Abstract
We introduce a family of preferential logics that are useful for handling information with different levels of uncertainty. The corresponding consequence relations are non-monotonic, paraconsistent, adaptive, and rational. It is also shown that any formalism in this family that is based on a well-founded ordering of the different types of uncertainty, can be embedded in a corresponding four-valued logic with at most three uncertainty levels.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Arieli, O.: Reasoning with modularly pointwise preferential relations. In: van den Bosch, A., Weigand, H. (eds.) Proc. BNAIC 2000, pp. 61–68. BNVKI (2000)
Arieli, O.: Useful adaptive logics for rational and paraconsistent reasoning. Technical Report CW286, Depatrment of Computer Science, University of Leuven (2001)
Arieli, O.: Paraconsistent declarative semantics for extended logic programs. Annals of Mathematics and Artificial Intelligence 36(4), 381–417 (2002)
Arieli, O., Avron, A.: Reasoning with logical bilattices. Journal of Logic, Language, and Information 5(1), 25–63 (1996)
Arieli, O., Avron, A.: The logical role of the four-valued bilattice. In: Proc. LICS 1998, pp. 218–226. IEEE Press, Los Alamitos (1998)
Arieli, O., Avron, A.: Nonmonotonic and paraconsistent reasoning: From basic entailments to plausible relations. In: Hunter, A., Parsons, S. (eds.) ECSQARU 1999. LNCS (LNAI), vol. 1638, pp. 11–22. Springer, Heidelberg (1999)
Arieli, O., Denecker, M.: Modeling paraconsistent reasoning by classical logic. In: Eiter, T., Schewe, K.-D. (eds.) FoIKS 2002. LNCS, vol. 2284, pp. 1–14. Springer, Heidelberg (2002)
Avron, A.: Simple consequence relations. Journal of Information and Computation 92, 105–139 (1991)
Avron, A.: Classical Gentzen-type methods in propositional many-valued logics. In: Fitting, M., Orlowska, E. (eds.) Theory and Applications in Multiple-Valued Logics, pp. 113–151. Springer, Heidelberg (2002)
Batens, D.: Inconsistency-adaptive logics. In: Orlowska, E. (ed.) Logic at Work, pp. 445–472. Physica Verlag, Heidelberg (1998)
Batens, D.: On a partial decision method for dynamic proofs. In: Decker, H., Villadsen, J., Waragai, T. (eds.) Proc. PCL 2002, ICLP 2002 Workshop on Paraconsistent Computational Logic, pp. 91–108 (2002)
Batens, D., Mortensen, C., Priest, G., Van Bendegem, J.: Frontiers of Paraconsistent Logic. In: Studies in Logic and Computation Vol. 8. Research Studies Press, Hertfordshire (2000)
Belnap, N.D.: A useful four-valued logic. In: Epstein, G., Dunn, J.M. (eds.) Modern Uses of Multiple-Valued Logic, pp. 7–37. Reidel Publishing Company, Dordrechtz (1977)
Belnap, N.D.: How a computer should think. In: Ryle, G. (ed.) Contemporary Aspects of Philosophy, pp. 30–56. Oriel Press (1977)
Benferhat, S., Besnard, P. (eds.): ECSQARU 2001. LNCS (LNAI), vol. 2143. Springer, Heidelberg (2001)
Bialynicki-Birula, A.: Remarks on quasi-boolean algebras. Bull. Acad. Polonaise des Sciences Cl. III V(6), 615–619 (1957)
Bialynicki-Birula, A., Rasiowa, H.: On the representation of quasi-boolean algebras. Bull. Acad. Polonaise des Sciences Cl. III V(3), 259–261 (1957)
Carnielli, W., Coniglio, M.E., D’Ottaviano, I.M.L.: Paraconsistency: The logical way to the inconsistent. Lecture Notes in Pure and Applied Mathematics, vol. 228. Marcel Dekker (2002)
da-Costa, N.C.A.: On the theory of inconsistent formal systems. Notre Dam Journal of Formal Logic 15, 497–510 (1974)
Damasio, C.M., Pereira, L.M.: A survey on paraconsistent semantics for extended logic programs. In: Gabbay, D.M., Smets, P. (eds.) Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 2, pp. 241–320. Kluwer, Dordrecht (1998)
Dubois, D., Lang, J., Prade, H.: Possibilistic logic. In: Gabbay, D., Hogger, C., Robinson, J. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, pp. 439–513. Oxford Science Publications (1994)
Hajek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht (1998)
Hunter, A., Parsons, S. (eds.): ECSQARU 1999. LNCS (LNAI), vol. 1638. Springer, Heidelberg (1999)
Gabbay, D.M.: Theoretical foundation for non-monotonic reasoning in expert systems. In: Apt, K.P. (ed.) Proc. of the NATO Advanced Study Inst. on Logic and Models of Concurrent Systems, pp. 439–457. Springer, Heidelberg (1985)
Kalman, J.A.: Lattices with involution. Trans. of the American Mathematical Society 87, 485–491 (1958)
Kifer, M., Lozinskii, E.L.: A logic for reasoning with inconsistency. Automated Reasoning 9(2), 179–215 (1992)
Kraus, S., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44(1–2), 167–207 (1990)
Lehmann, D., Magidor, M.: What does a conditional knowledge base entail? Artificial Intelligence 55, 1–60 (1992)
Lukasiewicz, T.: Fixpoint characterizations for many-valued disjunctive logic programs with probabilistic semantics. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 336–350. Springer, Heidelberg (2001)
Makinson, D.: General theory of cumulative inference. In: Reinfrank, M., Ginsberg, M.L., de Kleer, J., Sandewall, E. (eds.) Non-Monotonic Reasoning 1988. LNCS (LNAI), vol. 346, pp. 1–18. Springer, Heidelberg (1988)
Makinson, D.: General patterns in nonmonotonic reasoning. In: Gabbay, D., Hogger, C., Robinson, J. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming 3, pp. 35–110. Oxford Science Publications (1994)
McCarthy, J.: Circumscription – A form of non monotonic reasoning. Artificial Intelligence 13(1–2), 27–39 (1980)
Pearl, J.: Reasoning under uncertainty. Annual Review of Computer Science 4, 37–72 (1989)
Priest, G.: Minimally inconsistent LP. Studia Logica 50, 321–331 (1991)
Schlechta, K.: Unrestricted preferential structures. Journal of Logic and Computation 10(4), 573–581 (2000)
Shoham, Y.: Reasoning about change. MIT Press, Cambridge (1988)
Subrahmanian, V.S.: Mechanical proof procedures for many-valued lattice-based logic programming. Journal of Non-Classical Logic 7, 7–41 (1990)
Tarski, A.: Introduction to logic. Oxford University Press, Oxford (1941)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Arieli, O. (2003). Preferential Logics for Reasoning with Graded Uncertainty. In: Nielsen, T.D., Zhang, N.L. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2003. Lecture Notes in Computer Science(), vol 2711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45062-7_42
Download citation
DOI: https://doi.org/10.1007/978-3-540-45062-7_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40494-1
Online ISBN: 978-3-540-45062-7
eBook Packages: Springer Book Archive