Assertions in AFA Set Theory

In this paper we consider an application of the theory of non–wellfounded sets to the modelling of epistemic updates triggered by assertions in dialogue. We concentrate mainly on what we might call defective dialogue, i.e. dialogue in epistemic contexts where the speaker has either erroneous beliefs or is not sincere in his language use. We develop our theory within a special possible worlds framework which uses AFA set theory for representing information states of dialogue participants. We first characterise the use of assertions in ideal dialogue situations and then show how pragmatic principles connected to perspectives and speaker’s intentions define extended uses in defective situations. On the formal level, the pragmatic considerations lead to the introduction of operators which can be used systematically to extend the domain of assertions.