Abstract. This paper proposes a semiring formulation for reasoning about an agent's changing beliefs: a dynamic epistemic semiring (DES). A DES is a modal semiring extended with epistemic-action operators. The paper concentrates on the revision operator by proposing an axiomatisation, developing a basic calculus and deriving the classical AGM revision axioms in the algebra.
Abstract.A dually nondeterministic refinement algebra with a negation operator is proposed. The algebra facilitates reasoning about totalcorrectness preserving program transformations and nondeterministic programs. The negation operator is used to express enabledness and termination operators through a useful explicit definition. As a small application, a property of action systems is proved employing the algebra. A dually nondeterministic refinement algebra without the negation operator is also discussed.
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