Re: Minimal Logics in the 2020's: A Meteoric Rise (Was: The road to Artificial Intelligence)

Hi,
This has only become talk of the town recently
under the heading of Constructive S4 Modal Logic
or CS4. It somehow demonstrates that prejudice
against computer science, like lambda calculus is
too abstract, is possibly unfounded. The challenge
would be to draw connections and foster inter-
disciplinary dialog. The next challenge would
be to distill a simple didactical extract of it
and draw road maps!
Categorical and Kripke Semantics for Constructive S4 Modal Logic
Alechina et al. - 2003
https://www.cs.bham.ac.uk/~exr/papers/csl01.pdf
What they call fallible worlds, does Segerberg
1968 call abnormal worlds.
Bye
Mild Shock schrieb:

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.
>
Mild Shock schrieb:

>
Your new Scrum Master is here! - ChatGPT, 2023
https://www.bbntimes.com/companies/ai-will-make-agile-coaches-and-scrum-masters-redundant-in-less-than-2-years >
>
LoL
>
Thomas Alva Edison schrieb am Dienstag, 10. Juli 2018 um 15:28:05 UTC+2:

Prolog Class Signpost - American Style 2018
https://www.youtube.com/watch?v=CxQKltWI0NA

>

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