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.