Re: Negative translation for propositional linear (or affine) logic?

Liste des GroupesRevenir à s logic 
Sujet : Re: Negative translation for propositional linear (or affine) logic?
De : janburse (at) *nospam* fastmail.fm (Mild Shock)
Groupes : sci.logic
Date : 01. Dec 2024, 14:15:22
Autres entêtes
Message-ID : <vihnh9$lqqj$1@solani.org>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
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What would make me already happy , if we would be able
to make definitions of these terms, namely:
- Affine logic
- Linear logic
I found this helpful, which isn't behind a paywall:
https://en.wikipedia.org/wiki/Substructural_type_system
"Type system" can be another word for "logic with
proof terms", if you look at:
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
And substructural fits the idea to drop
some of the structural rules.
But to be precise one would need to distingish
left and right structural rules. For example
contraction can happen in at least these two forms:
A & A -> A
A -> A v A
If you have (A & B -> C) == (A -> (B -> C)) you most
lilely won't get rid of the first form.
Julio Di Egidio schrieb:
On 28/11/2024 09:04, Mild Shock wrote:
Affin and linear logic share the use once of a
hypothesis for implication, the unprovability of
P -o P * P being an example of this similarity.
 Should have been yesterday, but it's still the next frontier:
 <https://girard.perso.math.cnrs.fr/0.pdf>
 Of course more than half of it is under a pay wall, but we'll do what we can...
 -Julio
 

Date Sujet#  Auteur
18 Nov 24 * How to prove this theorem with intuitionistic natural deduction?34Julio Di Egidio
18 Nov 24 +* Re: How to prove this theorem with intuitionistic natural deduction?26Mild Shock
18 Nov 24 i`* Re: How to prove this theorem with intuitionistic natural deduction?25Julio Di Egidio
19 Nov 24 i `* can λ-prolog do it? (Was: How to prove this theorem with intuitionistic natural deduction?)24Mild Shock
19 Nov 24 i  `* Re: can λ-prolog do it? (Was: How to prove this theorem with intuitionistic natural deduction?)23Julio Di Egidio
19 Nov 24 i   `* Re: can λ-prolog do it? (Was: How to prove this theorem with intuitionistic natural deduction?)22Mild Shock
22 Nov 24 i    `* Re: can λ-prolog do it? (Was: How to prove this theorem with intuitionistic natural deduction?)21Julio Di Egidio
22 Nov 24 i     +* Re: can λ-prolog do it? (Was: How to prove this theorem with intuitionistic natural deduction?)5Julio Di Egidio
27 Nov 24 i     i`* Re: can λ-prolog do it? (Was: How to prove this theorem with intuitionistic natural deduction?)4Ross Finlayson
27 Nov 24 i     i `* Re: can λ-prolog do it? (Was: How to prove this theorem with intuitionistic natural deduction?)3Julio Di Egidio
27 Nov 24 i     i  `* Re: can λ-prolog do it? (Was: How to prove this theorem with intuitionistic natural deduction?)2Ross Finlayson
27 Nov 24 i     i   `- Re: can λ-prolog do it? (Was: How to prove this theorem with intuitionistic natural deduction?)1Julio Di Egidio
28 Nov 24 i     `* Re: can λ-prolog do it? (Was: How to prove this theorem with intuitionistic natural deduction?)15Mild Shock
28 Nov 24 i      +* Re: can λ-prolog do it? (Was: How to prove this theorem with intuitionistic natural deduction?)2Mild Shock
28 Nov 24 i      i`- Re: can λ-prolog do it? (Was: How to prove this theorem with intuitionistic natural deduction?)1Mild Shock
28 Nov 24 i      +* Negative translation for propositional linear (or affine) logic?10Julio Di Egidio
28 Nov 24 i      i+- Re: Negative translation for propositional linear (or affine) logic?1Julio Di Egidio
28 Nov 24 i      i`* Re: Negative translation for propositional linear (or affine) logic?8Mild Shock
28 Nov 24 i      i `* Re: Negative translation for propositional linear (or affine) logic?7Mild Shock
28 Nov 24 i      i  `* Re: Negative translation for propositional linear (or affine) logic?6Julio Di Egidio
28 Nov 24 i      i   `* Re: Negative translation for propositional linear (or affine) logic?5Mild Shock
28 Nov 24 i      i    `* Re: Negative translation for propositional linear (or affine) logic?4Mild Shock
1 Dec 24 i      i     `* Re: Negative translation for propositional linear (or affine) logic?3Julio Di Egidio
1 Dec 24 i      i      `* Re: Negative translation for propositional linear (or affine) logic?2Mild Shock
1 Dec 24 i      i       `- Re: Negative translation for propositional linear (or affine) logic?1Julio Di Egidio
1 Dec 24 i      `* Re: can λ-prolog do it? (Was: How to prove this theorem with intuitionistic natural deduction?)2Julio Di Egidio
1 Dec 24 i       `- I am busy with other stuff (Was: can λ-prolog do it?)1Mild Shock
1 Dec 24 `* Andrej Bauer is a red flag (Was: How to prove this theorem with intuitionistic natural deduction?)7Mild Shock
1 Dec 24  +- Re: Andrej Bauer is a red flag (Was: How to prove this theorem with intuitionistic natural deduction?)1Mild Shock
1 Dec 24  `* Re: Andrej Bauer is a red flag (Was: How to prove this theorem with intuitionistic natural deduction?)5Julio Di Egidio
1 Dec 24   `* Re: Andrej Bauer is a red flag (Was: How to prove this theorem with intuitionistic natural deduction?)4Mild Shock
1 Dec 24    `* Re: Andrej Bauer is a red flag (Was: How to prove this theorem with intuitionistic natural deduction?)3Mild Shock
1 Dec 24     `* Re: Andrej Bauer is a red flag (Was: How to prove this theorem with intuitionistic natural deduction?)2Mild Shock
1 Dec 24      `- Re: Andrej Bauer is a red flag (Was: How to prove this theorem with intuitionistic natural deduction?)1Mild Shock

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