Contraction in propositional logic

A study of contraction operators in propositional logic.Postulates and a representation theorem in terms of faithful assignments.Can be used as a basis for study contraction on weaker logics or for iterated contraction. The AGM model for the revision and contraction of belief sets provides rationality postulates for each of the two families of change operators. In the context of finite propositional logic, Katsuno and Mendelzon pointed out postulates for the revision of belief bases which correspond to the AGM postulates for the revision of beliefs sets. In this paper, we present postulates for the contraction of propositional belief bases which correspond to the AGM postulates for the contraction of belief sets. We highlight the existing connections with the revision of belief bases in the sense of Katsuno and Mendelzon thanks to Levi and Harper identities. We also present a representation theorem for contraction operators for propositional belief bases.

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