TITLE: What is the difference between relational logic and predicate logic?
QUESTION [5 upvotes]: I am studying the Introduction to logic course from Stanford University and I begin learning about relational logic. However when I search on google for the terms there I end up often with results from websites that teach predicate logic. Is there a difference between the two types of logic ?
I am talking about THIS course from Standford :
http://logic.stanford.edu/intrologic/notes/chapter_06.html

REPLY [4 votes]: In the Stanford course "relational logic" just means First-order logic (FOL) with Herbrand semantics. In other words, FOL without model theory. You could say that Herbrand semantics introduces a new kind of model theory, but it really is just a way to set model theory aside and focus on logic.
I think this is a good idea because it emphasizes the ancient distinction between logic and grammar, where logic is concerned with form, and grammar is concerned with meaning and interpretation. Taking this view to the extreme, we could say that model theory should not even be seen as part of logic, but rather grammar. They are closely related, but the distinction is important.