Local Models Semantics, or Contextual Reasoning = Locality + Compatibility

In this paper we present a new semantics, called Local Models Semantics, and use it to provide a foundation to reasoning with con texts. This semantics captures and makes precise the two main intuitions underlying contextual reasoning: (i) reasoning is mainly local and uses only part of what is potentially available (e.g. what is known, the available inference procedures), this part is what we call context (of reasoning); however (ii) the context may change and there is compatibil ity among the reasoning performed in dif ferent contexts. We validate our semantics by formalizing two important forms of con textual reasoning: reasoning with viewpoints and reasoning about belief.