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.

The aim of this paper is to provide a semantics for general logic programs (with negation by default) extended with explicit negation, subsuming well founded semantics [22]. The Well Founded semantics for extended logic programs (WFSX) is expressible by a default theory semantics we have devised [11]. This relationship improves the cross-fertilization between logic programs and default theories, since we generalize previous results concerning their relationship [3, 4, 7, 1, 2], and there is an increasing use of logic programming with explicit negation for nonmonotonic reasoning [7, 15, 16, 13, 23]. It also clarifies the meaning of logic programs combining both explicit negation and negation by default. In particular, it shows that explicit negation corresponds exactly to classical negation in the default theory, and elucidates the use of rules in logic programs. Like defaults, rules are unidirectional, so their contrapositives are not implicit; the rule connective, /, is not materi...

Our purpose is to define a semantics that extends Well Founded Semantics for programs with classical negation, and which avoids the absence of models caused by contradictions brought about by closed world assumptions. This extension relies on allowing to take back such closed world assumptions, through making their truth value become undefined, and thus permiting noncontradictory models to appear. We take back such assumptions in a minimal way for all alternative ways of removing contradictions, by means of simple transformations of the original program. The transformed programs have contradiction free Well Founded Models. Moreover, we identify a unique model that defines the semantics of the original program, which is included in all the alternative contradiction free models. This unique model coincides with the Well Founded Model when the latter is noncontradictory. The notions of minimality and contradiction removal employed are useful for dealing with Belief Revision. These techniq...

Recently several authors have stressed and showed the importance of having a second kind of negation in logic programs for use in deductive databases, knowledge representation, and nonmonotonic reasoning [6, 7, 8, 9, 13, 14, 15, 24]. Different semantics for logic programs extended with :-negation (extended logic programs) have appeared [1, 4, 6, 9, 11, 12, 17, 19, 24] but, contrary to what happens with semantics for normal logic programs, there is no general comparison among them, specially in what concerns the use and meaning of the newly introduced :-negation. The goal of this paper is to contrast a variety of these semantics in what concerns their use and meaning of :-negation, and its relation to classical negation and to the default negation of normal programs, here denoted by not : To this purpose we define a parametrizeable schema to encompass and characterize a diversity of proposed semantics for extended logic programs, where the parameters are two: one the axioms AX: defin...

Evaluation of counterfactual queries (e.g., "If A were true, would C have been true?") is important to fault diagnosis, planning, and determination of liability. We present a formalism that uses probabilistic causal networks to evaluate one's belief that the counterfactual consequent, C, would have been true if the antecedent, A, were true. The antecedent of the query is interpreted as an external action that forces the proposition A to be true, which is consistent with Lewis' Miraculous Analysis. This formalism offers a concrete embodiment of the "closest world" approach which (1) properly reflects common understanding of causal influences, (2) deals with the uncertainties inherent in the world, and (3) is amenable to machine representation. Introduction A counterfactual sentence has the form If A were true, then C would have been true where A, the counterfactual antecedent, specifies an event that is contrary to one's real-world observations, and C, the counterfactual consequen...

Our purpose is to exhibit a modular systematic method of representing non-- monotonic reasoning problems with the Well Founded Semantics WFS of extended logic programs augmented with eXplicit negation (WFSX), augmented by its Contradiction Removal Semantics (CRSX) when needed. We apply this semantics, and its contradiction removal semantics counterpart, to represent non-monotonic reasoning problems. We show how to cast in the language of logic programs extended with explicit negation such forms of non-monotonic reasoning as defeasible reasoning, abductive reasoning and hypothetical reasoning and apply them to such different domains of knowledge representation as hierarchies and reasoning about actions. We then abstract a modular systematic method of representing non-monotonic problems in a logic programming semantics comprising two forms of negation avoiding some drawbacks of other proposals, with which we relate our work.

We present derivation proof procedures for extended stable model semantics. Given program \Pi and goal G, G belongs to the well founded model of \Pi iff there is a WFM-derivation for G in \Pi. Likewise, given program \Pi and goal G, G belongs to some extended stable model of \Pi iff there is a XSM-derivation for G in \Pi. Correctness (completeness and soundness) of these procedures is discussed. Example derivations are exhibited, as well as a simple Prolog implementation that directly mirrors the procedures. 1 Introduction Well Founded Semantics (WFS) [ Van Gelder et al., 1990 ] adequately captures various forms of hypothetical reasoning [ Pereira et al., 1991c, Pereira et al., 1991d, Pereira et al., 1991b, Pereira et al., 1991a ] if we interpret the well-founded model (WFM) of a program \Pi as a (possibly incomplete) core view of the world, the extended stable models (XSMs) specifying alternative complementary consistent views of the world, all of each containing the core WFM . The...

The field of theory update has seen some major improvements in what concerns model updating. The update of models is governed by update rules and by inertia applied to the literals not directly aoeected by the update program. This is important but it is still necessary to tackle as well the updating of programs. Some results have been obtained on the issue of updating a logic program which encodes a set of models, to obtain a new program whose models are the desired updates of the initial models. But here the program only plays the rôle of a means to encode the models. A logic program encodes much more than a set of models: it encodes the relationships between the elements of those models. In this dissertation we advocate that the principle of inertia is advantageously applied to the rules of the initial program rather than to the individual literals in a model. Indeed, we show how this concept of program update generalizes simple interpretation update. We will consider both the 2-valued...

The focus of this paper is nonmonotonic reasoning as it relates to logic programming. I discuss the pre-history of nonmonotonic reasoning starting from approximately 1958. I then review the research that has been accomplished in the areas of circumscription, default theory, modal theories and logic programming. The overview includes the major results developed including complexity results that are known about the various theories. I then provide a summary which includes an assessment of the field and what must be done to further research in nonmonotonic reasoning and logic programming. 1 Introduction Classical logic has played a major role in computer science. It has been an important tool both for the development of architecture and of software. Logicians have contended that reasoning, as performed by humans, is also amenable to analysis using classical logic. However, workers in the field of artificial 1 This paper is an updated version of an invited Banquet Address, First Interna...

The present prolegomena consist, as all indeed do, in a critical discussion serving to introduce and interpret the extended works that follow in this book. As a result, the book is not a mere collection of excellent papers in their own specialty, but provides also the basics of the motivation, background history, important themes, bridges to other areas, and a common technical platform of the principal formalisms and approaches, augmented with examples. In the