A Model Counting Characterization of Diagnoses

Abstract : Given the description of a physical system in one of several forms (a set of constraints, Bayesian network etc.) and a set of observations made, the task of model-based diagnosis is to find a suitable assignment to the modes of behavior of individual components (this notion can also be extended to handle transitions and dynamic systems ?Kurien and Nayak 20001. Many formalisms have been proposed in the past to characterize diagnoses and systems. These include consistency-based diagnosis, fault models, abduction, combinatorial optimization, Bayesian model selection etc. Different approaches are apparently well suited for different applications and representational forms in which the system description is available. In this paper, we provide a unifying theme behind all these approaches based on the notion of model counting. By doing this, we are able to provide a universal characterization of diagnoses that is independent of the representational form of the system description. We also show how the shortcomings of previous approaches (mostly associated with their inability to reason about different elements of knowledge like probabilities and constraints) are removed in our framework. Finally, we report on the computational tractability of diagnosis-algorithms based on model counting.

[1]  David Poole,et al.  Probabilistic Horn Abduction and Bayesian Networks , 1993, Artif. Intell..

[2]  Kenneth D. Forbus,et al.  Building Problem Solvers , 1993 .

[3]  P. Pandurang Nayak,et al.  A Model-Based Approach to Reactive Self-Configuring Systems , 1996, AAAI/IAAI, Vol. 2.

[4]  ConsoleLuca,et al.  A spectrum of logical definitions of model-based diagnosis , 1991 .

[5]  Jürg Kohlas,et al.  Model-Based Diagnostics and Probabilistic Assumption-Based Reasoning , 1998, Artif. Intell..

[6]  Margherita Pagani,et al.  Second Edition , 2004 .

[7]  P. Pandurang Nayak,et al.  Back to the Future for Consistency-Based Trajectory Tracking , 2000, AAAI/IAAI.

[8]  Raymond Reiter,et al.  Characterizing Diagnoses and Systems , 1992, Artif. Intell..

[9]  Peter J. F. Lucas,et al.  Analysis of Notions of Diagnosis , 1998, Artif. Intell..

[10]  J. Dekleer.  An assumption-based TMS , 1986 .

[11]  Brian C. Williams,et al.  Diagnosis with Behavioral Modes , 1989, IJCAI.

[12]  P. Pandurang Nayak,et al.  Fast Context Switching in Real-Time Propositional Reasoning , 1997, AAAI/IAAI.

[13]  T. K. Satish Kumar.  An Information-Theoretic Characterization of Abstraction in Diagnosis and Hypothesis Selection , 2002, SARA.

[14]  Raymond Reiter,et al.  A Theory of Diagnosis from First Principles , 1986, Artif. Intell..

[15]  David Poole,et al.  A methodology for using a default and abductive reasoning system , 1989, Int. J. Intell. Syst..

[16]  Peter J. F. Lucas.  Bayesian model-based diagnosis , 2001, Int. J. Approx. Reason..

[17]  Verzekeren Naar Sparen,et al.  Cambridge , 1969, Humphrey Burton: In My Own Time.

[18]  Brian C. Williams,et al.  Diagnosing Multiple Faults , 1987, Artif. Intell..

[19]  Peter Struss,et al.  "Physical Negation" Integrating Fault Models into the General Diagnostic Engine , 1989, IJCAI.

[20]  Pieter J. Mosterman,et al.  Diagnosis of continuous valued systems in transient operating regions , 1999, IEEE Trans. Syst. Man Cybern. Part A.

[21]  Murray Shanahan,et al.  Explanation in the Situation Calculus , 1993, IJCAI.

[22]  Pietro Torasso,et al.  A Theory of Diagnosis for Incomplete Causal Models , 1989, IJCAI.

[23]  T. K. Satish Kumar.  QCBFS : Leveraging Qualitative Knowledge in Simulation-Based Diagnosis , .

[24]  Luca Console,et al.  Readings in Model-Based Diagnosis , 1992 .

[25]  Roberto J. Bayardo,et al.  Counting Models Using Connected Components , 2000, AAAI/IAAI.

[26]  Adnan Darwiche.  On the tractable counting of theory models and its application to belief revision and truth maintenance , 2000, ArXiv.

[27]  Richard M. Karp,et al.  Monte-Carlo Approximation Algorithms for Enumeration Problems , 1989, J. Algorithms.

[28]  Sheila A. McIlraith.  Explanatory Diagnosis: Conjecturing Actions to Explain Observations , 1998, KR.

[29]  Pietro Torasso,et al.  A spectrum of logical definitions of model‐based diagnosis 1 , 1991, Comput. Intell..