5.2 Compatibility

27 In MultiContext systems, these compatibility relations are formalized as a special kind of inference rules, called bridge rules 11. The form of a bridge rule is the following: (12) where c i and c j are contexts and 1 ; : : :; n are formulae belonging to the language of c i and n+1 is a formula belonging to the language of c j. Semantically, the eeect of a rule like this is to put a constraint on what counts as a model of a context: a local model of c j that does not satisfy n+1 is not compatible with a local model of c i that satisfy 1 ; : : :; n. It's quite simple to generalize bridge rules in such a way that the premises belong to diierent contexts. Acknowledgments This work is a rst attempt of clarifying some intuitions underlying most of the work which has been done by the Mechanized Reasoning Group in the last ten years. The authors are particularly indebted with Massimo Benerecetti, who read earlier versions of this paper and made lots of valuable comments, and with Chiara Ghidini, who helped clarifying some intuitions behind the semantics of contextual reasoning. A very important contribution came from discussions with Alessandra Ciceri, Alessandro Cimatti, Luciano Seraani, and with all other members of the group. 11 Bridge rules were introduced and intuitively discussed in 11]. A more technical presentation can be found in 13], where it is proved a syntactical equivalence between the most important classes of modal systems and a multi-context framework. 12 26 everyday life, we all often compare beliefs, discuss beliefs, learn from other people's beliefs, and so on. Does locality entails that we must give up all of this? Of course not. However, a diierent model is needed. Consider the following situation. There are two agents (say Paolo and Fausto), and Fausto is ready to believe whatever Paolo says. Now Paolo tells Fausto that he believes that (e.g. that Sooa is a nice city). The traditional formalization of this situation would involve an axioms whose content can be approximately described as follows: if Paolo believes and Paolo tells Fausto that he believes , then Fausto believes. This axiom is in contrast with locality because the meaning of the sentence is given independently of Paolo's and Fausto's belief contexts. Our explanation of the matter is therefore the following: Paolo …