Talk:Rule of inference
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One glaring omission is not to mention derived rules of inference, that some rules of inference can be deduced giving others. An example at least should be given, and mention made that there are some minimal sets of rules of inference that can be used to derive the rest. This may form another article later on.
- I did this (a while ago) Brighterorange 22:03, 25 Apr 2005 (UTC)
I take issue with the following statement: "If the premise set is empty, then the conclusion is said to be a theorem or axiom of the logic." An axiom for sure, but a theorem? Those two are opposites. A theorem requires reasoning and therefore qualifies as having a premise. --69.1.21.106 11:33, 22 January 2007 (UTC)
- It is standard to say that theorems of a theory T are derivable from the empty set "with respect to (the axioms of) T". Specifically, the derivation relation is generally relativized to a system, so that if ⊢T denotes derivability in T, then if A is a theorem of T, it is written ⊢T P to mean that P is derivable in T from the empty set. If we take derivation in a more abstract form, then usually we write T ⊢ A to mean that A is derivable solely from the theory T, where T may be the axioms of classical logic, and ⊢ some abstract derivation relation. Nortexoid 17:36, 22 January 2007 (UTC)
