Journal of Logic and Computation Advance Access published online on April 27, 2008
Journal of Logic and Computation, doi:10.1093/logcom/exn008
Original Papers |
Geodesic Revision
Department of Mathematics and Computer Science, John Jay College, City University of New York, 445 West 59th Street, New York, NY 10019, USA.
E-mail: kgeorgatos{at}jjay.cuny.edu
Received 17 February 2007.
The purpose of this article is to introduce a class of distance-based iterated revision operators generated by minimizing the geodesic distance on a graph. Such operators correspond bijectively to metrics and have a simple finite presentation. As distance is generated by distinguishability, our framework is appropriate for modelling contexts where distance is generated by threshold, and therefore, when measurement is erroneous.
Keywords: Belief revision; distance-based reasoning; similarity; indistinguishability; indiscernibility
References
- Alchourrón CE, Gärdenfors P, Makinson D. On the logic of theory change: partial meet contraction and revision functions. In: Journal of Symbolic Logic (1985) 50:510–530.[CrossRef][ISI]
- Bell JL. A new approach to quantum logic. In: The British Journal for the Philosophy of Science (1986) 37:83–99.[ISI]
- Fagin Ronald. On the logic of iterated belief revision. In: Proceedings of TARK 94 (1994) CA: Morgan Kaufmann, Pacific Grove. 5–23.
- Delgrande JP. Preliminary considerations on the modelling of belief change operators by metric spaces. In: Proceedings of the 10th International Workshop on Non-Monotonic Reasoning (NMR 2004) (2004) 118–125.
- Georgatos K. On distinguishability and prototypes. In: Logic Journal of the IGPL (2003) 5:531–545.
- Goldblatt RI. Semantic analysis of orthologic. In: Journal of Philosophical Logic (1974) 3:19–35.[CrossRef][ISI]
- Hansson SO. Similarity semantics and minimal changes of belief. In: Erkenntnis (1992) 37:401–429.[CrossRef]
- Hughes GE, Cresswell MJ. A Companion to Modal Logic (1984) London and New York: Methuen.
- Katsuno H, Mendelzon AO. On the difference between updating a knowledge base and revising it. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Third International Conference (KR '91) (1991) San Mateo, California: Morgan Kaufmann. 387–394.
- Katsuno H, Mendelzon AO. Propositional knowledge base revision and minimal change. In: Artificial Intelligence (1991) 52:263–294.[CrossRef][ISI]
- Lehmann D. Belief revision, revised. In: Proceedings of the 14th International Joint Conference of Artificial Intelligence (IJCAI '95) (1995) 1534–1540.
- Lehmann DJ, Magidor M, Schlechta K. Distance semantics for belief revision. In: Journal of Symbolic Logic (2001) 66:295–317.[CrossRef][ISI]
- Lewis D. Counterfactuals (1973) Cambridge, MA: Harvard University Press.
- Lewis DK. Counterfactuals and comparative possibility. In: Journal of Philosophical Logic (1973) 2:418–446.
- Pais J. Revision algebra semantics for conditional logic. In: Studia Logica (1992) 51:29–316.
- Tversky A. Features of similarity. In: Psychological Review (1977) 84:327–352.[CrossRef][ISI]
- Williamson T. First-order logics for comparative similarity. In: Notre Dame Journal of Formal Logic (1988) 29:457–481.[CrossRef]
- Zeeman EC. The topology of the brain and visual perception. In: The Topology of 3-Manifolds—Fort MK, ed. (1962) Englewood Cliffs, NJ: Prentice Hall. 240–256.
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