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-- 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...

Wireless sensor networks produce a large amount of data that needs to be processed, delivered, and assessed according to the application objectives. The way these data are manipulated by the sensor nodes is a fundamental issue. Information fusion arises as a response to process data gathered by sensor nodes and benefits from their processing capability. By exploiting the synergy among the available data, information fusion techniques can reduce the amount of data traffic, filter noisy measurements, and make predictions and inferences about a monitored entity. In this work, we survey the current state-of-the-art of information fusion by presenting the known methods, algorithms, architectures, and models of information fusion, and

This paper is about reasoning with presuppositions in natural language. Presupposition accommodation, as predicted by the linguistic theory of presuppositions as anaphoric expressions, is reconstructed logically as abductive inference in a framework that supports both anaphoric links and a context-dependent notion of propositionhood. Abductive inference arises as a side-effect of the use of the formalism and of characteristics of the communication situation. The proposal is illustrated by some examples and compared to related approaches. Keywords: presupposition resolution, abduction, logical frameworks, semantics-pragmatics interface, context-dependence 1 Introduction In this working note we will study the relation between the presupposition theory of [van der Sandt, 1992] and the type theory of Martin-Lof (MLTT) and its implications for inference processes at the semantics-pragmatics interface. The main claim will be that the anaphoric theory of presuppositions of [van der Sandt, ...

Abduction is a topic that attracts much interest in AI and automated reasoning research. Different approaches have been devised, that give a formalized account of explanatory reasoning, propose methods to compute explanations, frame abduction in the context of logic programming. However, the logical nature of abduction is still far from being clear and different specifications of the key underlying concepts have been given, that make it difficult to speak of abduction as a single welldefined form of reasoning. This work is a preliminary discussion on the logical nature of abductive reasoning, emphasizing the fundamental difference between abductive and deductive inference. Some logical properties of the inference to the "best explanation" are put forward and analyzed when the underlying logic is any extension of classical propositional logic (first order logic, modal logic) or a non monotonic system. Keywords: abduction, explanation, preference, nonmonotonic logic 1 Introduction Abdu...

We consider computational issues when combining logical knowledge bases represented by their characteristic models; in particular, we study taking their logical intersection.

OF THE DISSERTATION The Complexity of Querying Indefinite Information: Defined Relations, Recursion and Linear Order by Ronald van der Meyden, Ph.D. Dissertation Director: L.T. McCarty This dissertation studies the computational complexity of answering queries in logical databases containing indefinite information arising from two sources: facts stated in terms of defined relations, and incomplete information about linearly ordered domains. First, we consider databases consisting of (1) a DATALOG program and (2) a description of the world in terms of the predicates defined by the program as well as the basic predicates. The query processing problem in such databases is related to issues in database theory, including view updates and DATALOG optimization, and also to the Artificial Intelligence problems of reasoning in circumscribed theories and sceptical abductive reasoning. If the program is non-recursive, the meaning of the database can be represented by Clark's Predicate Completion,...

Abstract not found

Introduction: Characterizing the Questions of causal reasoning This chapter describes the mechanism approach to the study of causal reasoning. We will first offer a characterization of the central issues in human causal reasoning, and will discuss how the mechanism approach addresses these issues. In the course of this presentation, we will frequently compare the mechanism approach with alternative accounts based on analyses of covariation, or what is often termed the regularity view. The aims of this chapter are the following: to explain why covariation and mechanism are different, to discuss why such a distinction is actually a useful tool for our understanding of causal reasoning, and to explicate the complementary nature of the two views. Before presenting these two approaches, it is necessary first to offer a description of the domain or problem itself : namely, what are these alternative approaches to? Although there are a number of different ways of characterizing the study of