The semantics of disjunctive deductive databases

In his paper [12] Ross extends the well-founded semantics for normal logic programs [16] to disjunctive logic programs. His definition is top-down and it is closer to a procedural semantics than to the elegant fixpoint definition of the well-founded semantics for normal logic programs. In the present paper, we propose a declarative, bottom-up fixpoint definition of the well-founded semantics for disjunctive logic programs. Our construction of the greatest unfounded set of extended literals is similar with the construction of the greatest unfounded set for normal programs. As a consequence, the connection between the well-founded semantics for normal programs and the well-founded semantics for disjunctive programs is made clearer.KeywordsLogic ProgramDeductive DatabaseNormal ProgramDisjunctive ProgramExtended AtomThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Much work has been done on extending the well-founded semantics to general disjunctive logic programs and various approaches have been proposed. However, these semantics are different from each other and no consensus is reached about which semantics is the most intended. In this article, we look at disjunctive well-founded reasoning from different angles. We show that there is an intuitive form of the well-founded reasoning in disjunctive logic programming which can be characterized by slightly modifying some existing approaches to defining disjunctive well-founded semantics, including program transformations, argumentation, unfounded sets (and resolution-like procedure). By employing the techniques developed by Brass and Dix in their transformation-based approach, we also provide a bottom-up procedure for this semantics. The significance of our work is not only in clarifying the relationship among different approaches, but also shed some light on what is an intended well-founded semantics for disjunctive logic programs.

This paper presents a new knowledge representation language for expert systems and deductive databases, which extends disjunctive logic programming with inheritance and true negation. A modeltheoretic semantics of the proposed language is given, and it is shown to extend the stable model semantics of disjunctive logic programs. Finally, the complexity of inferring information from disjunctive ordered theories is analysed.

The paper proposes a new knowledge representation language, called DLP<, which extends disjunctive logic programming (with strong negation) by inheritance. The addition of inheritance enhances the knowledge modeling features of the language providing a natural representation of default reasoning with exceptions. A declarative model-theoretic semantics of DLP< is provided, which is shown to generalize the Answer Set Semantics of disjunctive logic programs. The knowledge modeling features of the language are illustrated by encoding classical nonmonotonic problems in DLP<. The complexity of DLP< is analyzed, proving that inheritance does not cause any computational overhead, as reasoning in DLP< has exactly the same complexity as reasoning in disjunctive logic programming. This is confirmed by the existence of an efficient translation from DLP< to plain disjunctive logic programming. Using this translation, an advanced KR system supporting the DLP< language has been implemented on top of the DLV system and has subsequently been integrated into DLV.

Argumentation-based abduction in disjunctive logic programming

Argumentation (abduction) is widely applied in artificial intelligence (AI) and law reasoning. However, the problem of how to perform argumentation in disjunctive logic programming (DLP) is still open. In addition, a unifying semantic framework is required for incorporating various semantics for DLP. An argumentation-theoretic framework for DLP by taking the disjuncts of negative literals as abducibles is presented. This semantics not only is a simple and intuitive framework for performing argumentation and abduction in DLP, but also provides a unifying framework for many key semantics of disjunctive logic programs. In particular, it is shown that the EGCWA, well-founded model and disjunctive stable models can all be embedded into this semantics.

The paper proposes a new knowledge representation language, called DLP<, which extends disjunctive logic programming (with strong negation) by inheritance. The addition of inheritance enhances the knowledge modeling features of the language providing a natural representation of default reasoning with exceptions. A declarative model-theoretic semantics of DLP< is provided, which is shown to generalize the Answer Set Semantics of disjunctive logic programs. The knowledge modeling features of the language are illustrated by encoding classical nonmonotonic problems in DLP<. The complexity of DLP< is analyzed, proving that inheritance does not cause any computational overhead, as reasoning in DLP< has exactly the same complexity as reasoning in disjunctive logic programming. This is confirmed by the existence of an efficient translation from DLP< to plain disjunctive logic programming. Using this translation, an advanced KR system supporting the DLP< language has been implemented on top of the DLV system and has subsequently been integrated into DLV.

The stable model semantics of disjunctive logic programs (DLPs) is based on minimal models [5,12] which makes atoms appearing in a disjunctive program false by default. This is often desirable from the knowledge representation point of view, but certain domains become awkward to formalize if all atoms are blindly subject to minimization. In contrast to this, parallel circumscription [11] provides a re.ned notion of minimal models as it distinguishes varying and fixed atoms in addition to those being falsified. This eases the task of knowledge presentation in many cases. For example, it is straightforward to formalize Reiter-style minimal diagnoses [13] for digital circuits using parallel circumscription.

A game semantics for disjunctive logic programming

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.

We show that stable models of logic programs may be viewed as minimal models of programs that satisfy certain additional constraints. To do so, we transform the normal programs into disjunctive logic programs and sets of integrity constraints. We show that the stable models of the normal program coincide with the minimal models of the disjunctive program thatsatisfy the integrity constraints. As a consequence, the stable model semantics can be characterized using theextended generalized closed world assumption for disjunctive logic programs. Using this result, we develop a bottomup algorithm for function-free logic programs to find all stable models of a normal program by computing the perfect models of a disjunctive stratified logic program and checking them for consistency with the integrity constraints. The integrity constraints provide a rationale as to why some normal logic programs have no stable models.

We study the relationship between argumentation (abduction) and disjunctive logic programming. Based on the paradigm of argumentation, an abductive semantic framework for disjunctive logic programming is presented, in which the disjunctions of negative literals are taken as possible assumptions rather than only negative literals as the case of non-disjunctive logic programming. In our framework, three semantics PDH, CDH and WFDH are defined by three kinds of acceptable hypotheses to represent credulous reasoning, moderate reasoning and skeptical reasoning in AI, respectively. On the other hand, our semantic framework could be established in a broader class than that of disjunctive programs (called bi-disjunctive logic programs) and, hence, the corresponding abductive framework is abbreviated as BDAS (Bi-Disjunctive Argumentation-theoretic Semantics). Besides its rich expressive power and nondeterminism, BDAS integrates and naturally extends many key semantics, such as the minimal models, EGCWA, the well-founded model, and the stable models. In particular, a novel and interesting argumentation-theoretic characterization of EGCWA is shown. Thus the framework in this paper does not only provides a new way of performing argumentation (abduction) in disjunctive logic programming, but also is a simple, intuitive and unifying semantic framework for disjunctive logic programming.KeywordsLogic ProgramLogic ProgrammingArgument FrameworkDisjunctive ProgramDisjunctive LogicThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

On the equivalence of the static and disjunctive well-founded semantics and its computation

Three-valued completion for abductive logic programs

Two natural ways to specify the declarative semantics of logic programs and deductive databases are the fixpoint theory of Van Emden and Kowalski [11] and Clark's predicate completion [2]. The fixpoint theory does not apply to general programs with negation; a generalization of the theory can be defined [1,12] only if the programs are stratified. Clark's predicate completion is defined for logic programs with negation. In general, it fails to capture their intended semantics [7,8,9].In this paper, we introduce a new notion of quasi-interpretation as a set of ground clauses of the form A ← ¬ B 1, ..., ← B n and extend the classic fixed point theory in [11] to quasi-interpretations. The semantics of a logic program P is defined by Clark's predicate completion of the least fixpoint of a continuous operator T P on quasi-interpretations. It is called the fixpoint completion of P, fixcomp(P). We then discuss the relations between fixcomp(P) and other approaches [5,7,8,9].KeywordsLogic ProgramStable ModelModel SemanticPerfect ModelDeductive DatabaseThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.