Talk:Independence-friendly logic

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Philosophy: Logic Low‑importance

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	Logic

2005

This entry should be carefully reviewed by an expert in the field.— Preceding unsigned comment added by 202.36.179.65 (talk • contribs)

Independence logic, dependence logic, and logics of imperfect information

At the moment, it seems that there is very little information on Wikipedia about logics of imperfect information (that is, IF logic, dependence logic, branching quantifiers logic and variants). I wrote a draft about dependence logic, my main area of expertise, here; when I have time, I will also try to add some information to the pages about IF logic, branching quantifiers, and game theoretic semantics.

But I was thinking: since these logical formalisms are very much related with each other, would it make sense to create a "logics of imperfect information" subcategory for them? My apologies if this is not the proper place for this suggestion, I am new here -Pietro Galliani (talk) 08:23, 9 March 2011 (UTC)[reply]

Ok, the page on Dependence Logic was accepted, it is now here. I added a section to this page with links to it an to a couple of other related pages, I hope it is ok. --Pietro Galliani (talk) 16:32, 9 March 2011 (UTC)[reply]

Clarifying or shortening?

Nortexoid changed (among other things)

This is because c may depend on a and d may depend on b, so these existential quantifications (∃) must come after the corresponding universal quantifications (∀). First-order logic could express either independence by reordering the quantifiers (say by putting ∃c ∀b instead of ∀b ∃c to express ∀b ∃c/b), but it cannot express both independences at once.

(written by me as 76.84.155.213) into

This is because c depend only on a and d depends only on b. First-order logic cannot express these independences by any linear reordering of the quantifiers.

with the edit summary "clarifying".

This doesn't seem clearer to me, quite the opposite in fact. However, brevity is also a reasonable goal, so I won't change it back; however, I'm preserving my version here, in case others want to think about how short and/or clear it should be. (However, I will fix the grammar, and revert an unwarranted spelling change while I'm at it.)

—Toby Bartels 11:28, 31 October 2007 (UTC)[reply]

On a second look, the word "only" (in both places) certainly does make it clearer, so anybody that prefers my longer version should still include Nortexoid's "only"s. —Toby Bartels 11:44, 31 October 2007 (UTC)[reply]

Feferman

I added a cite to an interesting article of Feferman that criticises IF logic and Hintikka's claims for it.[1] IF-logic at first sounded too good to be true and Feferman's article cleared things up somewhat for me. I don't think I explained the issue very well though. Maybe someone more expert than I am could take a look. —Preceding unsigned comment added by 75.62.4.229 (talk) 09:05, 21 November 2007 (UTC)[reply]

Already done by another name?

I vaguely remember that this same idea was invented previously by someone else (sounds like "Hanken"). He used curly braces and put "forall a exists c" one one line above "forall b exists d" on the second line. Each existentially quantified variable could be made dependent on an arbitrary subset of the universally quantified variables. This is equivalent to putting existential quantifiers for functions first and then following them by universal quantifiers for individual objects, then substituting the universally quantified variables into the slots of the function variables to get the desired dependences. JRSpriggs (talk) 06:32, 29 October 2012 (UTC)[reply]

You're probably thinking of Henkin aka branching quantifiers. This article was/is very bad providing context and relations with other notions. Tijfo098 (talk) 16:10, 29 October 2012 (UTC)[reply]

It would be interesting to have an article on the metalogical properties of existential second-order logic (ESO) because all three of branching quantifiers (on FOL), IF logic, and dependence logic essentially are equivalent to ESO and its metalogical properties are quite different from full SO. ESO is basically the logic of Skolem forms, so it's naturally related to game semantics as well. Tijfo098 (talk) 16:20, 29 October 2012 (UTC)[reply]

Actually Hintikka and Sandu (1996) established the equivalence of IF with ESO by showing IF equivalence with FO + Henkin quantifiers and using the result of Enderton (1970) for the equivalence between ESO and FO + Henkin quantifiers. I did some patching :-) The actual controversy was caused by Hintikka's proposal to use (extended) IF as foundation for maths. Alas that wasn't even mentioned in this article, but now it is so the critique/controversy looks less strange now (to me anyway). Tijfo098 (talk) 02:48, 30 October 2012 (UTC)[reply]

Yes, I believe it was the Henkin quantifiers of which I was thinking. Thank you for reminding me. JRSpriggs (talk) 07:41, 30 October 2012 (UTC)[reply]