Bestiary of Logical and Probabilistic Relations and Structures

[sthippo]

There are many conceivable relations that could be described as logical or probabilistic. The first step is to take an inventory, erring on the side of inclusion -- we can always winnow the collection later. What distinct species of logical and probabilistic relations and structures are there?

[sthippo]

Here's a first go at categories of relations. For the sake of simplicity I'm not explicitly listing probabilistic variations.

1. Logical implication: if A then B
2. Modal implication: if A then it might be that B
3. Deontic implication: if A then it should be that B
4. Composition: A includes B (A is a conjunction of statements including B)
5. Abstraction: A abstracts B (A is a statement about a class, and B is the same statement replacing the class with a subclass or an instance of the class.)

You could argue that 4 & 5 are just special types of implication, because in both cases if the relation between A and B is as described then it's also true that if A then B. But in my own logical thinking, they are fundamental relations. Admittedly, this is probably because they are extremely useful in the context of computer programming. But that's probably a good sign.