I am studying the Introduction to Logic course from Stanford University and I began learning about relational logic. However when I searched 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?
Relational logic is, in all likelihood, a subset of predicate logic and has to do with, as the name implies, relations.
Examples:
Jones (j) is Smith's (s) brother. Bxy = x is brother to y. So Bjs. This relation is symmetric i.e. Bjs implies and is implied by Bsj
Brown (b) is as fat as Smith. Fxy = x is as fat as y. So Fbs and also Fbb (the relation is reflexive)
Smith is taller than Jones. Txy = x is taller than y. So Tsj. Now for some relational logic: (Tsj & Tjb) implies Tsb (the relation is transitive).
The above are dyadic relations.
An example of a triadic relation is Smith (s) asked Jones (j) to call Brown (b) which in symbolic form would be Csjb; the general expression is Cxyz which translates as x asked y to call z.
Chapter 9 of the Stanford Introduction to Logic offers the following distinction between Relational Logic and First Order Logic:
Relational Logic, as defined in Chapter 6, allows us to axiomatize worlds with varying numbers of objects. The main restriction is that the worlds must be finite (since we have only finitely many constants to refer to these objects).
Often, we want to describe worlds with infinitely many objects. For example, it would be nice to axiomatize arithmetic over the integers or to talk about sequences of objects of varying lengths. Unfortunately, this is not possible due to the finiteness restriction of Relational Logic.
One difference is "the finiteness restriction of Relational Logic".
Stanford Introduction to Logic. Retrieved on September 2, 2019 at http://intrologic.stanford.edu/notes/chapter_09.html
