There has been no nuanimous analysis of specific indefinites. It is still disputed even whether specificity is a matter of semantics of pragmatics. In this paper, I introduce some properties of specific indefinites, and explain them based on the meaning of specificity. Specificity intuitively means that the speaker or someone else in the context has some individual in mind, which is generally accepted among liguistics. The main issue is how to represent the meaning of 'have-in-mind'. I review some philosophical discusstions of cognitive contact and show that when the use of an expression involves 'have-in-mind', the expression is rigid designator in the belief of the agent who has an individual in mind. in the use of a specific indefinite, this applies only to the information state of the agent of 'have-in-mind'. To represent this asymmetry, I propose a new theory of dynamic semantics, in which a common ground consists of multiple information states, as many as the number of the participants in a conversation. Moreover, each information state is structured as a set of epistemic alternatives, which is a set of possible information states of a participant in the context. Based on this semantics, the properties of specific indefinites are explained.
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