Article <v67ta1$6pt0$1@solani.org>

Warning: mysqli::__construct(): (HY000/1203): User howardkn already has more than 'max_user_connections' active connections in D:\Inetpub\vhosts\howardknight.net\al.howardknight.net\includes\artfuncs.php on line 21
Failed to connect to MySQL: (1203) User howardkn already has more than 'max_user_connections' active connections
Warning: mysqli::query(): Couldn't fetch mysqli in D:\Inetpub\vhosts\howardknight.net\al.howardknight.net\index.php on line 66
Article <v67ta1$6pt0$1@solani.org>

Deutsch English Français Italiano

<v67ta1$6pt0$1@solani.org>

View for Bookmarking (what is this?)
Look up another Usenet article

Path: ...!eternal-september.org!feeder3.eternal-september.org!weretis.net!feeder8.news.weretis.net!reader5.news.weretis.net!news.solani.org!.POSTED!not-for-mail
From: Mild Shock <janburse@fastmail.fm>
Newsgroups: sci.logic
Subject: Re: Minimal Logics in the 2020's: A Meteoric Rise
Date: Fri, 5 Jul 2024 06:37:22 +0200
Message-ID: <v67ta1$6pt0$1@solani.org>
References: <v67685$6fr5$1@solani.org>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Fri, 5 Jul 2024 04:37:21 -0000 (UTC)
Injection-Info: solani.org;
	logging-data="223136"; mail-complaints-to="abuse@news.solani.org"
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
 Firefox/91.0 SeaMonkey/2.53.18.2
Cancel-Lock: sha1:WAhXvwzKDg4C7e5RPOl8zN84etk=
In-Reply-To: <v67685$6fr5$1@solani.org>
X-User-ID: eJwFwYEBwDAEBMCVgvdkHBX2H6F3bhR2gE74+vaMC5CWWzyiV1FXLbuORRKpD+/4bU3lfOLcMLZF5EBqfynZFFI=
Bytes: 3123
Lines: 60

The meteoric rise of Curry-Howard isomorphism
and minimal logic, possibly because proof assistants
such as Lean, Agda, etc… all use it, is quite ironic,
in the light of this statement:

 > Because of the vagueness of the notions of “constructive
 > proof”, “constructive operation”, the BHK-interpretation
 > has never become a versatile technical tool in the way
 > classical semantics has. Perhaps it is correct to say
 > that by most people the BHK-interpretation has never been
 > seen as an intuitionistic counterpart to classical semantics.
 > https://festschriften.illc.uva.nl/j50/contribs/troelstra/troelstra.pdf

Mild Shock schrieb:
> Could be a wake-up call this many participants
> already in the commitee, that the whole logic
> world was asleep for many years:
> 
> Non-Classical Logics. Theory and Applications XI,
> 5-8 September 2024, Lodz (Poland)
> https://easychair.org/cfp/NCL24
> 
> Why is Minimal Logic at the core of many things?
> Because it is the logic of Curry-Howard isomoprhism
> for symple types:
> 
> ----------------
> Γ ∪ { A } ⊢ A
> 
> Γ ∪ { A } ⊢ B
> ----------------
> Γ ⊢ A → B
> 
> Γ ⊢ A → B           Δ ⊢ A
> ----------------------------
> Γ ∪ Δ ⊢ B
> 
> And funny things can happen, especially when people
> hallucinate duality or think symmetry is given, for
> example in newer inventions such as λμ-calculus,
> 
> but then omg ~~p => p is nevertheless not provable,
> because they forgot an inference rule. LoL
> 
> Recommended reading so far:
> 
> Propositional Logics Related to Heyting’s and Johansson’s
> February 2008 - Krister Segerberg
> https://www.researchgate.net/publication/228036664
> 
> The Logic of Church and Curry
> Jonathan P. Seldin - 2009
> https://www.sciencedirect.com/handbook/handbook-of-the-history-of-logic/vol/5/suppl/C 
> 
> 
> Meanwhile I am going back to my tinkering with my
> Prolog system, which even provides a more primitive
> logic than minimal logic, pure Prolog is minimal
> 
> logic without embedded implication.