Talk:Rule of inference

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Merge?

Moved from Talk:Inference rule.

As far as I can see, this article ought to be merged with Rule of inference. Does anyone disagree? Neilc 06:04, 12 Aug 2004 (UTC)

glaring omission

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. — Preceding unsigned comment added by 208.38.7.220 (talk) 15:50, 7 July 2004 (UTC)

I did this (a while ago) —Brighterorange 22:03, 25 Apr 2005 (UTC)

Potential issues

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)

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List of rules of inference

Talk:List of rules of inference#The table with 3 columns and 12 rows under the heading "Table: Rules of Inference" is currently missing 8 different rows. 88.241.82.180 (talk) 14:15, 21 January 2025 (UTC)

Changes to the article

I was thinking about implementing changes to this article with the hope of moving it in the direction of GA status. Most of the text is currently unreferenced. Usually, the lead should summarize information found in the body of the article, not present new information, like it is done here.

Contentwise, a lot of information is currently missing. There are countless rules of inference and at least the most important ones should be discussed. It should be better explained that rules of inference belong to systems of logic. Different systems of logic have different rules of inference, like the contrasts between propositional logic and predicate logic or between classical and intuitionistic logic. Another point to mention would be the different formalisms of Hilbert systems, natural deduction, and sequent calculus. Other things to discuss would be the relation between rules of inference and logical truths, the problem of fallacies, and the role of rules of inference in the philosophy of logic regarding the contrast between the semantic and the syntactic conception of logic. Since some of these topics are quite abstract, one could add a section called "Basic concepts" to explain what logic, systems of logic, propositions, and inferences are. It further wouldn't hurt to mention some applications in fields like mathematical reasoning, computer science, expert systems, automated theorem proving, etc.

There are more things to consider, but they can be addressed later since the ones mentioned so far will already involve a lot of work to implement. I was hoping to get some feedback on these ideas and possibly other suggestions. Phlsph7 (talk) 13:36, 16 March 2025 (UTC)