I'm not sure if this is the right stack to post this question.

Given there are many types of logic; Syllogistic, Symbolic, Modal, Deontic, Temporal, Epistemic, (non)monotonic, formal, informal, FOL, Propositional, Predicate, and the list goes on, I am struggling to understand how they relate to one another (some more than others).

Can they be represented in some form of (approximately) directed graph? Has anyone made an attempt to do this? Is there a reference I can read that would help me understand how the categories relate to one another?

I am, in asking this question, more interested in developing an overall mental map than looking for specific differences between the categories, which I can determine by reading about each. Cheers.

  • Some are order by inclusion according to the expressive power of the language: propositional logic is the simplest (there is no analysis inside the elementary sentence). The next step is predicate logic: first order, second order and so on, according to linguistic entities that we can quantify: first order- only individual variables, second order- quantifier apply to predicate of individual variables, and so on. – Mauro ALLEGRANZA Nov 14 '20 at 8:58
  • Syllogism is a subset of FOL: monadic predicate logic, i.e. predicates of individual variables are unary predicates (properties) only. – Mauro ALLEGRANZA Nov 14 '20 at 8:59

I recommend working through Graham Priest's Introduction to Non-Classical Logic. It'll give you an outline of the logical terrain and indicate relationships among logics in terms of what they count as valid.

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