A Revision System of Circular Objects and Its Applications to Dynamic Semantics of Dialogues

Since Peter Aczel’s theory[1] of hypersets, many applications to formalizations of a circular object such as a mutual belief has been proposed [3, 2, 4]. This paper will propose Membership Description Systems (MDSs), a partial revision system of circular objects and their applications to a dynamic semantics of a dialogue in the sense that a dialogue can be considered as a revision process of mutual beliefs between its agents. Although usual dynamic semantics [9] updates a variable assignment or a set of information states, our proposal of a semantics of dialogues directly updates situations, which is specified by MDSs, as dynamic semantics of circular propositions [10] directly updates situations. Furthermore, using MDSs as updated objects in the semantics makes a partial and direct update of circular situations themselves possible. As a result, a dynamic semantics of a language with the ↓-operator, which is introduced by [3] to describe circular propositions, can be provided.