In this paper we present an extension of the spectrum of logical de nitions of model-based diagnosis introduced in (Console &Torasso 1991b). The extended spectrum considers the case of temporal model-based diagnosis and generalizes the logical characteriza

A few remarks are worth in conclusion on the computation of temporal diagnoses, which is a very complex problem (an underconstrained problem, as already noticed in (Hamscher& Davis 1984)). In (Brusoni et al. 1995) we presented an algorithm for computing diagnoses in a restricted case of our general framework, namely in the case where only one episode for each ground atom is allowed this allows us to deal only with limited forms of dynamic and time-varying behavior and thus the attention is focused on temporal non-dynamic behavior. Allen, J. 1983. Maintaining knowledge about temporal intervals. Communications of the ACM 26:832{ 843. Besnard, P., and Cordier, M. 1994. Explanatory diagnoses and their characterization by circumscription. Annals of Mathematics and Arti cial Intelligence 11(1-4):75{96. Brusoni, V. Console, L. Terenziani, P. and Theseider Dupre, D. 1995. An e cient algorithm for computing temporal abductive diagnoses. In Proc. DX 95, Sixth Int. Workshop on Principles of Diagnosis. Brusoni, V. Console, L. Terenziani, P. and Theseider Dupre, D. 1996. Characterizing temporal abductive diagnosis. Technical report, Dip. Informatica, Universita' di Torino. A short version appeared in Proc. DX 95, Sixth Int. Workshop on Principles of Diagnosis. Brusoni, V. Console, L. Pernici, B. and Terenziani, P. February 1997. Later: an e cient, general purpose manager of temporal information. IEEE Expert (to appear). Console, L., and Torasso, P. 1991a. On the cooperation between abductive and temporal reasoning in medical diagnosis. Arti cial Intelligence in Medicine 3(6):291{311. Console, L., and Torasso, P. 1991b. A spectrum of logical de nitions of model-based diagnosis. Computational Intelligence 7(3):133{141. Console, L. Portinale, L. Theseider Dupre, D. and Torasso, P. 1994. Diagnosing time-varying misbehavior: an approach based on model decomposition. Annals of Mathematics and Arti cial Intelligence 11(14):381{398. Console, L. Theseider Dupre, D. and Torasso, P. 1991. On the relationship between abduction and deduction. Journal of Logic and Computation 1(5):661{ 69

0. Davis, R. 1984. Diagnostic reasoning based on structure and behavior. Arti cial Intelligence 24(1-3):347{ 410. de Kleer, J., and Williams, B. 1987. Diagnosing multiple faults. Arti cial Intelligence 32(1):97{130.

References

de Kleer, J. Mackworth, A. and Reiter, R. 1992. Characterizing diagnoses and systems. Arti cial Intelligence 56(2{3):197{222. DeCoste, D. 1991. Dynamic across-time measurement interpretation. Arti cial Intelligence 51(1-3):273{341. Downing, K. 1992. Consistency-based diagnosis in physiological domains. In Proc. AAAI-92, 558{563. Dvorak, D., and Kuipers, B. 1989. Model-based monitoring of dynamic systems. In Proc. 11th IJCAI, 1238{1243. Friedrich, G., and Lackinger, F. 1991. Diagnosing temporal misbehaviour. In Proc. 12th IJCAI, 1116{ 1122. Genesereth, M. 1984. The use of design descriptions in automated diagnosis. Arti cial Intelligence 24(13):411{436. Guckenbiehl, T., and Schafer-Richter, G. 1990. SIDIA: Extending prediction based diagnosis to dynamic models. In Gottlob, G., and Nejdl, W., eds., Proc. Int. Workshop on Expert Systems in Engineering. Springer Verlag LNCS 462. 53{68. Hamscher, W., and Davis, R. 1984. Diagnosing circuit with state: an inherently underconstrained problem. In Proc. AAAI 84, 142{147. Hamscher, W. Console, L. and de Kleer, J., eds. 1992. Readings in Model-Based Diagnosis. Morgan Kaufmann. Hamscher, W. 1991. Modeling digital circuits for troubleshooting. Arti cial Intelligence 51(1-3):223{ 271. Lackinger, F., and Nejdl, W. 1991. Integrating modelbased monitoring and diagnosis of complex dynamic systems. In Proc. 12th IJCAI, 1123{1128. Long, W. 1983. Reasoning about state from causation and time in a medical domain. In Proc AAAI 83, 251{ 254. Nejdl, W., and Gamper, J. 1994. Harnessing the power of temporal abstractions in model-based diagnosis of dynamic systems. In Proc. 11th ECAI, 667{ 671. Ng, H. 1991. Model-based, multiple fault diagnosis of dynamic, continuous physical devices. IEEE Expert 6(6):38{43. Nokel, K. 1989. Temporal matching: Recognizing dynamic situations from discrete measurements. In Proc. 11th IJCAI, 1255{1260. Pan, J. 1984. Qualitative reasoning with deep-level mechanism models for diagnoses of mechanisms failures. In Proc. 1st IEEE Conference on AI Applications (CAIA), 295{301. Poole, D. 1989. Normality and faults in logic-based diagnosis. In Proc. 11th IJCAI, 1304{1310. Preist, C. Eshghi, K. and Bertolino, B. 1994. Consistency-based and abductive diagnoses as gen-