Modelling (Un)Bounded Beliefs

This paper is concerned with providing a context based logic (language + semantics) for the representation of agents's beliefs. While different approaches that make use of a single theory have been proposed in order to model agent's beliefs, such as modal logics, these often suffer from problems, as lack of modularity, logical omniscence, and dissimilarity with implementations. A partial solution to these problems is to distribute the agent's knowledge into different and separated modules which interact each others. Our approach is to provide these modules, but in the form of (multi) contexts, each one with its own local language and semantics, and to model the relations among modules as compatibility relations among contexts. We extend here this approach to capture important aspects of "ideal" agents, namely their logically omniscent nature, and of "real" agents, namely their non logically omniscent nature due to some resource-boundedness. The logic we use is based on a logic for contextual reasoning, called Local Models Semantics, which allows a (multi) context-based representation of agent's belief. A tableau system for a simple instance of such a logic is also presented.