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.

In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten- sions of the language of definite logic programs by classical (strong) negation, disjunc- tion, and some modal operators and show how each of the added features extends the representational power of the language.

We present SLDNFA, an extension of SLDNF-resolution for abductive reasoning on abductive logic programs. SLDNFA solves the floundering abduction problem: non-ground abductive atoms can be selected. SLDNFA provides also a partial solution for the floundering negation problem. Different abductive answers can be derived from an SLDNFA-refutation; these answers provide different compromises between generality and comprehensibility. Two extensions of SLDNFA are proposed which satisfy stronger completeness results. The soundness of SLDNFA and its extensions is proven. Their completeness for minimal solutions with respect to implication, cardinality and set inclusion is investigated. The formalisation of SLDNFA presented here is an update of an older version presented in [13] and does not rely on skolemisation of abductive atoms. 1

this paper we extend the language A and its translation to allow reasoning about the effects of concurrent actions. The logic programming formalization of situation calculus with concurrent actions presented in the paper is of independent interest and may serve as a test bed for the investigation of various transformations and logic programming inference mechanisms. ! 1. INTRODUCTION

this paper, we present an equational logic framework for objects, methods, inheritance and overriding of methods. Overriding is achieved via the concept of specificity, which states that more specific methods are preferred to less specific ones. Specificity is computed with the help of negation as failure. We specify equational logic programs and show that their completed versions behave as intended. Furthermore, we prove that SLDENF-resolution is complete if the equational theory is finitary, the completed programs are consistent, and no derivation flounders or is infinite; and we give syntactic conditions which guarantee non-floundering and finiteness. Finally, we discuss how the approach can be extended to reasoning about the past in the context of incompletely specified objects or situations. It will turn out that constructive negation is needed to solve these problems

We propose a modification L 1 of the action description language A. The language L 1 allows representation of hypothetical situations and hypothetical occurrence of actions (as in A) as well as representation of actual occurrences of actions and observations of the truth values of fluents in actual situations. The corresponding entailment relation formalizes various types of common-sense reasoning about actions and their effects not modeled by previous approaches. As an application of L 1 we also present an architecture for intelligent agents capable of observing, planning and acting in a changing environment based on the entailment relation of L 1 and use logic programming approximation of this entailment to implement a planning module for this architecture. We prove the soundness of our implementation and give a sucient condition for its completeness.

Abstract. In this paper we describe a language for reasoning about actions that can be used for modelling and for programming rational agents. We propose a modal approach for reasoning about dynamic domains in a logic programming setting. Agent behavior is specified by means of complex actions which are defined using modal inclusion axioms. The language is able to handle knowledge producing actions as well as actions which remove information. The problem of reasoning about complex actions with incomplete knowledge is tackled and the temporal projection and planning problems is addressed; more specifically, a goal directed proof procedure is defined, which allows agents to reason about complex actions and to generate conditional plans. We give a non-monotonic solution for the frame problem by making use of persistency assumptions in the context of an abductive characterization. The language has been used for implementing an adaptive web-based system.

Abduction-- from observations and a theory, find using hypotheses an explanation for the observations -- gained increasing interest during the last years. This form of reasoning has wide applicability in different areas of computer science; in particular, it has been recognized as an important principle of common-sense reasoning. In this paper, we define a general abduction model for logic programming, where the inference operator (i.e., the semantics to be applied on programs), can be specified by the user. Advanced forms of logic programming have been proposed as valuable tools for knowledge representation and reasoning. We show that logic programming semantics can be more meaningful for abductive reasoning than classical inference by providing examples from the area of knowledge representation and reasoning. The main part of the paper is devoted to an extensive study of the computational complexity of the principal problems in abductive reasoning, which are: Given an inst...

The logic program formalism is commonly viewed as a modal or default logic. In this paper, we propose an alternative interpretation of the formalism as a terminological logic. A terminological logic is designed to represent two different forms of knowledge. A TBox represents definitions for a set of concepts. An ABox represents the assertional knowledge of the expert. In our interpretation, a logic program is a TBox providing definitions for all predicates; this interpretation is present already in Clark's completion semantics. We extend the logic program formalism such that some predicates can be left undefined and use classical logic as the language for the ABox. The resulting logic can be seen as an alternative interpretation of abductive logic program formalism. We study the expressivity of the formalism for representing uncertainty by proposing solutions for problems in temporal reasoning, with null values and open domain knowledge. 1 Introduction The logic program formalism is c...

The paper presents a logic for action theory based on a modal language, where modalities represent actions. Persistency is achieved by using a nonmonotonic formalism which maximizes persisitency assumptions. The problem of ramification is tackled by introducing a modal causality operator which is used to represent causal rules. Assumptions on the value of fluents in the initial state allow to reason with incomplete initial states and to do postdiction. The action theory can also deal with non-minimal change and nondeterministic actions. 1 Introduction Reasoning about action and change is one of the main topics which must be addressed in building intelligent agents. Among the various approaches to reasoning about actions, one of the most popular is still the situation calculus. The situation calculus represents states of the world (situations) as sequences of actions, and fluents are relations whose truth values vary from state to state. The situation calculus is formulated in ...