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Distance-based paraconsistent logics. (English) Zbl 1189.03035
Summary: We introduce a general framework that is based on distance semantics and investigate the main properties of the entailment relations that it induces. It is shown that such entailments are particularly useful for nonmonotonic reasoning and for drawing rational conclusions from incomplete and inconsistent information. Some applications are considered in the context of belief revision, information integration systems, and consistent query answering for possibly inconsistent databases.

MSC:
03B53 Paraconsistent logics
03B50 Many-valued logic
68T37 Reasoning under uncertainty in the context of artificial intelligence
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[1] Abiteboul, S.; Hull, R.; Vianu, V., Foundations of databases, (1995), Addison-Wesley
[2] Alchourrón, C.E.; Gärdenfors, P.; Makinson, D., On the logic of theory change: partial meet contraction and revision function, Journal of symbolic logic, 50, 510-530, (1985) · Zbl 0578.03011
[3] M. Arenas, L. Bertossi, J. Chomicki. Consistent query answers in inconsistent databases, in: Proceedings of the 18th Symposium on Principles of Database Systems (PODS’99), 1999, pp. 68-79. · Zbl 1079.68026
[4] Arenas, M.; Bertossi, L.; Chomicki, J., Answer sets for consistent query answering in inconsistent databases, Theory and practice of logic programming, 3, 4-5, 393-424, (2003) · Zbl 1079.68026
[5] Arieli, O., Paraconsistent preferential reasoning by signed quantified Boolean formulae, (), 773-777 · Zbl 1367.68274
[6] O. Arieli, Paraconsistent reasoning and preferential entailments by signed quantified Boolean formulae, ACM Transactions on Computational Logic, 8(3) (2007), Article 18. · Zbl 1367.68274
[7] Arieli, O.; Avron, A., The value of the four values, Artificial intelligence, 102, 1, 97-141, (1998) · Zbl 0928.03025
[8] Arieli, O.; Denecker, M., Reducing preferential paraconsistent reasoning to classical entailment, Journal of logic and computation, 13, 4, 557-580, (2003) · Zbl 1034.03023
[9] Arieli, O.; Denecker, M.; Bruynooghe, M., Distance-based repairs of databasese, (), 43-55 · Zbl 1152.68434
[10] Arieli, O.; Denecker, M.; Van Nuffelen, B.; Bruynooghe, M., Computational methods for database repair by signed formulae, Annals of mathematics and artificial intelligence, 46, 1-2, 4-37, (2006) · Zbl 1097.68549
[11] Avron, A., Natural 3-valued logics: characterization and proof theory, Journal of symbolic logic, 56, 1, 276-294, (1991) · Zbl 0745.03017
[12] Batens, D., Dynamic dialectical logics, (), 187-217 · Zbl 0695.03011
[13] Batens, D., Inconsistency-adaptive logics, (), 445-472 · Zbl 0923.03036
[14] ()
[15] Belnap, N.D., How a computer should think, (), 30-56
[16] Belnap, N.D., A useful four-valued logic, (), 7-37
[17] Ben Naim, J., Lack of finite characterizations for the distance-based revision, (), 239-248
[18] S. Benferhat, C. Cayrol, D. Dubois, J. Lang, H. Prade, Inconsistency management and prioritized syntax-based entailment, in: Proceedings of the 13th International Joint Conference on Artificial Intelligence (IJCAI’93), 1993, pp. 640-645.
[19] L. Bravo, L. Bertossi, Logic programming for consistently querying data integration systems, in: G. Gottlob, T. Walsh (Eds.), Proceedings of the 18th International Joint Conference on Artificial Intelligence (IJCAI’03), 2003, pp. 10-15.
[20] ()
[21] Chomicki, J., Consistent query answering: five easy pieces, (), 1-17
[22] Chomicki, J.; Marchinkowski, J., Minimal-change integrity maintenance using tuple deletion, Information and computation, 197, 1-2, 90-121, (2005) · Zbl 1075.68022
[23] da Costa, N.C.A., On the theory of inconsistent formal systems, Notre dame journal of formal logic, 15, 497-510, (1974) · Zbl 0236.02022
[24] Dalal, M., Investigations into a theory of knowledge base revision, (), 475-479
[25] de Amo, S.; Carnielli, W.A.; Marcos, J., A logical framework for integrating inconsistent information in multiple databases, (), 67-84 · Zbl 1044.68049
[26] J. Delgrande, Preliminary considerations on the modelling of belief change operators by metric spaces, in: Proceedings of the 10th International Workshop on Non-Monotonic Reasoning (NMR’04), 2004, pp. 118-125.
[27] Delgrande, J.; Dubois, D.; Lang, J., Iterated revision and prioritized merging, (), 210-220
[28] D’ottaviano, I., The completeness and compactness of a three-valued first-order logic, Revista colombiana de matematicas, XIX, 1-2, 31-42, (1985)
[29] Dubois, D.; Prade, H., Belief change and possibility theory, (), 142-182
[30] D. Eckert, G. Pigozzi, Belief merging, judgment aggregation, and some links with social choice theory, in: J. Delgrande, J. Lang, H. Rott, J. Tallon (Eds.), Proceedings of Dagstuhl Seminar No. 05321. 2005.
[31] Eiter, T.; Fink, M.; Greco, G.; Lembo, D., Efficient evaluation of logic programs for querying data integration systems, (), 163-177 · Zbl 1204.68080
[32] Epstein, R.L., The semantic foundations of logic, Propositional logics, vol. I, (1990), Kluwer
[33] Fitting, M., Kleene’s logic, generalized, Logic and computation, 1, 797-810, (1990) · Zbl 0744.03025
[34] Gabbay, D., Theoretical foundation for non-monotonic reasoning, part II: structured non-monotonic theories, (), 19-39
[35] Greco, S.; Zumpano, E., Querying inconsistent databases, (), 308-325 · Zbl 0988.68061
[36] Grove, A., Two modellings for theory change, Journal of philosophical logic, 17, 157-180, (1988) · Zbl 0639.03025
[37] Katsumo, H.; Mendelzon, A.O., Propositional knowledge base revision and minimal change, Artificial intelligence, 52, 263-294, (1991) · Zbl 0792.68182
[38] Hájek, P., Metamatematics of fuzzy logic, (1998), Kluwer
[39] Kleene, S.C., Introduction to metamathematics, (1950), Van Nostrand · Zbl 0047.00703
[40] Konieczny, S.; Lang, J.; Marquis, P., Distance-based merging: a general framework and some complexity results, (), 97-108
[41] Konieczny, S.; Pino Pérez, R., Merging information under constraints: a logical framework, Logic and computation, 12, 5, 773-808, (2002) · Zbl 1020.68086
[42] Kraus, S.; Lehmann, D.; Magidor, M., Nonmonotonic reasoning, preferential models and cumulative logics, Artificial intelligence, 44, 1-2, 167-207, (1990) · Zbl 0782.03012
[43] Lafage, C.; Lang, J., Logical representation of preference for group decision making, (), 457-468
[44] Lafage, C.; Lang, J., Propositional distances and preference representation, (), 48-59 · Zbl 1005.68547
[45] Lehmann, D.; Magidor, M., What does a conditional knowledge base entail?, Artificial intelligence, 55, 1-60, (1992) · Zbl 0762.68057
[46] Lehmann, D.; Magidor, M.; Schlechta, K., Distance semantics for belief revision, Journal of symbolic logic, 66, 1, 295-317, (2001) · Zbl 0985.03012
[47] Lin, J.; Mendelzon, A.O., Knowledge base merging by majority, () · Zbl 0926.68135
[48] Makinson, D., General patterns in nonmonotonic reasoning, (), 35-110
[49] McCarthy, J., Circumscription – a form of non monotonic reasoning, Artificial intelligence, 13, 1-2, 27-39, (1980) · Zbl 0435.68073
[50] Peppas, P.; Chopra, S.; Foo, N., Distance semantics for relevance-sensitive belief revision, (), 319-328
[51] Pigozzi, G., Two aggregation paradoxes in social decision making: the ostrogorski paradox and the discursive dilemma, Episteme: A journal of social epistemology, 2, 2, 33-42, (2005)
[52] Priest, G., Reasoning about truth, Artificial intelligence, 39, 231-244, (1989) · Zbl 0694.03021
[53] Priest, G., Minimally inconsistent LP, Studia logica, 50, 321-331, (1991) · Zbl 0748.03017
[54] Priest, G., Paraconsistent logic, (), 287-393
[55] Reiter, R., On closed world databases, (), 55-76
[56] Rozoner, L.I., On interpretation of inconsistent theories, Information sciences, 47, 243-266, (1989) · Zbl 0677.03019
[57] Schlechta, K., Coherent systems, Studies in logic and practical reasoning, vol. 2, (2004), Elsevier · Zbl 1061.03002
[58] Shoham, Y., Reasoning about change: time and causation from the standpoint of artificial intelligence, (1988), MIT Press
[59] Spohn, W., Ordinal conditional functions: a dynamic theory of epistemic states, (), 105-134
[60] Tarski, A., Introduction to logic, (1941), Oxford University Press · Zbl 0025.00401
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