A Polynomial Translation of Logic Programs with Nested Expressions into Disjunctive Logic Programs: Preliminary Report

Nested logic programs have recently been introduced in order to allow for arbitrarily nested formulas in the heads and the bodies of logic program rules under the answer sets semantics. Nested expressions can be formed using conjunction, disjunction, as well as the negation as failure operator in an unrestricted fashion. This provides a very flexible and compact framework for knowledge representation and reasoning. Previous results show that nested logic programs can be transformed into standard (unnested) disjunctive logic programs in an elementary way, applying the negation as failure operator to body literals only. This is of great practical relevance since it allows us to evaluate nested logic programs by means of off-the-shelf disjunctive logic programming systems, like DLV. However, it turns out that this straightforward transformation results in an exponential blow-up in the worst-case, despite the fact that complexity results indicate that there is a polynomial translation among both formalisms. In this paper, we take up this challenge and provide a polynomial translation of logic programs with nested expressions into disjunctive logic programs. Moreover, we show that this translation is modular and (strongly) faithful. We have implemented both the straightforward as well as our advanced transformation; the resulting compiler serves as a front-end to DLV and is publicly available on the Web.Comment: 10 pages; published in Proceedings of the 9th International Workshop on Non-Monotonic Reasonin

Applications of Intuitionistic Logic in Answer Set Programming

We present some applications of intermediate logics in the field of Answer Set Programming (ASP). A brief, but comprehensive introduction to the answer set semantics, intuitionistic and other intermediate logics is given. Some equivalence notions and their applications are discussed. Some results on intermediate logics are shown, and applied later to prove properties of answer sets. A characterization of answer sets for logic programs with nested expressions is provided in terms of intuitionistic provability, generalizing a recent result given by Pearce. It is known that the answer set semantics for logic programs with nested expressions may select non-minimal models. Minimal models can be very important in some applications, therefore we studied them; in particular we obtain a characterization, in terms of intuitionistic logic, of answer sets which are also minimal models. We show that the logic G3 characterizes the notion of strong equivalence between programs under the semantic induced by these models. Finally we discuss possible applications and consequences of our results. They clearly state interesting links between ASP and intermediate logics, which might bring research in these two areas together.Comment: 30 pages, Under consideration for publication in Theory and Practice of Logic Programmin

On the Effect of Default Negation on the Expressiveness of Disjunctive Rules

In this paper, the expressive power of disjunctive rules involving default negation is analyzed within a framework based on polynomial, faithful and modular (PFM) translations. The analysis is restricted to the stable semantics of disjunctive logic programs. A particular interest is understanding what is the effect if default negation is allowed in the heads of disjunctive rules. It is established in the paper that occurrences of default negation can be removed from the heads of rules using a PFM translation when default negation is allowed in the bodies of rules. In this case, we may conclude that default negation appearing in the heads of rules does not affect expressive power of rules. However, in the case that default negation may not be used in the bodies of rules, such a PFM translation is no longer possible. Moreover, there is no PFM translation for removing default negation from the bodies of rules. Consequently, disjunctive logic programs with default negation in the bodies of rules are strictly more expressive than those without

Dokumentverifikation mit Temporaler Beschreibungslogik

The thesis proposes a new formal framework for checking the content of web documents along individual reading paths. It is vital for the readability of web documents that their content is consistent and coherent along the possible browsing paths through the document. Manually ensuring the coherence of content along the possibly huge number of different browsing paths in a web document is time-consuming and error-prone. Existing methods for document validation and verification are not sufficiently expressive and efficient. The innovative core idea of this thesis is to combine the temporal logic CTL and description logic ALC for the representation of consistency criteria. The resulting new temporal description logics ALCCTL can - in contrast to existing specification formalisms - compactly represent coherence criteria on documents. Verification of web documents is modelled as a model checking problem of ALCCTL. The decidability and polynomial complexity of the ALCCTL model checking problem is proven and a sound, complete, and optimal model checking algorithm is presented. Case studies on real and realistic web documents demonstrate the performance and adequacy of the proposed methods. Existing methods such as symbolic model checking or XML-based document validation are outperformed in both expressiveness and speed.Die Dissertation stellt ein neues formales Framework für die automatische Prüfung inhaltlich-struktureller Konsistenzkriterien an Web-Dokumente vor. Viele Informationen werden heute in Form von Web-Dokumenten zugänglich gemacht. Komplexe Dokumente wie Lerndokumente oder technische Dokumentationen müssen dabei vielfältige Qualitätskriterien erfüllen. Der Informationsgehalt des Dokuments muss aktuell, vollständig und in sich stimmig sein. Die Präsentationsstruktur muss unterschiedlichen Zielgruppen mit unterschiedlichen Informationsbedürfnissen genügen. Die Sicherstellung grundlegender Konsistenzeigenschaften von Dokumenten ist angesichts der Vielzahl der Anforderungen und Nutzungskontexte eines elektronischen Dokuments nicht trivial. In dieser Arbeit werden aus der Hard-/Softwareverifikation bekannte Model-Checking-Verfahren mit Methoden zur Repräsentation von Ontologien kombiniert, um sowohl die Struktur des Dokuments als auch inhaltliche Zusammenhänge bei der Prüfung von Konsistenzkriterien berücksichtigen zu können. Als Spezifikationssprache für Konsistenzkriterien wird die neue temporale Beschreibungslogik ALCCTL vorgeschlagen. Grundlegende Eigenschaften wie Entscheidbarkeit, Ausdruckskraft und Komplexität werden untersucht. Die Adäquatheit und Praxistauglichkeit des Ansatzes werden in Fallstudien mit eLearning-Dokumenten evaluiert. Die Ergebnisse übertreffen bekannte Ansätze wie symbolisches Model-Checking oder Methoden zur Validierung von XML-Dokumenten in Performanz, Ausdruckskraft hinsichtlich der prüfbaren Kriterien und Flexibilität hinsichtlich des Dokumenttyps und -formats