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 contexts. 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 compatibility among the reasoning performed in different contexts. We validate our semantics by formalizing two important forms of contextual reasoning: reasoning with viewpoints and reasoning about belief. 1 Introduction Contexts are an important topic in many research areas, for example in the semantics of natural language (see, e.g., [Kaplan, 1978]), and in computational linguistics (see, e.g., [Fauconnier, 1985]). Lately, contexts have been independently proposed in [Giunchiglia, 1993] and [McCarthy, 1987] ...