A functional partial semantics for intensional logic.
Serge Lapierre · Notre Dame Journal of Formal Logic · 1992
In this paper a partial semantics for the higher order modal language of Intensional Logic is suggested.Partial semantic values of functional types are defined as monotone functions on partially ordered sets; it is shown that this characterization is materially adequate for representing partial values and that it overcomes the difficulties that arise when we attempt to introduce one-place partial functions in the hierarchy of types.Partial values of any type are related to classical values of the same type by means of a relation of approximation.This allows us to compare partial models with classical models.Classical semantics then appears to be a part of partial semantics to the extent that there exists a bijective mapping from classical models onto totally defined partial models.This also allows us to define, according to the partial semantics, a notion of entailment which is coextensive with the classical notion.