epatters

Within the Julia ecosystem, you might be interested in Catlab (https://github.com/epatters/Catlab.jl), as we are actively working to build something very much along these lines. We already have in place a system for describing generalized algebraic theories (GATs) in Julia and generating symbolic expressions for them. In the future, we intend to implement pushouts of GATs as an algebraic approach to theory fusion. We are currently in the planning stage of this part of the project and hope to get something working this year.

What do you mean? Categorical logic is hardly restricted to syllogistic reasoning.