Development Exercise/Project

CATEGORY LOGIC

for

Natural Transformations

employing

Natural Transformation Diagrams

and

AutoLog Equality Consequent Conditions

The first two introductory lectures illustrate how "category logic" is related to AutoLog's indexical forcing.

This short Lecture describes an extended exercise/project involving natural transformations in categoty theory. The goal here is to design a lecture providing an AutoLog theory representing the intentions of relevant category diagrams for Natural Transformations and the related category logic via AutoLog.

The CategoryLogic is associated with an AutoLog theory that specifies equality consequences based on term matching for the indexical literals in a rule as was exemplified in the Lecture1 and Lecture2.

Here are some online reference articles regarding Natural Transformations for Category Theory:

https://ncatlab.org/nlab/show/natural+transformation
https://en.wikipedia.org/wiki/Natural_transformation

We need to formulate natural transformation category logic specifications concerning covariant and contravarint Functors. Some experimentation with the rules will be required in order to make the antecedent rule literal Functor specifications useful. This seemed to be fairly straightforward for Lecture1 and Lecture2, but we do not yet have a satisfying specification for Natural Transformations. Some difficulty arisess depending on the specific formulations for the diagrams and the AutoLog logic.

The comments on this page describe lecture goals in a general manner, and readers are invited to develope thei own versions of detailed design specifications. We look forward to posting more detailed information for Lecture3 at a later date.