Quasi-Possibilistic Logic and its Measures of Information and Conflict

• Autorzy: Dubois D. , Konieczny S. , Prade H.
• Języki publikacji: EN

Abstrakty

EN

Possibilistic logic and quasi-classical logic are two logics that were developed in artificial intelligence for coping with inconsistency in different ways, yet preserving the main features of classical logic. This paper presents a new logic, called quasi-possibilistic logic, that encompasses possibilistic logic and quasi-classical logic, and preserves the merits of both logics. Indeed, it can handle plain conflicts taking place at the same level of certainty (as in quasi-classical logic), and take advantage of the stratification of the knowledge base into certainty layers for introducing gradedness in conflict analysis (as in possibilistic logic). When querying knowledge bases, it may be of interest to evaluate the extent to which the relevant available information is precise and consistent. The paper review measures of (im)precision and inconsistency/conflict existing in possibilistic logic and quasi-classical logic, and proposes generalized measures in the unified framework.

Słowa kluczowe

EN

possibilistic logic; paraconsistent logic; measures of information; inconsistency; uncertainty

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2003
• Tom: Vol. 57, nr 2-4
• Strony: 101--125
• Opis fizyczny: Bibliogr. 32 poz.

Twórcy

autor

Dubois D.

• Institut de Recherche en Informatique de Tuluse, 118 rute de Narbonne, 31062 Toulouse, Cedex 4, France

autor

Konieczny S.

• Institut de Recherche en Informatique de Tuluse, 118 rute de Narbonne, 31062 Toulouse, Cedex 4, France

autor

Prade H.

• Institut de Recherche en Informatique de Tuluse, 118 rute de Narbonne, 31062 Toulouse, Cedex 4, France

Bibliografia

• [1] Belnap, N.: A useful four-valued logic, Modern uses of multiple-valued logic, 1977, 8-37.
• [2] Benferhat, S., Dubois, D., Prade, H.: Some syntactic approaches to the handling of inconsistent knowledge bases: a comparative study, part 1: the flat case, Studia Logica, 58, 1997, 17-45.
• [3] Benferhat, S., Dubois, D., Prade, H.: An overview of inconsistency-tolerant inferences in prioritized knowledge bases, in: Fuzzy Sets, Logic and Reasoning about Knowledge, vol. 15 of Applied Logic Series, Kluwer, 1999, 395-417.
• [4] Besnard, P., Hunter, A.: Quasi-classical logic: Non-trivializable classical reasoning from inconsistent information, Proceedings of the 3rd European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty (ECSQARU’95), LNAI 946, Springer Verlag, 1995.
• [5] Besnard, P., Lang, J.: Possibility and necessity functions over non-classical logics, Proceedings of the 10th Int. Conf. on Uncertainty in Artificial Intelligence (UAI’94), 1994.
• [6] Cayrol, C., Lagasquie-Schiex, M.: Non-monotonic syntax-based entailment: a classification of consequence relations, Proceedings of the 3rd European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty (ECSQARU’95), LNAI 946, Springer Verlag, 1995.
• [7] Dubois, D., Lang, J., Prade, H.: Automated reasoning using possibilistic logic: Semantics, belief revision and variable certainty weights, IEEE Trans. Data and Knowledge Engineering, 6, 1994, 64-71.
• [8] Dubois, D., Lang, J., Prade, H.: Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, chapter Possibilistic logic, Oxford University Press, 1994, 439-513.
• [9] Dubois, D., Prade, H.: Properties of measures of information in evidence and possibility theories, Fuzzy Sets and Systems, 24, 1987, 161-182, Reprinted in Fuzzy Sets and Systems, supplement to Vol. 100, 35-49, 1999.
• [10] Dupin de Saint-Cyr, F., Lang, J., Schiex, T.: Penalty logic and its links with Dempster-Shafer theory, Proceedings of the 10th Int. Conf. on Uncertainty in Artificial Intelligence (UAI’94), 1994.
• [11] Gärdenfors, P.: Knowledge in flux, MIT Press, 1988.
• [12] Hartley, R. V. L.: Transmission of information, The Bell Systems Technical Journal, 1928, 535-563.
• [13] Higashi, M., Klir, G. J.: Measures of uncertainty and information based on possibility distributions, International Journal of General Systems, 9, 1983, 43-58.
• [14] Hunter, A.: Handbook of Defeasible Reasoning and Uncertain Information, vol. 2, chapter Paraconsistent logics, Kluwer, 1998.
• [15] Hunter, A.: Reasoning with conflicting information using quasi-classical logic, Journal of Logic and Computation, 10, 2000, 677-703.
• [16] Hunter, A.: Measuring inconsistency in knowledge via quasi-classical models, Proceedings of the American National Conference on Artificial Intelligence (AAAI’02), 2002.
• [17] Hunter, A.: Evaluating coherence and compromise in inconsistent information, 2003, Manuscript. University College London.
• [18] Hunter, A.: Evaluating significance of inconsistencies, Proceedings of the 18th International Joint Conference in Artificial Intelligence (IJCAI’03), 2003.
• [19] Katsuno, H., Mendelzon, A. O.: On the difference between updating a knowledge base and revising it, Proceedings of the 2nd International Conference on Principles of Knowledge Representation and Reasoning (KR’91), 1991.
• [20] Konieczny, S., Lang, J., Marquis, P.: Quantifying information and contradiction in propositional logic through test actions, Proceedings of the 18th International Joint Conference in Artificial Intelligence (IJCAI’ 03), 2003.
• [21] Konieczny, S., Pino Pérez, R.: Merging information under constraints: a qualitative framework, Journal of Logic and Computation, 12(5), 2002, 773-808.
• [22] Kraus, S., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics, Artificial Intelligence, 44, 1990, 167-207.
• [23] Lang, J.: Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 5, Kluwer, 2000.
• [24] Lang, J., Marquis, P.: In Search of the Right Extension, Proceedings of the 7th International Conference on Principles of Knowledge Representation and Reasoning (KR’00), 2000.
• [25] Lang, J., Marquis, P.: Resolving Inconsistencies by Variable Forgetting, Proceedings of the 8th International Conference on Principles of Knowledge Representation and Reasoning (KR’02), 2002.
• [26] Lozinskii, E.: Information and evidence in logic systems, Journal of Experimental and Theoretical Artificial Intelligence, 6, 1994, 163-193.
• [27] Lozinskii, E.: Resolving contradictions: a plausible semantics for inconsistent systems, Journal of Automated Reasoning, 12, 1994, 1-31.
• [28] Marquis, P., Porquet, N.: Computational aspects of quasi-classical entailment, Journal of Applied Non-Classical Logics, 11, 2001, 295-312.
• [29] Nebel, B.: Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 3, chapter How hard is it to revise a belief base?, Kluwer Academic Publishers, 1998, 77-145.
• [30] Ramer, A.: Concepts of fuzzy information measures on continuous domains, International Journal of General Systems, 17, 1990, 241-248.
• [31] Rescher, N., Manor, R.: On inference from inconsistent premises, Theory and Decision, 1, 1970, 179-219.
• [32] Yager, R. R.: Entropy and specificity in a mathematical theory of evidence, International Journal of General Systems, 9, 1983, 249-260.