A Local Models Semantics for Propositional Attitudes

Our starting point is a formulation of modal logics, described in previous papers, defined in terms of a hierarchy of distinct (that is, not amalgamated) metatheories. These logics, called Hierarchical Multilanguage Belief (HMB) systems formalize the current practice in the implementation of propositional attitudes, and in particular belief, inside complex reasoning systems. Our goal is to define e new semantics for HMB systems, called local models semantics, which captures their underlying intuitions. In local models semantics each (meta)theory defines a set of first order models, called ‘local models’; belief is a unary predicate; and the extension of the belief predicate is computed by enforcing constraints among sets of local model