Talk:Proof calculus
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More Methods
[edit]The article could list more methods, like Tableaux proof systems, Resolution proof system, Connection graph proof systems, etc..
Jan Burse (talk) 09:39, 19 March 2019 (UTC)
- Hi Jan. The article is in dreadful shape as it stands: no inline refs, hardly any sources, dubious editorialising. Any love you want to give it would be appreciated. — Charles Stewart (talk) 01:26, 20 March 2019 (UTC)
Proof system = deductive system?
[edit]I fail to understand the difference between a proof system and a deductive system. I allow to forward this argumentum ad populum: it seems that in other wikis the terms are used synonymously[1] [2] which seems to correspond to the entity defined by this article. May someone shed some light on the distinction, if any? Leonry (talk) 18:48, 25 October 2020 (UTC)
- I like to mention another reference that adds to my confusion. On the Proof Wiki, a Deductive apparatus is understood to be a more general term than proof systems.[3] However, what is called there a proof system seems to correspond to the Deductive system or deductive apparatus as defined here on Wikipedia (in the article linked). Leonry (talk) 13:14, 17 December 2020 (UTC)
- I've never seen deductive apparatus used the way the Proof Wiki uses it: i.e. a deductive system plus an intended model. Since they give no source for their definition, I am inclined to ignore it. In general, when we use the word 'calculus' rather than 'system', we are indicating that we regard the formalisation as a tool rather than just a way of specifying a theory. — Charles Stewart (talk) 22:03, 20 December 2020 (UTC)
- From what I understand, the intended definition of deductive apparatus on ProofWiki is not plus but and/or, to allow for the notion of 'apparatus' to capture both the proof-theoretic (i.e., proof systems) and model-theoretic (i.e. semantic) approaches to formal systems. Tule-hog (talk) 20:51, 13 December 2024 (UTC)
- I've never seen deductive apparatus used the way the Proof Wiki uses it: i.e. a deductive system plus an intended model. Since they give no source for their definition, I am inclined to ignore it. In general, when we use the word 'calculus' rather than 'system', we are indicating that we regard the formalisation as a tool rather than just a way of specifying a theory. — Charles Stewart (talk) 22:03, 20 December 2020 (UTC)
- Toss in Proof procedure if you really want to get confused... Tule-hog (talk) 21:03, 13 December 2024 (UTC)
References
- ^ "formal system". planetmath.org. Retrieved 2020-10-25.
- ^ "natural deduction in nLab". ncatlab.org. Retrieved 2020-10-25.
- ^ "Definition:Deductive Apparatus - ProofWiki". proofwiki.org. Retrieved 2020-12-17.