a foundation for applications of FCA in ontology research and similar areas, where morphisms help formalize the interplay among distributed knowledge bases. [ABSTRACT FROM AUTHOR]

Multidimensional dynamic logic programs are a paradigm which allows to express (partially) hierarchically ordered evolving knowledge bases through (partially) ordered multi sets of logic programs and allowing to solve contradictions among rules in different programs by allowing rules in more important programs to reject rules in less important ones. This class of programs extends the class of dynamic logic program that provides meaning and semantics to sequences of logic programs. Recently a semantics named refined stable model semantics has fixed some counterintuitive behaviour of previously existing semantics for dynamic logic programs. However, it is not possible to directly extend the definitions and concepts of the refined semantics to the multidimensional case and hence more sophisticated principles and techniques are in order. In this paper we face the problem of defining a proper semantics for multidimensional dynamic logic programs by extending the idea of well supported model to this class of programs and by showing that this concept alone is enough for univocally characterizing a proper semantics. We then show how the newly defined semantics coincides with the refined one when applied to sequences of programs. [ABSTRACT FROM AUTHOR]

W.C. Rounds and G.-Q. Zhang have proposed to study a form of disjunctive logic programming generalized to algebraic domains [1]. This system allows reasoning with information which is hierarchically structured and forms a (suitable) domain. We extend this framework to include reasoning with default negation, giving rise to a new nonmonotonic reasoning framework on hierarchical knowledge which encompasses answer set programming with extended disjunctive logic programs. We also show that the hierarchically structured knowledge on which programming in this paradigm can be done, arises very naturally from formal concept analysis. Together, we obtain a default reasoning paradigm for conceptual knowledge which is in accordance with mainstream developments in nonmonotonic reasoning. [ABSTRACT FROM AUTHOR]