Geodesic Revision

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.

[1]  Sven Ove Hansson,et al.  Similarity semantics and minimal changes of belief , 1992 .

[2]  Timothy Williamson,et al.  First-order logics for comparative similarity , 1988, Notre Dame J. Formal Log..

[3]  Konstantinos Georgatos On Indistinguishability and Prototypes , 2003, Log. J. IGPL.

[4]  David Lewis Counterfactuals and Comparative Possibility , 1973 .

[5]  Robert Goldblatt,et al.  Semantic analysis of orthologic , 1974, J. Philos. Log..

[6]  James P. Delgrande,et al.  Preliminary considerations on the modelling of belief change operators by metric spaces , 2004, NMR.

[7]  Hirofumi Katsuno,et al.  On the Difference between Updating a Knowledge Base and Revising It , 1991, KR.

[8]  Hirofumi Katsuno,et al.  Propositional Knowledge Base Revision and Minimal Change , 1991, Artif. Intell..

[9]  Max J. Cresswell,et al.  A companion to modal logic , 1984 .

[10]  Peter Gärdenfors,et al.  On the logic of theory change: Partial meet contraction and revision functions , 1985, Journal of Symbolic Logic.

[11]  Donald Nute,et al.  Counterfactuals , 1975, Notre Dame J. Formal Log..

[12]  A. Tversky Features of Similarity , 1977 .

[13]  Karl Schlechta,et al.  Distance semantics for belief revision , 1996, Journal of Symbolic Logic.

[14]  John Pais Revision algebra semantics for conditional logic , 1992, Stud Logica.

[15]  J. Pearl,et al.  On the Logic of Iterated Belief Revision , 1994, Artif. Intell..

[16]  John L. Bell,et al.  A New Approach to Quantum Logic , 1986, The British Journal for the Philosophy of Science.

[17]  Daniel Lehmann,et al.  Belief Revision, Revised , 1995, IJCAI.