Abstract
In this paper we develop labelled and uniform tableau methods for some fundamental system of propositional conditional logics. We consider the well-known system CE (that can be seen as a generalization of preferential nonmonotonic logic), and some related systems. Our tableau proof procedures are based on a possible-worlds structures endowed with a family of preference relations. The tableau procedure gives the first practical decision procedure for CE.
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Broda, K., Gabbay, D., Lamb, L., Russo, A.: Labelled Natural Deduction for Conditional Logic of Normality. Logic Journal of the IGPL 10(2), 123–163 (2002)
Artosi, A., Governatori, G., Rotolo, A.: Labelled tableaux for non-monotonic reasoning: Cumulative consequence relations. Journal of Logic and Computation 12 (2002)
Boutilier, C.: Conditional logics of normality: a modal approach. Artificial Intelligence 68, 87–154 (1994)
Crocco, G., Fariñas del Cerro, L.: Structure, Consequence relation and Logic, vol. 4, pp. 239–259. Oxford University Press, Oxford (1992)
Crocco, G., Fariñas del Cerro, L., Herzig, A.: Conditionals: From philosophy to computer science. Studies in Logic and Computation, Oxford University Press, Oxford (1995)
Crocco, G., Lamarre, P.: On the Connection between Non-Monotonic Inference Systems and Conditional Logics. In: Nebel, B., Sandewall, E. (eds.) Principles of Knowledge Representation and Reasoning: Proceedings of the 3rd International Conference, pp. 565–571 (1992)
Delgrande, J.P.: A first-order conditional logic for prototypical properties. Artificial Intelligence (33), 105–130 (1987)
de Swart, H.C.M.: A Gentzen-or Beth-type system, a practical decision procedure and a constructive completeness proof for the counterfactual logics VC and VCS. Journal of Symbolic Logic 48, 1–20 (1983)
Fitting, M.: Proof methods for Modal and Intuitionistic Logic. Synthese library, vol. 169. D. Reidel, Dordrecht (1983)
Friedman, N., Halpern, J.: On the complexity of conditional logics. In: Principles of Knowledge Representation and Reasoning: Proceedings of the 4th International Conference, KR 1994, pp. 202–213 (1994)
Gabbay, D.M.: Labelled Deductive Systems. Oxford Logic Guides, vol. I, Oxford University Press, Oxford (1996)
Gent, I.P.: A sequent or tableaux-style system for Lewis’s counterfactual logic VC. Notre Dame j. of Formal Logic 33(3), 369–382 (1992)
Ginsberg, M.L.: Counterfactuals. Artificial Intelligence 30(2), 35–79 (1986)
Giordano, L., Gliozzi, V., Olivetti, N.: Iterated Belief Revision and Conditional Logic. Studia Logica, special issue on Belief Revision 70(1), 23–47 (2002)
Goré, R.: Tableau Methods for Modal and Temporal Logics Rajeev Goré. In: D’Agostino, M., Gabbay, D., Haehnle, R., Posegga, J. (eds.) Handbook of Tableau Methods, pp. 297–396. Kluwer Academic Publishers, Dordrecht (1999)
Grahne, G.: Updates and Counterfactuals. Journal of Logic and Computation 8(1), 87–117 (1998)
Groeneboer, C., Delgrande, J.: A general approach for determining the validity of commonsense assertions using conditional logics. International Journal of Intelligent Systems (5), 505–520 (1997)
Kraus, S., Lehmann, D., Magidor, M.: Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44, 167–202 (1990)
Lamarre, P.: Etude des raisonnements non-monotones: apports des logiques des conditionnels et des logiques modales. PhD thesis, université Paul Sabatier, Toulouse (1992)
Lamarre, P.: A tableaux prover for conditional logics. In: Principles of Knowledge Representation and Reasoning: Proceedings of the 4th International Conference, KR 1994, pp. 572–580 (1994)
Lewis, D.: Counterfactuals. Basil Blackwell Ltd, Malden (1973)
Nute, D.: Topics in Conditional Logic. Reidel, Dordrecht (1980)
Olivetti, N., Schwind, C.: A sequent calculus and a complexity bound for minimal conditional logic. In: Restivo, A., Ronchi Della Rocca, S., Roversi, L. (eds.) ICTCS 2001. LNCS, vol. 2202, pp. 384–404. Springer, Heidelberg (2001)
Schwind, C.B.: Causality in Action Theories. Electronic Articles in Computer and Information Science, section A 3, 27–50 (1999)
Viganó, L.: Labelled Non-classical Logics. Kluwer Academic Publishers, Dordrecht (2000)
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Giordano, L., Gliozzi, V., Olivetti, N., Schwind, C. (2003). Tableau Calculi for Preference-Based Conditional Logics. In: Cialdea Mayer, M., Pirri, F. (eds) Automated Reasoning with Analytic Tableaux and Related Methods . TABLEAUX 2003. Lecture Notes in Computer Science(), vol 2796. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45206-5_9
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DOI: https://doi.org/10.1007/978-3-540-45206-5_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40787-4
Online ISBN: 978-3-540-45206-5
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