Modeling Ambiguity in a Multi-Agent System

This paper investigates the formal pragmatics of ambiguous expressions by modeling ambiguity in a multi-agent system. Such a framework allows us to give a more refined notion of the kind of information that is conveyed by ambiguous expressions. We analyze how ambiguity affects the knowledge of the dialog participants and, especially, what they know about each other after an ambiguous sentence has been uttered. The agents communicate with each other by means of a TELL-function, whose application is constrained by an implementation of some of Grice's maxims. The information states of the multi-agent system itself are represented as a Kripke structures and TELL is an update function on those structures. This framework enables us to distinguish between the information conveyed by ambiguous sentences vs. the information conveyed by disjunctions, and between semantic ambiguity vs. perceived ambiguity.Comment: 7 page

A logic for reasoning about ambiguity

Standard models of multi-agent modal logic do not capture the fact that information is often \emph{ambiguous}, and may be interpreted in different ways by different agents. We propose a framework that can model this, and consider different semantics that capture different assumptions about the agents' beliefs regarding whether or not there is ambiguity. We examine the expressive power of logics of ambiguity compared to logics that cannot model ambiguity, with respect to the different semantics that we propose.Comment: Some of the material in this paper appeared in preliminary form in "Ambiguous langage and differences of belief" (see arXiv:1203.0699