Fixed Point Theory for Consistent Rewriting in Logic of Action with Reverse

ABSTRACT. This paper is concerned with an action structure to recursively derive actions by rewriting, where the action is abstract as in process algebra and has its reverse action. A representation method of action denotations with action defaults is given by fixed point theory, where the denotations are owing to coexistence of actions and their reverses. As another method, the reverse action is thought of as multiplicative inverse in a semiring, which can be formed by algebraic compositions of action structures to primarily express sequences of actions with the action denotations. In both ways, consistency between an action and its reverse is respected.