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.

this paper, we argue that no such set of postulates will be adequate for every application. In particular, we make a fundamental distinction between two kinds of modifications to a knowledge base. The first one, update, consists of bringing the knowledge base up to date when the world described by it changes. For example, most database updates are of this variety, e.g. "increase Joe's salary by 5%". Another example is the incorporation into the knowledge base of changes caused in the world by the actions of a robot (Ginsberg and Smith 1987, Winslett 1988, Winslett 1990) . We show that the AGM postulates must be drastically modified to describe update. The second type of modification, revision, is used when we are obtaining new information about a static world. For example, we may be trying to diagnose a faulty circuit and want to incorporate into the knowledge base the results of successive tests, where newer results may contradict old ones. We claim the AGM postulates describe only revision.

In a multi-agent environment, where self-motivated agents try to pursue their own goals, cooperation cannot be taken for granted. Cooperation must be planned for and achieved through communication and negotiation. We present a logical model of the mental states of the agents based on a representation of their beliefs, desires, intentions, and goals. We present argumentation as an iterative process emerging from exchanges among agents to persuade each other and bring about a change in intentions. We look at argumentation as a mechanism for achieving cooperation and agreements. Using categories identified from human multi-agent negotiation, we demonstrate how the logic can be used to specify argument formulation and evaluation. We also illustrate how the developed logic can be used to describe different types of agents. Furthermore, we present a general Automated Negotiation Agent which we implemented, based on the logical model. Using this system, a user can analyze and explore differe...

We study the complexity of several recently proposed methods for updating or revising propositional knowledge bases. In particular, we derive complexity results for the following problem: given a knowledge base T , an update p, and a formula q, decide whether q is derivable from T p, the updated (or revised) knowledge base. This problem amounts to evaluating the counterfactual p > q over T . Besides the general case, also subcases are considered, in particular where T is a conjunction of Horn clauses, or where the size of p is bounded by a constant.

Belief revision leads to temporal nonmonotonicity, i.e., the set of beliefs does not grow monotonically with time. Default reasoning leads to logical nonmonotonicity, i.e., the set of consequences does not grow monotonically with the set of premises. The connection between these forms of nonmonotonicity will be studied in this paper focusing on syntaxbased approaches. It is shown that a general form of syntax-based belief revision corresponds to a special kind of partial meet revision in the sense of the theory of epistemic change, which in turn is expressively equivalent to some variants of logics for default reasoning. Additionally, the computational complexity of the membership problem in revised belief sets and of the equivalent problem of derivability in default logics is analyzed, which turns out to be located at the lower end of the polynomial hierarchy. 1 INTRODUCTION Belief revision is the process of incorporating new information into a knowledge base while preserving consist...

this paper, we examine Gardenfors's criticisms of the foundations approach. We argue that the coherence and foundations approaches differ less than has been supposed, in that the fundamental concerns of the coherence approach for conservatism in belief revision apply in exactly the same way in the foundations approach. We also argue that the foundations approach represents the most direct way of mechanizing the coherence approach. Moreover, the computational costs of revisions based on epistemic entrenchment appear to equal or exceed those of revisions based on reasons, in the sense that any entrenchment ordering from which information about reasons may be recovered will be at least as costly to update as the reasons it represents. We conclude that while the coherence approach offers a valuable perspective on belief revision, it does not yet provide an adequate theoretical or practical basis for characterizing or mechanizing belief revision.

this paper, we adopt the former perspective. In order to distinguish operations on syntactic descriptions -- on belief bases -- from operations on belief sets, belief base changes are called base revision and base contraction.

If a new piece of information contradicts our previously held beliefs, we have to revise our beliefs. This problem of belief revision arises in a number of areas in Computer Science and Artificial Intelligence, e.g., in updating logical database, in hypothetical reasoning, and in machine learning. Most of the research in this area is influenced by work in philosophical logic, in particular by Gardenfors and his colleagues, who developed the theory of belief revision. Here we will focus on the computational aspects of this theory, surveying results that address the issue of the computational complexity of belief revision.

Theories of rational belief revision recently proposed by Alchourr'on, Gardenfors, Makinson, and Nebel illuminate many important issues but impose unnecessarily strong standards for correct revisions and make strong assumptions about what information is available to guide revisions. We reconstruct these theories according to an economic standard of rationality in which preferences are used to select among alternative possible revisions. By permitting multiple partial specifications of preferences in ways closely related to preference-based nonmonotonic logics, the reconstructed theory employs information closer to that available in practice and offers more flexible ways of selecting revisions. We formally compare this new conception of rational belief revision with the original theories, adapt results about universal default theories to prove that there is unlikely to be any universal method of rational belief revision, and examine formally how different limitations on rationality affe...

: This paper is concerned with the construction of a base contraction (revision) operation such that the theory contraction (revision) operation generated by it will be fully AGM-rational. It is shown that the theory contraction operation generated by Fuhrmann's minimal base contraction operation, even under quite strong restrictions, fails to satisfy the "supplementary postulates" of belief contraction. Finally Fuhrmann's construction is appropriately modified so as to yield the desired properties. The new construction may be described as involving a modification of safe (base) contraction so as to make it maxichoice. Descriptors: belief, change, contraction, revision, base, theory. We often change our beliefs. We learn new things, occasionally things that conflict with our current beliefs. On such occasions new beliefs replace the old ones. It is as if this process is completed in two steps: (1) first we identify and throw out the beliefs that conflict with the new information and t...