Qualifying the Expressivity/Eiticiency Tradeoff: Reformation-Based Diagnosis

This paper presents an approach to model-based diagnosis that first compiles a first-order system description to a propositional representation, and then solves the diagnostic problem as a linear programming instance. Relevance reasoning is employed to isolate parts of the system that are related to certain observation types and to economically instantiate the theory, while methods from operations research offer promising results to generate near-optimal diagnoses efficiently. Introduction and Motivation A central problem of model-based diagnosis is the computational complexity of the underlying diagnostic reasoning task (see, e.g. Eiter and Gottlob (1995)). Therefore, several researchers have proposed to preprocess a given system description, mostly a propositional theory, such that the ’compiled’ form can be processed more efficiently (Williams & Nayak 1996; Darwiche 1998). In many cases, however, it is more natural to describe systems in a more expressive language, such as firstorder logic. In this paper, we will consider the case where the system description is given as a first-order Horn theory (without function symbols), and compile this description to a propositional one. Techniques from relevance reasoning (Levy, Fikes, ~ Sagiv 1997; Schurz 1999) will be employed to keep the resulting propositional theory within manageable size. More specifically, relevance reasoning is used to filter out the part of the system that is ’relevant’ for certain observation types, and to economically instantiate variables by appropriate constants (usually denoting values of system attributes). In this way, we may preserve the compactness of first-order descriptions, and allow for processing an efficient propositional theory. Thus we qualify the notorious expressivity/efficiency tradeoff. Given a propositional system description, we will use the Networked Bubble Propagation (NBP) mechanism (Ohsawa & Ishizuka 1997), a high-speed hypothetical (’abductive’) reasoner, as the diagnostic engine. Focusing on most-probable (least-expensive) diagnoses Copyright Q1999, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. realized by assigning a numerical weight to each hypothesis (possible system fault). The NBP mechanism tries to find an optimal solution, i.e., a diagnosis with a minimal sum of individual faults’ weights, and actually generates a near-optimal solution in polynomial time of approximately 0(n14), where n the number of hypotheses in the problem formulation. The efficiency of the NBP mechanism relies on methods from the area of 0-1 integer linear programming. Following a comprehensive step-by-step approach, we show how a general definition of model-based diagnosis can be translated to a integer linear programming problem. Although the possibility of such a translation is not completely surprising, we are not aware of any previous attempts in the literature. In the planning field, however, Bylander (1997) shows how to translate propositional STRIPS planning instances to linear programming instances, and Williams and Nayak (1996) recast their model-based configuration manager as a combinatorial optimization problem. The main contribution of this paper can be seen as bringing together methods from the fields of deductive databases and operations research. In particular, relevance reasoning is employed to preprocess a given behavioral model encoded in first-order Horn logic, and operations research methods allow to efficiently solve diagnosis problems. The rest of the paper is organized as follows. In the following section, we explain some notions related to model-based diagnosis. Then we introduce a general framework for extracting information relevant to finding diagnoses, relative to certain observation types and the structure of the system. Moreover, we discuss a sophisticated instantiation method based on relevance reasoning. Next, we explain how hypothetical reasoning problems (corresponding to diagnostic problems) can recast as problems of integer linear programming. We also report on some preliminary experimental results obtained in testing our approach. Finally, we discuss related work and draw some conclusions. Model-based Diagnosis A diagnostic problem is characterized by a set of observations to be explained, given a behavioral model From: AAAI-99 Proceedings. Copyright © 1999, AAAI (www.aaai.org). All rights reserved.