Asymmetric combination of logics is functorial: A survey

TL;DR

This survey explores the functorial nature of asymmetric logic combinations, examining how they develop features over base logics and addressing related questions on translations, property preservation, and natural transformations.

Contribution

It provides a comprehensive overview of the functorial perspective on asymmetric logic combinations, highlighting its implications for logic development and translation.

Findings

Logic combinations exhibit functorial properties.

Natural transformations relate different asymmetric combinations.

The approach aids in understanding property preservation.

Abstract

Asymmetric combination of logics is a formal process that develops the characteristic features of a specific logic on top of another one. Typical examples include the development of temporal, hybrid, and probabilistic dimensions over a given base logic. These examples are surveyed in the paper under a particular perspective - that this sort of combination of logics possesses a functorial nature. Such a view gives rise to several interesting questions. They range from the problem of combining translations (between logics), to that of ensuring property preservation along the process, and the way different asymmetric combinations can be related through appropriate natural transformations.