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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: Minimal Logics in the 2020's: A Meteoric Rise
Date: Thu, 4 Jul 2024 17:14:07 -0500
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On 7/4/2024 5:03 PM, Mild Shock wrote:
> 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.
Prolog logic such that provable means true and false
means unprovable is the key foundation of correct reasoning.
It simply implicitly rejects expressions that would otherwise
result in mathematical incompleteness as not truth bearers
within its system. This is the way that correct reasoning
actually works.
When expressions of language are self-contradictory such
that X and ~X cannot be proven within the system Prolog
rejects X. Mathematical logic would conclude that the
system is incomplete.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer