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 describes a generic, knowledge-based mechanism used to make selections between a fixed set of alternatives. The mechanism, termed sponsor-selector has been used as a control mechanism in a number of different knowledge-based systems including design, planning and problem-solver integration applications. We will discuss the general applicability of the sponsor-selector mechanism and describe a number of systems in which has been successfully used. 1 Introduction Selection is a recurring problem that has occurred throughout work in knowledge-based systems. Knowledge-based selection has two components. The first is the problem of selection itself, that is the design of a mechanism for selecting an item from a fixed set of alternatives. Many early problem-solving systems encountered the selection problem and devised mechanism for dealing with it: ffl conflict resolution in production systems like OPS5 [9, 10], which is the procedure for selecting which of several applicable ...