Weak AGM postulates and strong Ramsey Test: A logical formalization

Authors:
Laura Giordano;Valentina Gliozzi;Nicola Olivetti
Affiliations:
Dipartimento di Informatica, Università del Piemonte Orientale “A. Avogadro”, Via Bellini 25/g, 15100 Alessandria, Italy;Dipartimento di Informatica, Università del Piemonte Orientale “A. Avogadro”, Via Bellini 25/g, 15100 Alessandria, Italy;Dipartimento di Informatica, Università di Torino, C.so Svizzera 185, 10149 Torino, Italy
Venue:
Artificial Intelligence
Year:
2005

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Abstract

We reformulate AGM postulates for belief revision systems that may contain conditional formulas. We show that we can establish a mapping between belief revision systems and conditionals by means of the so called Ramsey Test, without incurring Gardenfors triviality result. We then derive the conditional logic BCR from our revision postulates by means of a strong version of the Ramsey Test. We give a sound and complete axiomatization of this logic with respect to its standard selection-function models semantics, and we prove its decidability. We finally show that there is an isomorphism between belief revision systems and selection function models of BCR via a representation theorem. The logic BCR provides a logical formalization of belief revision in the language of conditional logic.