Abduction in Logic Programming started in the late 80s, early 90s, in an attempt to extend logic programming into a framework suitable for a variety of problems in Artificial Intelligence and other areas of Computer Science. This paper aims to chart out the main developments of the field over the last ten years and to take a critical view of these developments from several perspectives: logical, epistemological, computational and suitability to application. The paper attempts to expose some of the challenges and prospects for the further development of the field.

We present an abstract framework for default reasoning, which includes Theorist, default logic, logic programming, autoepistemic logic, non-monotonic modal logics, and certain instances of circumscription as special cases. The framework can be understood as a generalisation of Theorist. The generalisation allows any theory formulated in a monotonic logic to be extended by a defeasible set of assumptions. An assumption can be defeated (or "attacked") if its "contrary" can be proved, possibly with the aid of other conflicting assumptions. We show that, given such a framework, the standard semantics of most logics for default reasoning can be understood as sanctioning a set of assumptions, as an extension of a given theory, if and only if the set of assumptions is conflict-free (in the sense that it does not attack itself) and it attacks every assumption not in the set. We propose a more liberal, argumentation-theoretic semantics, based upon the notion of admissible extension in logic pro...

The notion of assumption-based framework generalises and refines the use of abduction to give a formalisation of non-monotonic reasoning. In this framework, a sentence is a non-monotonic consequence of a theory if it can be derived monotonically from a theory extended by means of acceptable assumptions. The notion of acceptability for such assumptions is formulated in terms of their ability successfully to "counterattack" any "attacking" set of assumptions. One set of assumptions is said to "attack" another if the first set monotonically implies a consequence which is inconsistent with an assumption in the second set. This argumentation-theoretic criterion of acceptability is based on notions first introduced for logic programming and used to give a unified account of such diverse semantics for logic programming as stable models, partial stable models, preferred extensions, stable theories, well-founded semantics, and stationary semantics. The new framework makes it possible to general...

This paper presents the framework of Abductive Constraint Logic Programming (ACLP), which integrates Abductive Logic Programming (ALP) and Constraint Logic Programming (CLP). In ACLP, the task of abduction is supported and enhanced by its non-trivial integration with constraint solving. This integration of constraint solving into abductive reasoning facilitates a general form of constructive abduction and enables the application of abduction to computationally demanding problems

Stable models have been first introduced in the domain of total interpretations (T- stable models), where the existence of multiple T-stable models for the same program provides a powerful mechanism to express non-determinism. Stable models have been later extended to the domain of partial interpretations (P-stable models). In this paper, we show that the presence of multiple P-stable models need not be a direct manifestation of non-determinism, for it can be instead an expression of assorted degrees of undefinedness. To separate the two factors, non-determinism and undefinedness, this paper introduces the notion of deterministic stable models and strictly non-deterministic ones. Deterministic stable models form an interesting family, having a lattice structure where the well-founded model serves as the bottom; the top of the lattice, the maximum deterministic stable model, resolves differences between any two P-stable models in the family. On the other hand, every two models in a fam...

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this paper, a characterization of partial stable models for disjunctive datalog programs is given using a suitable extension of the notion of unfounded set. Two interesting subclasses of partial stable models, M-stable (Maximal-stable) (also called regular models, preferred extension, and maximal stable classes) and L-stable (Least undefined-stable) models, are then extended from normal to disjunctive datalog programs. L-stable models are shown to be the natural relaxation of the notion of total stable model; on the other hand the less strict M-stable models, endowed with a nice modularity property, may be appealing from the programming and computational point of view. Mstable and L-stable models are also compared with the regular models for disjunctive datalog programs recently proposed in the literature. 1 Introduction Deductive dat

We provide a simple formulation of a framework where some extensions of logic programming with non-monotonic reasoning are treated uniformly, namely two kinds of negation and abduction. The resulting semantics is purely model-theoretic, and gives meaning to any noncontradictory abductive logic program. Moreover, it embeds and generalizes some existing semantics which deal with negation and abduction. The framework is equipped with a correct top-down proof procedure. Keywords: Programming languages, Logic programming, Non-monotonic reasoning, Negation, Abduction. Dipartimento di Informatica, Universit`a di Pisa, Corso Italia 40, Pisa, Italy. brogi@di.unipi.it y DEIS, Universit`a di Bologna, Viale Risorgimento 2, 40136 Bologna, Italy. elamma@deis.unibo.it z Dipartimento di Informatica, Universit`a di Pisa, Corso Italia 40, Pisa, Italy. paolo@di.unipi.it x DEIS, Universit`a di Ferrara, Via Saragat, 41100 Ferrara, Italy. pmello@ing.unife.it Contents 1 Introduction and Motiva...

This paper investigates the expressive power and complexity of partial model semantics for disjunctive deductive databases. In particular,...

. While it is well-known how normal logic programs may be viewed as a form of abduction and argumentation, the problem of how disjunctive programs may be used for abductive reasoning is rarely discussed. In this paper we propose an abductive semantics for disjunctive logic programs with default negation and show that Eshghi and Kowalski 's abductive proof procedure for normal programs can be adopted to compute abductive solutions for disjunctive programs. 1 Introduction In the simplest form abduction is the problem: From A and A / B, infer B as a possible explanation of A. Nonmonotonic reasoning has been explored as a form of abductive reasoning. In particular, default assumptions in logic programs have been treated as abductive hypotheses and a number of reasoning mechanisms and semantics have been proposed [7, 10, 16, 18, 19]. Chief among these is Eshghi and Kowalski's formulation of an elegant abductive proof procedure for normal programs where default assumptions are viewed as a...