Unification as negotiation: a context-based approach

We start from a notion of similarity-based unification, as defined by the Arcelli et al. (1998), and we introduce a more structured process that can be seen more adequately as a form of unification as negotiation between agents, each of them equipped with the own notion of context. We start by modeling a context through a particular t-norm, i.e. a way of interpreting the conjunction according to capture the features of a given context and we show how it is possible to represent a context through the choice of a suitable t-norm. We assume that each agent is situated in a particular context or, more precisely, that he believes to be in a particular context and chooses a t-norm accordingly. Then we introduce a process of negotiation among the agents, each of them endowed with a notion of similarity associated to the context; for this purpose we attempt to formulate a theory of negotiation as a fragment of modal logic and in particular we show that similarity-based unification can be expressed in terms of modal logic, by means of an "acceptance" operator.