Talk:Tautological consequence: Difference between revisions

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Philosophy: Logic Stub‑class Mid‑importance

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Past discussion at entailment

Readers may be interested in the past discussion on this topic at Talk:Entailment#Entailment corresponds exactly to tautological consequence, not logical consequence? Hanlon1755 (talk) 21:29, 17 January 2012 (UTC)[reply]

Problems

There are some problematic statements here. I have deleted the paragraph sourced to Kleene, since Kleene did not use the term "tautological consequence." If this article is defining $\models$ , it needs to be brought into line with standard wording. If it is intended to support the ideas at Talk:Entailment#Entailment corresponds exactly to tautological consequence, not logical consequence?, the those ideas need to be supported. -- 202.124.75.182 (talk) 06:51, 22 January 2012 (UTC)[reply]

Uncomprehensible

I do not understand the article at all. The article should make clear (a) what's the difference between "tautological entailment" and entailment, and (b) what's the purpose of tautological entailment. The example doesn't help (me) to understand anything. Why should (a ^ b) entail c? I think the article should be rewritten or deleted, for it leads to much more confusion than clarity. 109.44.3.32 (talk) 20:53, 11 September 2015 (UTC)[reply]

Admissible Rules

I suspect that the person who wrote the first paragraph was trying to describe something often called Admissible Rules in proof theory [1]. These rules can take logical theorems (tautologies) as input and give more theorems (tautologies) as output. This is why Admissible Rules never change the set of theorems. However, the rest of this article on "tautological consequence" appears to change topic entirely. After the first paragraph, we seem to be talking about the regular old, familiar, semantic concept of logical consequence instead of a special relation that holds between tautologies. This is a mess. I agree with comments above that the article is confusing. Since there is already a nice wiki article on Admissible Rules, perhaps this article on "tautological consequence" can just be deleted. --Paraconsistent (talk) 15:33, 21 February 2022 (UTC)[reply]

@@ Line 11: / Line 11: @@
 I do not understand the article at all. The article should make clear (a) what's the difference between "tautological entailment" and entailment, and (b) what's the purpose of tautological entailment. The example doesn't help (me) to understand anything. Why should (a ^ b) entail c? I think the article should be rewritten or deleted, for it leads to much more confusion than clarity. [[Special:Contributions/109.44.3.32|109.44.3.32]] ([[User talk:109.44.3.32|talk]]) 20:53, 11 September 2015 (UTC)
+== Admissible Rules ==
+I suspect that the person who wrote the first paragraph was trying to describe something often called Admissible Rules in proof theory  [https://en.wikipedia.org/wiki/Admissible_rule]. These rules can take logical theorems (tautologies) as input and give more theorems (tautologies) as output. This is why Admissible Rules never change the set of theorems. However, the rest of this article on "tautological consequence" appears to change topic entirely. After the first paragraph, we seem to be talking about the regular old, familiar, semantic concept of logical consequence instead of a special relation that holds between tautologies. This is a mess. I agree with comments above that the article is confusing. Since there is already a nice wiki article on Admissible Rules, perhaps this article on "tautological consequence" can just be deleted.
+--[[User:Paraconsistent|Paraconsistent]] ([[User talk:Paraconsistent|talk]]) 15:33, 21 February 2022 (UTC)