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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
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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.