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Resolution principles in possibilistic logic. (English) Zbl 0697.68083
Summary: An extension of the resolution principle was recently proposed by Dubois and Prade for logical clauses weighted by certainty degrees and was used in theorem proving under uncertainty. These certainty degrees were lower bounds on necessity measures. In the case considered here, the available information may also be an upper bound on a necessity measure, or, if one prefers, a lower bound on the dual possibility measure. It leads to a second resolution principle for clauses weighted in terms of possibility or necessity degrees. The formal analogy between these two resolution principles and the ones existing in modal logic is stressed. Finally, the case where the uncertain clauses include fuzzy predicates, to which the excluded-middle law no longer applies, is studied, and a suitable adaptation of the extended resolution principles is proposed.

68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
03B48 Probability and inductive logic
Full Text: DOI
[1] Zadeh, L.A., Fuzzy sets as a basis for a theory of possibility, Fuzzy sets syst., 1, 3-28, (1978) · Zbl 0377.04002
[2] Dubois, D.; Prade, H.; Dubois, D.; Prade, H., Possibility theory. an approach to computerized processing of uncertainty, (1988), Plenum New York, English version · Zbl 0741.68091
[3] Dubois, D.; Prade, H., An introduction to possibilistic and fuzzy logics (with discussions), (), 287-326
[4] Dubois, D.; Prade, H., Necessity measures and the resolution principle, IEEE trans. syst., man cybern., 17, 474-478, (1987) · Zbl 0643.94053
[5] Robinson, J.A., A machine-oriented logic based on the resolution principle, J. assoc. comput. Mach., 12, 23-41, (1965) · Zbl 0139.12303
[6] Dubois, D.; Lang, J.; Prade, H., Theorem proving under uncertainty—a possibility theory-based approach, (), 984-986
[7] Dubois, D.; Prade, H., The management of uncertainty in expert systems: the possibilistic approach, (), 949-964
[8] Dubois, D.; Prade, H., The management of uncertainty in fuzzy expert systems and some applications, (), 39-58
[9] Dubois, D.; Prade, H., A theorem on implication functions defined from triangular norms, Stochastica VIII, 267-279, (1984) · Zbl 0581.03016
[10] Fariñas del Cerro, L., Resolution modal logic, Logique anal., No. 110-111, 153-172, (1985), (Belgium) · Zbl 0631.03007
[11] Fariñas del Cerro, L.; Penttonen, M., A note on the complexity of the satisfiability of modal Horn clauses, J. logic programming, 4, 1-10, (1987) · Zbl 0624.03010
[12] Hughes, G.E.; Cresswell, M.J., An introduction to modal logic, (1972), Methuen London · Zbl 0855.03002
[13] Dubois, D.; Prade, H.; Testemale, C., In search of a modal system for possibility theory, (), 501-506
[14] Lee, R.C.T., Fuzzy logic and the resolution principle, J. assoc. comput. Mach., 19, 109-119, (1972) · Zbl 0245.02020
[15] Zadeh, L.A., A theory of approximate reasoning, (), 149-194
[16] Zadeh, L.A., Fuzzy sets, Inf. control, 8, 338-353, (1965) · Zbl 0139.24606
[17] Dubois, D.; Prade, H., Properties of measures of information in evidence and possibility theories, Fuzzy sets syst., 24, 161-182, (1987) · Zbl 0633.94009
[18] Prade, H., Reasoning with fuzzy default values, (), 191-197
[19] Orlowska, E.; Wierzchon, S., Mechanical reasoning in fuzzy logic, Logique anal. (Belgium), No. 110-111, 193-207, (1985) · Zbl 0623.03012
[20] Dubois, D.; Lang, J.; Prade, H.; Dubois, D.; Lang, J.; Prade, H., Tech. rep. 304, (), 95-99, Extended version in
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