Minimal Logics in the 2020's: A Meteoric Rise

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Sujet : Minimal Logics in the 2020's: A Meteoric Rise
De : janburse (at) *nospam* fastmail.fm (Mild Shock)
Groupes : sci.logic
Date : 05. Jul 2024, 00:03:51
Autres entêtes
Message-ID : <v67685$6fr5$1@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
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.

Date Sujet#  Auteur
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