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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: Sun, 7 Jul 2024 23:05:25 +0200
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Hi,

There are possibly issues of interdisciplinary
work. For example Sorensen & Urzyczyn in their
Lectures on the Curry-Howard Isomorphism say that
the logic LP has no name in literature.

On the other hand Segerbergs paper, shows that
a logic LP, in his labeling JP, that stems from
accepting Peice's Law is equivalent to a logic
accepting Curry's Refutation rule,

i.e the logic JE with:

      Γ, A => B |- A
     -----------------
          Γ |- A

But the logic JE also implies that LEM was added!

Bye

Mild Shock schrieb:
> 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.
>