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Probabilistic consistency of knowledge bases in inference systems

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Book cover Symbolic and Quantitative Approaches to Reasoning and Uncertainty (ECSQARU 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 747))

Abstract

We consider a probabilistic knowledge base represented by a conditional probability assessment on an arbitrary finite family of conditional events. Following the approach of de Finetti to conditional events, we use the concept of generalized atom to introduce a suitable matrix representing the truth values of the given conditional events. Moreover, we prove some theoretical results, by means of which using the linear programming technique a procedure to check the probabilistic consistency of the given knowledge base can be easily constructed. Finally, a simple example is examined.

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References

  1. B. De Finetti: Theory of probability. A.F.M. Smith and A. Machì (trs.), 2 Voll. New York: John Wiley 1974, 1975

    Google Scholar 

  2. A. Gilio, R. Scozzafava: Le probabilita' condizionate coerenti nei sistemi esperti. In: Atti Giornate di lavoro A.I.R.O. su “Ricerca Operativa e Intelligenza Artificiale”. Pisa: Offset Grafica, 1988, pp. 317–330

    Google Scholar 

  3. G. Coletti, A. Gilio, R. Scozzafava: Coherent qualitative probability and uncertainty in Artificial Intelligence.In: C. N. Manikopoulos (ed.): Proc. of The 8th Int. Congr. of Cybernetics and Systems 1. New York: The NJIT Press 1990, pp. 132–138

    Google Scholar 

  4. G. Coletti, A. Gilio, R. Scozzafava: Conditional events with vague information in expert systems. In: B. Bouchon-Meunier, R. R. Yager, L. A. Zadeh (eds.): Uncertainty in knowledge bases. Lecture Notes in Computer Science 521. Berlin: Springer — Verlag 1991, pp. 106–114

    Google Scholar 

  5. G. Coletti, A. Gilio, R. Scozzafava: Assessment of qualitative judgements for conditional events in expert systems. In: R. Kruse, P. Siegel (eds.): Symbolic and quantitative approaches to uncertainty. Lecture Notes in Computer Science 548. Berlin: Springer — Verlag 1991, pp. 135–140

    Google Scholar 

  6. G. Coletti, A. Gilio, R. Scozzafava: Comparative probability for conditional events: a new look through coherence. Theory and Decision. (To appear)

    Google Scholar 

  7. G. Coletti: Comparative probabilities ruled coherence conditions and use in expert systems. Intern. Journal of General Systems. (To appear)

    Google Scholar 

  8. G. Coletti: Coherent numerical and ordinal probabilistic assessments. IEEE Transactions on Systems, Man, and Cybernetics. (To appear)

    Google Scholar 

  9. R. Scozzafava: Subjective probability versus belief functions in artificial intelligence. Intern. Journal of General Systems. (To appear)

    Google Scholar 

  10. A. Gilio, F. Spezzaferri: Knowledge integration for conditional probability assessments. In: D. Dubois, M. P. Wellman, B. D'Ambrosio, P. Smets (eds.): Uncertainty in Artificial Intelligence. San Mateo, California: Morgan Kaufmann Publishers 1992, pp. 98–103

    Google Scholar 

  11. A. Gilio: Criterio di penalizzazione e condizioni di coerenza nella valutazione soggettiva della probabilità. Bollettino della Unione Matematica Italiana (7) 4-B, 645–660 (1990)

    Google Scholar 

  12. A. Gilio, R. Scozzafava: Conditional events in probability assessment and revision. IEEE Transactions on Systems, Man, and Cybernetics. (To appear)

    Google Scholar 

  13. P.G. Calabrese: Deduction and inference using conditional logic and probability. In: I.R. Goodman, M. M. Gupta, H. T. Nguyen, G. S. Rogers (eds.): Conditional Logic in Expert Systems. Amsterdam: North-Holland 1991, pp. 71–100

    Google Scholar 

  14. D. Dubois, H. Prade: Conditioning, non-monotonic logic and non-standard uncertainty models. In: I. R. Goodman, M. M. Gupta, H. T. Nguyen, G. S. Rogers (eds.): Conditional Logic in Expert Systems. Amsterdam: North — Holland 1991, pp. 115–158

    Google Scholar 

  15. I. R. Goodman, H. T. Nguyen, E. A. Walker: Conditional inference and logic for intelligent systems: a theory of measure-free conditioning. Amsterdam: North-Holland 1991

    Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Metodi e Modelli Matematici, Via A. Scarpa 10, 00161, Roma, Italy

    Angelo Gilio

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  1. Angelo Gilio
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Michael Clarke Rudolf Kruse Serafín Moral

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© 1993 Springer-Verlag Berlin Heidelberg

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Gilio, A. (1993). Probabilistic consistency of knowledge bases in inference systems. In: Clarke, M., Kruse, R., Moral, S. (eds) Symbolic and Quantitative Approaches to Reasoning and Uncertainty. ECSQARU 1993. Lecture Notes in Computer Science, vol 747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028196

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  • DOI: https://doi.org/10.1007/BFb0028196

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57395-1

  • Online ISBN: 978-3-540-48130-0

  • eBook Packages: Springer Book Archive

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