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

Towards Closed World Reasoning in Dynamic Open Worlds (Extended Version)

The need for integration of ontologies with nonmonotonic rules has been gaining importance in a number of areas, such as the Semantic Web. A number of researchers addressed this problem by proposing a unified semantics for hybrid knowledge bases composed of both an ontology (expressed in a fragment of first-order logic) and nonmonotonic rules. These semantics have matured over the years, but only provide solutions for the static case when knowledge does not need to evolve. In this paper we take a first step towards addressing the dynamics of hybrid knowledge bases. We focus on knowledge updates and, considering the state of the art of belief update, ontology update and rule update, we show that current solutions are only partial and difficult to combine. Then we extend the existing work on ABox updates with rules, provide a semantics for such evolving hybrid knowledge bases and study its basic properties. To the best of our knowledge, this is the first time that an update operator is proposed for hybrid knowledge bases.Comment: 40 pages; an extended version of the article published in Theory and Practice of Logic Programming, 10 (4-6): 547 - 564, July. Copyright 2010 Cambridge University Pres

On the evolution of the instance level of DL-lite knowledge bases

Recent papers address the issue of updating the instance level of knowledge bases expressed in Description Logic following a model-based approach. One of the outcomes of these papers is that the result of updating a knowledge base K is generally not expressible in the Description Logic used to express K. In this paper we introduce a formula-based approach to this problem, by revisiting some research work on formula-based updates developed in the '80s, in particular the WIDTIO (When In Doubt, Throw It Out) approach. We show that our operator enjoys desirable properties, including that both insertions and deletions according to such operator can be expressed in the DL used for the original KB. Also, we present polynomial time algorithms for the evolution of the instance level knowledge bases expressed in the most expressive Description Logics of the DL-lite family

A set-based reasoner for the description logic \shdlssx (Extended Version)

We present a \ke-based implementation of a reasoner for a decidable fragment of (stratified) set theory expressing the description logic \dlssx (\shdlssx, for short). Our application solves the main TBox and ABox reasoning problems for \shdlssx. In particular, it solves the consistency problem for \shdlssx-knowledge bases represented in set-theoretic terms, and a generalization of the \emph{Conjunctive Query Answering} problem in which conjunctive queries with variables of three sorts are admitted. The reasoner, which extends and optimizes a previous prototype for the consistency checking of \shdlssx-knowledge bases (see \cite{cilc17}), is implemented in \textsf{C++}. It supports \shdlssx-knowledge bases serialized in the OWL/XML format, and it admits also rules expressed in SWRL (Semantic Web Rule Language).Comment: arXiv admin note: text overlap with arXiv:1804.11222, arXiv:1707.07545, arXiv:1702.0309

Elimination of Cuts in First-order Finite-valued Logics

A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand’s theorem for the four-valued knowledge-representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information