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AGM contraction and revision of rules. (English) Zbl 1396.03015
Summary: In this paper we study AGM contraction and revision of rules using input/output logical theories. We replace propositional formulas in the AGM framework of theory change by pairs of propositional formulas, representing the rule based character of theories, and we replace the classical consequence operator \(Cn\) by an input/output logic. The results in this paper suggest that, in general, results from belief base dynamics can be transferred to rule base dynamics, but that a similar transfer of AGM theory change to rule change is much more problematic. First, we generalise belief base contraction to rule base contraction, and show that two representation results of Hansson still hold for rule base contraction. Second, we show that the six so-called basic postulates of AGM contraction are consistent only for some input/output logics, but not for others. In particular, we show that the notorious recovery postulate can be satisfied only by basic output, but not by simple-minded output. Third, we show how AGM rule revision can be defined in terms of AGM rule contraction using the Levi identity. We highlight various topics for further research.
MSC:
03B42 Logics of knowledge and belief (including belief change)
03B70 Logic in computer science
68T27 Logic in artificial intelligence
68T30 Knowledge representation
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[1] Alchourrón, C. E., & Makinson, D. (1981). Hierarchies of regulations and their logic in Hilpinen, pp. 125-148. · Zbl 0964.03002
[2] Alchourrón, CE; Makinson, D, On the logic of theory change: contraction functions and their associated revision functions, Theoria, 48, 14-37, (1982) · Zbl 0503.03008
[3] Alchourrón, CE; Gärdenfors, P; Makinson, D, On the logic of theory change: partial meet contraction and revision functions, Journal of Symbolic Logic, 50, 510-530, (1985) · Zbl 0578.03011
[4] Billington, D., Antoniou, G., Governatori, G., & Maher, M. (1999). Revising non-monotonic belief sets: The case of defeasible logic. In: KI-99: Advances in artificial intelligence, Berlin: Springer, pp. 101-112. · Zbl 0957.03017
[5] Boella, G., Pigozzi, G., & van der Torre, L. (2009). Normative framework for normative system change. In: 8th International joint conference on autonomous agents and multiagent systems (AAMAS 2009), Budapest, Hungary, May 10-15, vol. 1, pp. 169-176.
[6] Corapi, D., De Vos, M., Padget, J., Russo, A., & Satoh, K. (2011). Norm refinement and design through inductive learning. In M. De Vos, N. Fornara, J. Pitt, & G. Vouros (Eds.), Coordination, organizations, institutions, and norms in agent systems VI (vol. 6541, pp. 77-94). Lecture Notes in Computer Science Berlin Heidelberg: Springer. · Zbl 1222.68054
[7] Delgrande, J, A program-level approach to revising logic programs under the answer set semantics, Theroy and Practice of Logic Programming, 10, 565-580, (2010) · Zbl 1209.68090
[8] Delgrande, J., Schaub, T., Tompits, H., & Woltran, S. (2008). Belief revision of logic programs under answer set semantics. In G. Brewka, J. Lang (Eds.), (pp. 411-421). KR: AAAI Press. · Zbl 1251.68057
[9] Gärdenfors, P, Conditionals and changes of belief, Acta Philosophica Fennica, 30, 381-404, (1978) · Zbl 0413.03011
[10] Gärdenfors, P., & Rott, H. (1995). Belief revision. In: D. M. Gabbay, C. J. Hogger, & J. Robinson (Eds.) Handbook of logic in artificial intelligence and logic programming. vol. IV: Epistemic and temporal reasoning. Oxford: Oxford University Press, pp. 35-132. · Zbl 0578.03011
[11] Governatori, G., & DiGiusto, P. (1999). Modifying is better than deleting: A new approach to base revision. In: E. Lamma, & P. Mello (Eds.) AI*IA 99, Pitagora, pp. 145-154.
[12] Governatori, G., & Rotolo, A. (2010). Changing legal systems: Legal abrogations and annulments in defeasible logic. Logic Journal of IGPL 18(1):157-194, http://jigpal.oxfordjournals.org/cgi/content/abstract/jzp075v1 · Zbl 1197.68071
[13] Governatori, G., Rotolo, A., Olivieri, F., & Scannapieco, S. (2013). Legal contractions: a logical analysis. In E. Francesconi & B. Verheij (Eds.) (pp. 63-72). ACM: ICAIL. · Zbl 0993.03039
[14] Grove, A, Two modellings for theory change, Journal of Philosophical Logic, 17, 157-170, (1988) · Zbl 0639.03025
[15] Hansson, S, Reversing the Levi identity, Journal of Philosophical Logic, 22, 637-669, (1993) · Zbl 0788.03033
[16] Makinson, D; Torre, L, Input-output logics, Journal of Philosophical Logic, 29, 383-408, (2000) · Zbl 0964.03002
[17] Makinson, D; Torre, L, Constraints for input-output logics, Journal of Philosophical Logic, 30, 155-185, (2001) · Zbl 0993.03039
[18] Makinson, D; Torre, L, Permissions from an input-output perspective, Journal of Philosophical Logic, 32, 391-416, (2003) · Zbl 1028.03017
[19] Nute, D. (1984). Conditional logic. In: Handbook of philosophical logic, synthese library, vol. 165, Berlin: Springer, pp. 387-439. · Zbl 0875.03017
[20] Parent, X; Torre, L; Gabbay, D (ed.); Horty, J (ed.); Parent, X (ed.); Meyden, R (ed.); Torre, L (ed.), Input/output logics, 499-544, (2013), London · Zbl 1367.03044
[21] Stolpe, A, Norm-system revision: theory and application, Artificial Intelligence and Law, 18, 247-283, (2010)
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