Generic partiality for $\frac{3}{2}$-institutions

Abstract

$\frac{3}{2}$-institutions have been introduced as an extension of institution theory that accommodates implicitly partiality of the signature morphisms together with its syntactic and semantic effects. In this paper we show that ordinary institutions that are equipped with an inclusion system for their categories of signatures generate naturally $\frac{3}{2}$ -institutions with explicit partiality for their signature morphisms. This provides a general uniform way to build 3 -institutions for the foundations of conceptual blending and software evolution. Moreover our general construction allows for an uniform derivation of some useful technical properties.