The algebraic face of minimality

Frank Wolter

DOI: http://dx.doi.org/10.12775/LLP.1998.013

Abstract


Operators which map subsets of a given set to the set of their minimal elements with respect to some relation R form the basis of a semantic approach in non-monotonic logic, belief revision, conditional logic and updating. In this paper we investigate operators of this type from an algebraic viewpoint. A representation theorem is proved and various properties of the resulting algebras are investigated. It is shown that they behave quite differently from known algebras related to logics, e.g. modal algebras and Heyting algebras.

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