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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?

Frank Hubeny
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yoyo_fun
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    If these lecture notes from Stanford are about what you call "relational logic" then it is just another name for predicate calculus. There used to be something else called relational logic (or logic of relatives) developed by De Morgan and Peirce in 19th century (logic of intensional predicates in modern terms) but it is a rather niche subject today. – Conifold Jan 24 '17 at 18:54
  • @Conifold Indeed THAT is the course I am learning now. So I can consider that I am learning predicate logic right ? – yoyo_fun Jan 24 '17 at 19:00
  • No difference; see page 1. – Mauro ALLEGRANZA Jan 24 '17 at 19:54
  • @MauroALLEGRANZA Thanks for pointing out. – yoyo_fun Jan 24 '17 at 21:06
  • @Conifold That should really be an answer (the potential ambiguity is worth having in an answer to the question, since it's not in the existing answer). – Noah Schweber May 29 '20 at 21:11
  • See Dagobert Runes' Dictionary Of Philosophy ( at archive.org) , Logic entry by Alonzo Church –  May 30 '20 at 08:33
  • Sometimes, binary relations are defined as two-place predicates. –  May 30 '20 at 08:37
  • I have always thought of the predicates of predicate logic as relations over their arguments. – polcott Jun 01 '20 at 02:44
  • Here is a good article about relational logic. http://intrologic.stanford.edu/chapters/chapter_06.html It looks like it may be from the same course. Since it includes semantic logical entailment it extends beyond predicate logic. – polcott Jun 01 '20 at 03:38
  • Here is another article that I found. Do a key word search for "relation" in this article: https://plato.stanford.edu/entries/algebra-logic-tradition/ – polcott Jun 01 '20 at 03:48

2 Answers2

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Relational logic is, in all likelihood, a subset of predicate logic and has to do with, as the name implies, relations.

Examples:

  1. 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

  2. Brown (b) is as fat as Smith. Fxy = x is as fat as y. So Fbs and also Fbb (the relation is reflexive)

  3. 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.

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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

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Frank Hubeny
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