Strong Completeness Results for Paraconsistent Logic Programming

In [6], we introduced a means of allowing logic programs to contain negations in both the head and the body of a clause. Such programs were called generally Horn programs (GHPs, for short). The model-theoretic semantics of GHPs were defined in terms of four-valued Belnap lattices [5]. For a class of programs called well-behaved programs, an SLD-resolution like proof procedure was introduced. This procedure was proven (under certain restrictions) to be sound (for existential queries) and complete (for ground queries). In this paper, we remove the restriction that programs be well-behaved and extend our soundness and completeness results to apply to arbitrary existential queries and to arbitrary GHPs. This is the strongest possible completeness result for GHPs. The results reported here apply to the design of very large knowledge bases and in processing queries to knowledge bases that possibly contain erroneous information

05171 Abstracts Collection -- Nonmonotonic Reasoning, Answer Set Programming and Constraints

From 24.04.05 to 29.04.05, the Dagstuhl Seminar 05171 ``Nonmonotonic Reasoning, Answer Set Programming and Constraints\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Towards a unified theory of logic programming semantics: Level mapping characterizations of selector generated models

Currently, the variety of expressive extensions and different semantics created for logic programs with negation is diverse and heterogeneous, and there is a lack of comprehensive comparative studies which map out the multitude of perspectives in a uniform way. Most recently, however, new methodologies have been proposed which allow one to derive uniform characterizations of different declarative semantics for logic programs with negation. In this paper, we study the relationship between two of these approaches, namely the level mapping characterizations due to [Hitzler and Wendt 2005], and the selector generated models due to [Schwarz 2004]. We will show that the latter can be captured by means of the former, thereby supporting the claim that level mappings provide a very flexible framework which is applicable to very diversely defined semantics.Comment: 17 page

Extension-based argumentation semantics via logic programming semantics with negation as failure

Extension-based argumentation semantics have been shown to be a suitable approach for performing practical reasoning. Since extension-based argumentation semantics were formalized in terms of relationships between atomic arguments, it has been shown that extension-based argumentation semantics (such as the grounded semantics and stable semantics) can be characterized by logic programming semantics with negation as failure. Recently, it has been shown that argumentation semantics such as the preferred semantics and the CF2 semantics can be characterized in terms of logic programming semantics. In this paper, we make a short overview w.r.t. recent results in the close relationship between extension-based semantics and logic programming semantics with negation as failure. We also show that there is enough evidence to believe that the use of declarative approaches based on logic programming semantics with negation as failure is a practical approach for performing practical reasoning following an argumentation reasoning approach.Peer ReviewedPostprint (published version

G’3-stable semantics and inconsistency

We present an overview on how to perform non-monotonic reasoning based on paraconsistent logics. In particular, we show that one can define a logic programming semantics based on the paraconsistent logic G’3 which is called G’3-stable semantics. This semantics defines a frame for performing non-monotonic reasoning in domains which are pervaded with vagueness and inconsistencies. In fact, we show that, by considering also a possibilistic logic point of view, one can use this extended framework for defining a possibilistic logic programming approach able to deal with reasoning, which is at the same time non-monotonic and uncertain.Peer ReviewedPostprint (published version

Reasoning with Inconsistencies in Hybrid MKNF Knowledge Bases

This article is concerned with the handling of inconsistencies occurring in the combination of description logics and rules, especially in hybrid MKNF knowledge bases. More precisely, we present a paraconsistent semantics for hybrid MKNF knowledge bases (called para-MKNF knowledge bases) based on four-valued logic as proposed by Belnap. We also reduce this paraconsistent semantics to the stable model semantics via a linear transformation operator, which shows the relationship between the two semantics and indicates that the data complexity in our paradigm is not higher than that of classical reasoning. Moreover, we provide fixpoint operators to compute paraconsistent MKNF models, each suitable to different kinds of rules. At last we present the data complexity of instance checking in different para-MKNF knowledge bases