Definition talk:Proof System/Rule of Inference

I may be a bit out of my depth here, but should this be linked to Definition:Natural Deduction? The two seem to be quite similar, at least without having ever studied formal systems. --Cynic (talk) 05:45, 2 August 2010 (UTC)

Technically, "natural deduction" can be considered as a formal language, in which the proof rules are instances of "rules of inference". But the concept of a formal language is far wider than just propositional logic / propcalc.

It's a reasonable approach to define natural deduction as a formal language (after all, that was why formal languages were initially devised in the first place) but it gets a bit unwieldy to do so. The approach taken by the Propositional Calculus section is a somewhat more pared-down approach which makes it easier to see the detail of the structure of what is actually going on. --Prime.mover 17:54, 2 August 2010 (UTC)