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.

Abduction is an important form of nonmonotonic reasoning allowing one to find explanations for certain symptoms or manifestations. When the application domain is described by a logical theory, we speak about logic-based abduction. Candidates for abductive explanations are usually subjected to minimality criteria such as subsetminimality, minimal cardinality, minimal weight, or minimality under prioritization of individual hypotheses. This paper presents a comprehensive complexity analysis of relevant decision and search problems related to abduction on propositional theories. Our results indicate that abduction is harder than deduction. In particular, we show that with the most basic forms of abduction the relevant decision problems are complete for complexity classes at the second level of the polynomial hierarchy, while the use of prioritization raises the complexity to the third level in certain cases.

The problem of abduction can be characterized as finding the best explanation of a set of data. In this paper we focus on one type of abduction in which the best explanation is the most plausible combination of hypotheses that explains all the data. We then present several computational complexity results demonstrating that this type of abduction is intractable (NP-hard) in general. In particular, choosing between incompatible hypotheses, reasoning about cancellation effects among hypotheses, and satisfying the maximum plausibility requirement are major factors leading to intractability. We also identify a tractable, but restricted, class of abduction problems. Thanks to B. Chandrasekaran, Ashok Goel, Jack Smith, and Jon Sticklen for their comments on the numerous versions of this paper. The referees have also made a substantial contribution. Any remaining errors are our responsibility, of course. This research has been supported in part by the National Library of Medicine, grant LM-...

This paper surveys the main results appeared in the literature on the computational complexity of non-monotonic inference tasks. We not only give results about the tractability/intractability of the individual problems but we also analyze sources of complexity and explain intuitively the nature of easy/hard cases. We focus mainly on non-monotonic formalisms, like default logic, autoepistemic logic, circumscription, closed-world reasoning and abduction, whose relations with logic programming are clear and well studied. Complexity as well as recursion-theoretic results are surveyed. Work partially supported by the ESPRIT Basic Research Action COMPULOG and the Progetto Finalizzato Informatica of the CNR (Italian Research Council). The first author is supported by a CNR scholarship 1 Introduction Non-monotonic logics and negation as failure in logic programming have been defined with the goal of providing formal tools for the representation of default information. One of the ideas und...

Abduction is a form of non-monotonic reasoning that has gained increasing interest in the last few years. The key idea behind it can be represented by the following inference rule $$O = \mathop C\limits_| - N = \mathop P\limits_|^| - O - \mathop C\limits_|^| - .$$ i.e., from an occurrence of ohgr and the rule ldquophiv implies ohgrrdquo, infer an occurrence of phiv as aplausible hypothesis or explanation for ohgr. Thus, in contrast to deduction, abduction is as well as induction a form of ldquodefeasiblerdquo inference, i.e., the formulae sanctioned are plausible and submitted to verification. In this paper, a formal description of current approaches is given. The underlying reasoning process is treated independently and divided into two parts. This includes a description of methods for hypotheses generation and methods for finding the best explanations among a set of possible ones. Furthermore, the complexity of the abductive task is surveyed in connection with its relationship to default reasoning. We conclude with the presentation of applications of the discussed approaches focusing on plan recognition and plan generation.

Diagnosis was among the first subjects investigated when digital computers became available. It still remains an important research area, in which several new developments have taken place in the last decade. One of these new developments is the use of detailed domain models in knowledge-based systems for the purpose of diagnosis, often referred to as model-based diagnosis. Typically, such models embody knowledge of the normal or abnormal structure and behaviour of the modelled objects in a domain. Models of the structure and workings of technical devices, and causal models of disease processes in medicine are two examples. In this article, the most important notions of diagnosis and their formalisation are reviewed and brought in perspective. In addition, attention is focused on a number of general frameworks of diagnosis, which offer sufficient flexibility for expressing several types of diagnosis.

A new inductive learning system, Lab (Learning for ABduction), is presented which acquires abductive rules from a set of training examples. The goal is to find a small knowledge base which, when used abductively, diagnoses the training examples correctly and generalizes well to unseen examples. This contrasts with past systems that inductively learn rules that are used deductively. Each training example is associated with potentially multiple categories (disorders) , instead of one as with typical learning systems. Lab uses a simple hill-climbing algorithm to efficiently build a rule base for a set-covering abductive system. Lab has been experimentally evaluated and compared to other learning systems and an expert knowledge base in the domain of diagnosing brain damage due to stroke. Introduction Most work in symbolic concept acquisition assumes a deductive model of classification in which an example is a member of a concept if it satisfies a logical specification represented in dis...

In the following report, we describe a new shell for building abductive problem solving agents. This shell, called Peirce-IGTT 1 , can be used in conjunction with other problem solving tools constructed at the Laboratory for Artificial Intelligence Research at The Ohio State University in order to build large knowledgebased systems. Peirce itself is a tool for building agents to solve the abductive tasks of hypothesis assembly and critique. This report will discuss the Peirce tool and its algorithm, some brief history of the construction of the tool and a sample case that was constructed from it. Abductive Problem Solving Abduction is inference to the best explanation[9]. It is a form of problem solving where hypotheses are formed and selected to explain a set of data or findings. This form of inference can be used in solving diagnostic and related sort of problems[5, 6, 12, 14, 19]. In attempting to solve an abductive problem, there generally needs to be a means to generate hypothe...

This paper surveys the work on abductive inference within the field of artificial intelligence (AI), with particular attention to logic-based abduction. The paper commences with a formal description of three popular characterizations of abductive inference. This is followed by an examination of several specific logic-based abductive frameworks, each of which applies syntactic restrictions to the formulation of the abductive reasoning problem and the resultant explanation. Mechanisms for computing logic-based abductive explanations, and the complexity of variants of the abduction task are examined in the sections to follow. This paper also surveys different applications of abduction in AI, and the connections between abduction and other types of nonmonotonic reasoning. The paper concludes with a discussion of potential future research areas. Revision of an earlier draft written while the author was a doctoral candidate at the University of Toronto. Contents 1 Introduction 3 2 Chara...

This paper discusses the extension of ViewGen, a program for belief ascription, to the area of inten-sional object identification with applications to battle environments, and its combination in a overall sys-tem with MGR, a Model-Generative Reasoning system, and PREMO a semantics-based parser for robust parsing of noisy message data. ViewGen represents the beliefs of agents as explicit, partitioned proposition-sets known as environ-ments. Environments are convenient, even essential, for addressing important pragmatic issues of reason-ing. The paper concentrates on showing that the transfer of information in intensional object identification and belief ascription itself can both be seen as different manifestations of a single environment-amalgamation process. The entities we shall be concerned with will be ones, for example, the system itself believes to be separate entities while it is computing the beliefs and reasoning of a hos-tile agent that believes them to be the same entity (e.g. we believe enemy radar shows two of our ships to be the same ship, or vice-versa. The KAL disaster should bring the right kind of scenario to mind). The representational issue we address is how to represent that fictional single entity in the belief space of the other agent, and what content it should have given that it is an amalgamation of two real entities. A major feature of the paper is our work on embedding within the ViewGen belief-and-point-of-view system the knowledge representation system of our MGR reasoner, and then bringing together the multiple viewpoints offered by ViewGen with the multiple representations of MGR. The fusing of these techniques, we believe, offers a very strong system for extracting message gists from texts and reasoning about them.