On the transformation between possibilistic logic bases and possibilistic causal networks. (English) Zbl 1015.68204

Summary: Possibilistic logic bases and possibilistic graphs are two different frameworks of interest for representing knowledge. The former ranks the pieces of knowledge (expressed by logical formulas) according to their level of certainty, while the latter exhibits relationships between variables. The two types of representation are semantically equivalent when they lead to the same possibility distribution (which rank-orders the possible interpretations). A possibility distribution can be decomposed using a chain rule which may be based on two different kinds of conditioning that exist in possibility theory (one based on the product in a numerical setting, one based on the minimum operation in a qualitative setting). These two types of conditioning induce two kinds of possibilistic graphs. This article deals with the links between the logical and the graphical frameworks in both numerical and quantitative settings. In both cases, a translation of these graphs into possibilistic bases is provided. The converse translation from a possibilistic knowledge base into a min-based graph is also described.


68T35 Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence
68T30 Knowledge representation
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[1] S. Benferhat, D. Dubois, S. Kaci, H. Prade, A graphical reading of possibilistic knowledge bases, in: 17th Conference on Uncertainty in Artificial Intelligence, Seattle, August 1-5, 2001 · Zbl 1001.68573
[2] Ben Amor, N.; Benferhat, S.; Dubois, D.; Geffner, H.; Prade, H., Independence in qualitative uncertainty frameworks, (), 235-246
[3] Benferhat, S.; Dubois, D.; Prade, H., Nonmonotonic reasoning, conditional objects and possibility theory, Art. int., 92, 1-2, 259-276, (1997) · Zbl 1017.68539
[4] Benferhat, S.; Dubois, D.; Prade, H., Syntactic combination of uncertain information: a possibilistic approach, (), 30-42
[5] Benferhat, S.; Dubois, D.; Prade, H., Some syntactic approaches to the handling of inconsistent knowledge bases: a comparative study. part II: the prioritized case, (), 473-511 · Zbl 0930.68149
[6] Benferhat, S.; Dubois, D.; Garcia, L.; Prade, H., Directed possibilistic graphs and possibilistic logic, (), 365-379
[7] Benferhat, S.; Dubois, D.; Garcia, L.; Prade, H., Possibilistic logic bases and possibilistic graphs, (), 57-64
[8] de Campos, L.M.; Huete, J.F., Independence concepts in possibility theory parts I, II, Fuzzy sets syst., 103, (1999), 127-152; 487-505 · Zbl 0951.68150
[9] Cowell, R.G.; Dawid, A.P.; Lauritzen, S.L.; Spiegelhalter, D.J., Probabilistic networks and expert systems, (1999), Springer Berlin · Zbl 0937.68121
[10] Dawid, A.P., Conditional independence in statistical theory, J. roy. statist. soc. A, 41, 1-31, (1979) · Zbl 0408.62004
[11] Dubois, D.; Fariñas del Cerro, L.; Herzig, A.; Prade, H., An ordinal view of independence with application to plausible reasoning, (), 195-203
[12] Dubois, D.; Lang, J.; Prade, H., Possibilistic logic, (), 439-513
[13] Dubois, D.; Prade, H., Fuzzy sets and systems: theory and applications, (1980), Academic Press New York · Zbl 0444.94049
[14] Dubois, D.; Prade, H., Possibility theory – an approach to computerized processing of uncertainty, (1988), Plenum Press New York, (with the collaboration of H. Farreny, R. Martin-Clouaire, C. Testemale)
[15] Dubois, D.; Prade, H., Representation and combination of uncertainty with belief functions and possibility measures, Comput. intell., 4, 4, 244-264, (1988)
[16] Dubois, D.; Prade, H., The logical view of conditioning and its application to possibility and evidence theories, Int. J. approx. reason., 4, 1, 23-46, (1990) · Zbl 0696.03006
[17] Dubois, D.; Prade, H., Inference in possibilistic hypergraphs, (), 250-259
[18] Dubois, D.; Prade, H., Possibilistic logic, preferential models, non-monotonicity and related issues, (), 419-424 · Zbl 0744.68116
[19] Dubois, D.; Prade, H., Possibility theory: qualitative and quantitative aspects, (), 169-226 · Zbl 0924.68182
[20] P. Fonck, Réseaux d’inférence pour le traitement possibiliste, Thèse de doctorat, Univ. de Liège, 1993
[21] Gebhardt, J., Learning from data: possilistic graphical models, (), 315-390
[22] Hisdal, E., Conditional possibilities independence and noninteraction, Fuzzy sets and systems, 1, 283-297, (1978) · Zbl 0393.94050
[23] Jensen, F.V., An introduction to Bayesian networks, (1996), UCL Press University College, London
[24] Lehmann, D.; Magidor, M., What does a conditional knowledge base entail?, Art. int., 55, 1, 1-60, (1992) · Zbl 0762.68057
[25] Lang, J., Possibilistic logic: complexity and algorithms, (), 179-220 · Zbl 0984.03022
[26] Pearl, J., Probabilistic reasoning in intelligent systems: networks of plausible inference, (1988), Morgan Kaufmann Los Altos, CA
[27] Sangüesa, R.; Cortés, U.; Gisolfi, A., A parallel algorithm for building possibilistic causal networks, Int. J. approx. reason., 18, 251-270, (1998) · Zbl 0951.68154
[28] Shenoy, P., Valuation-based systems for discrete optimization, (), 385-400 · Zbl 0741.68094
[29] Shafer, G., A mathematical theory of evidence, (1976), Princeton University Press Princeton, NJ · Zbl 0359.62002
[30] Williams, M.A., Iterated theory base change: a computational model, (), 1541-1550
[31] Zadeh, L.A., Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, 1, 3-28, (1978) · Zbl 0377.04002
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