and is it possible to provide an example to illustrate, or would that only kill of my remaining brain cells?
I’ve never heard of modular logic. I’ve heard of modal logic, which deals with deductions involving possibility and necessity in addition to plain old truth.
I tend to associate ‘modular logic’ with computers. A little googling did confirm this association. See link1 and link2.
These links describe ‘modular logic programming’ as nothing more than the idea of programming in a logic programming language with ‘modules’. Modules IIRC are definite entities (mostly subroutines with variables) in a program that function as a ‘black box’. The idea is that modular programming makes it possible to change the inner functioning of one module without affecting the remainder of the program/system. This would ease maintenance and bug fixing. See also ‘information hiding’.
So-called object oriented languages have taken this idea one step further by offering objects that are like modules, except that modules in the classic sense encapsulate functions, while objects represent user-defined ‘data types’ with specific user-defined functions applicable to the objects.
I also believe ‘modular logic’ may be used in reference to logic circuits, PLC’s or the like, but I didn’t quickly find a reference.
I’m trying to put all this in relatively simple language; sorry if an expert finds it imprecise.
If the above is not helpful or doesn’t fit with what you have in mind, you might provide an example of the context where you encountered the term.