How to combine diagrammatic logics

TL;DR

This paper introduces a categorical framework for combining diagrammatic logics, enabling the use of categorical constructions like opfibrations to analyze complex logical systems and their applications to computational effects.

Contribution

It defines the category of diagrammatic logics and demonstrates how categorical tools can be used to combine different logics, illustrated by combining logics with opfibrations for studying state effects.

Findings

Categorical constructions facilitate combining diagrammatic logics.

Opfibration-based combination models computational side-effects.

Framework supports modular logic integration.

Abstract

This paper is a submission to the contest: How to combine logics? at the World Congress and School on Universal Logic III, 2010. We claim that combining "things", whatever these things are, is made easier if these things can be seen as the objects of a category. We define the category of diagrammatic logics, so that categorical constructions can be used for combining diagrammatic logics. As an example, a combination of logics using an opfibration is presented, in order to study computational side-effects due to the evolution of the state during the execution of an imperative program.