Talk:Many-sorted logic

Definition

The current definition many-sorted logic can reflect formally our intention not to handle the universe as a homogeneous collection of objects leaves me with more questions than answers:

if it "can reflect", what else can it do? Does this mean also that in some circumstances it does not reflect?
whose intention can it reflect? Man's, the authors', some other group?

I would try to improve the definition myself, but I do not know the answers to these questions. -AndrewDressel (talk) 17:18, 26 July 2013 (UTC)[reply]

I thought about improving the article's lead, too, yet still without success.

I think, it should first define what is a logic in general (which seems to me not an easy task if one tries to be compatible to the very abstract setting of the Caleiro+Gonçalves article cited in section Many-sorted_logic#Algebraization), and then what is a many-sorted logic in particular (the existing introductory sentence could be used for that).

Another approach could be first to explain what is first-order predicate logic in general, then to define what is many-sorted first-order predicate logic in particular (I think, I'd be able to do both), and afterwards to mention that there are more abstract views, as in the Caleiro+Gonçalves article (I'm unable to do the latter).

In fact, the Many-sorted_logic#Example section and the Many-sorted_logic#Order-sorted_logic section both is about many-sorted first-order predicate logic, not about general many-sorted logic. Jochen Burghardt (talk) 13:05, 27 July 2013 (UTC)[reply]

Merge?

Isn't this matter identified with Type theory? Millbug ^talk 03:21, 8 May 2016 (UTC)[reply]

I think, it is somewhat similar to morning star and evening star in Frege's Puzzle: both matters are closely related, but usually tackled from different viewpoints. The section Type theory#Difference from set theory gives some description of the differences, when read with the understanding that many-sorted logic typically belongs to what is called set theories there. In addition, as far as I know, different communities of computer-science researchers are concerned with both matters; and type theory usually happens to deal with some kind of higher-order logic (i.e. allowing for function and/or predicate variables to appear in formulas), while many-sorted logic usually does not. While it would certainly be worthwhile to have an article (part) comparing both approaches, I'm afraid it would have to contain some original research. - Jochen Burghardt (talk) 09:27, 10 May 2016 (UTC)[reply]

So how we could improve it in order to make it "more understandable"? Millbug ^talk 17:07, 10 May 2016 (UTC)[reply]

I would not merge it with type theory. Type theory usually refers to something much more complex - e.g. there are usually infinitely many types. Multi-sorted logic usually refers to systems with just a few types (e.g. just two). More importantly, multi-sorted logic usually refers to a version of first-order logic, while type theory is often formalized with different inference rules that are not present in first-order logic (e.g. for making judgements about typing). — Carl (CBM · talk) 21:12, 10 May 2016 (UTC)[reply]

Thank you both. Now it's clearer for me. Can we reach a consensus in order to insert in the beginning of the page something like "it's a kind of first order logic" (and to develop it)? Millbug ^talk 00:01, 11 May 2016 (UTC)[reply]

I think there is a lot of room for improving the article. Right now the only mention of first-order logic is in the see also section. We could add a section on first-order logic and a section on type theory. — Carl (CBM · talk) 00:40, 11 May 2016 (UTC)[reply]

If there is no opposition, I can start. Okay? Millbug ^talk 02:28, 11 May 2016 (UTC)[reply]

Okay for me. - Jochen Burghardt (talk) 07:39, 11 May 2016 (UTC)[reply]

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