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-...

Abduction is an important inference process underlying much of human intelligent activities, including text understanding, plan recognition, disease diagnosis, and physical device diagnosis. In this paper, we describe some problems encountered using abduction to understand text, and present some solutions to overcome these problems. The solutions we propose center around the use of a different criterion, called explanatory coherence, as the primary measure to evaluate the quality of an explanation. In addition, explanatory coherence plays an important role in the construction of explanations, both in determining the appropriate level of specificity of a preferred explanation, and in guiding the heuristic search to efficiently compute explanations of sufficiently high quality.

this paper is to enlarge in an unified way the scope of XLP applications to diagnosis, and to declarative debugging. The expressive power of XLP to do so is attained by allowing would be contradictory programs to be adequately revised by a contradiction removal semantics which withdraws assumptions that support contradiction and revises them to false. We elaborate on the work of [15, 16] on contradiction removal of extended logic programs (CRSX), and also show how Reiter's algorithm DIAGNOSE [25, 10] is used to implement a sound contradiction removal algorithm based on the Well Founded Semantics meta-interpreters of [19, 18], so as to obtain three-valued revisions (to the undefined truth-value) of (negative) assumptions. To obtain a two-valued revision, assumptions are changed instead into their complements. Since this may introduce fresh contradictions, the contradiction removal algorithm must be iterated. So the algorithm consists of iterated two-valued partial revisions as directed by three-valued revision oppurtunities. As a result we obtain more accumulating evidence that a large class of problems can be solved with a contradiction removal approach. Its relationship to abduction is studied in [1, 14]. In short, minimal contradiction removal is comparable to maximal consistent abduction. [3] unifies the abductive and consistency-based approaches to diagnosis, and so, for generality, we present a methodology that transforms a diagnostic problem of [3] into an extended logic program and solve it with contradiction removal. Another unifying approach to diagnosis with logic programming [23] uses Generalised Stable Models [11]. They present criticisms of Console and Torasso's approach which do not carry over to our representation, ours having the advantage of a more expr...

Formal AI systems traditionally represent knowledge using logical formulas. Sometimes, however, a model-based representation is more compact and enables faster reasoning than the corresponding formula-based representation. The central idea behind our work is to represent a large set of models by a subset of characteristic models. More specifically, we examine model-based representations of Horn theories, and show that there are large Horn theories that can be exactly represented by an exponentially smaller set of characteristic models. We show that deduction based on a set of characteristic models requires only polynomial time, as it does using Horn theories. More surprisingly, abduction can be performed in polynomial time using a set of characteristic models, whereas abduction using Horn theories is NP-complete. Finally, we discuss algorithms for generating efficient representations of the Horn theory that best approximates a general set of models. 1 Introduction Logical formulas are...

Suppose that HY P is a set of hypotheses which we currently entertain about some state of affairs represented by a propositional sentence \Sigma. In a diagnostic setting, HY P might consist of all the diagnoses of some device whose description is given by \Sigma, although our analysis is not restricted to diagnosis. Our concern is with tests -- how they can be designed, and what conclusions can be drawn about the hypotheses in HY P as a result of performing tests. Specifically, we define the concept of a test and the concept of the outcome of a test. We characterize those tests whose outcomes refute or confirm an hypothesis, and discriminate between competing hypotheses. These characterizations are in terms of the prime implicates of \Sigma, and hence are implementable using assumption-based truth maintenance systems. In addition, we characterize the impact of a test outcome on consistency-based and abductive hypothesis spaces. Finally, we provide a characterization of differential dia...

We present IDA --- an Incremental Diagnostic Algorithm which computes minimal diagnoses from diagnoses, and not from conflicts. As a consequence of this, and by using different models, one can control the computational complexity. In particular, we show that by using a model of the normal behavior, the worst-case complexity of the algorithm to compute the k + 1-st minimal diagnosis is O(n 2k ), where n is the number of components. On the practical side, an experimental evaluation indicates that the algorithm can efficiently diagnose devices consisting of a few thousand components. We propose to use a hierarchy of models: first a structural model to compute all minimal diagnoses, then a normal behavior model to find the additional diagnoses if needed, and only then a fault model for their verification. IDA separates model interpretation from the search for minimal diagnoses in the sense that the model interpreter is replaceable. In particular, we show that in some domains it is advan...

Abstract. Abduction is the process of explaining a given query with respect to some background knowledge. For instance, p is an explanation for the query q given the knowledge p → q. This problem is well-known to have many applications, in particular in Artificial Intelligence, and has been widely studied from both an AI and a complexity-theoretic point of view. In this paper we completely classify the complexity of propositional abduction in Schaefer’s famous framework. We consider the case where knowledge bases are taken from a class of formulas in generalized conjunctive normal form. This means that the propositional formulas considered are conjunctions of constraints taken from a fixed finite language. We show that according to the properties of this language, deciding whether at least one explanation exists is either polynomial, NP-complete or ΣP 2-complete. Our results are stated for a query consisting of a single, positive literal and for assumption-based solutions, i.e., the solutions must be formed upon a distinguished subset of the variables that is part of the input. We however show that our results can be interpreted “dually ” for negative queries, and thus also for unrestricted (positive or negative) queries.

We address the problem of propositional logic-based abduction, i.e., the problem of searching for a best explanation for a given propositional observation according to a given propositional knowledge base. We give a general algorithm, based on the notion of projection; then we study restrictions over the representations of the knowledge base and of the query, and find new polynomial classes of abduction problems. We also show that our algorithm unifies several previous results.

Diagnosis is an important application area of Artificial Intelligence. First generation expert diagnostic systems had exhibited difficulties which motivated the development of model-based reasoning techniques. Model-based diagnosis is the activity of locating malfunctioning components of a system solely on the basis of its structure and behavior. The paper gives a brief overview of the main concepts, problems, and research results in this area. 1 Introduction Diagnosis is one of the earliest areas in which application of Artificial Intelligence techniques was attempted. The diagnosis of a system which behaves abnormally consists of locating those subsystems whose abnormal behavior accounts for the observed behavior. For example, a system being diagnosed might be a mechanical device exhibiting malfunction, or a human patient. There are two fundamentally different approaches to diagnostic reasoning. In the first, heuristic approach, one attempts to codify diagnostic rules of thumb and p...