3/2-Institutions: an institution theory for conceptual blending

TL;DR

This paper extends institution theory using ordered-enriched categorical structures to better model the partiality of signature morphisms, primarily for applications in conceptual blending and potentially other domains like software evolution.

Contribution

It introduces a novel extension of institution theory that accounts for partial signature morphisms through ordered-enriched categories, enhancing its applicability.

Findings

Provides a formal framework for partial signature morphisms

Enables better modeling of conceptual blending processes

Potential applications in software evolution

Abstract

We develop an extension of institution theory that accommodates implicitly the partiality of the signature morphisms and its syntactic and semantic effects. This is driven primarily by applications to conceptual blending, but other application domains are possible (such as software evolution). The particularity of this extension is a reliance on ordered-enriched categorical structures.