RanaldClouston · @RanaldClouston
278 followers · 1304 posts · Server fediscience.org

A first has gone out for (Formal Structures for Computation and Deduction) on at least one mailing list, although the website cs.ioc.ee/fscd24/ is not yet updated with it. The conference "covers all aspects of formal
structures for computation and deduction from theoretical foundations to
applications" and will be held in Talinn in July next year.

#ProofTheory #typetheory #fscd2024 #fscd #callforpapers

Last updated 1 year ago

hxameer :qed: · @xameer
197 followers · 5457 posts · Server mathstodon.xyz

folks any pointers?
The relationship between Herbrand’s theorem and Gentzen’s
“versch ̈after Haupsatz” is difficult to pinpoint, also for proof-theory specialists: to Gentzen,
Herbrand’s is a particular case of his own, with empty antecedent and only one prenex
formula in the consequent; but Gentzen’s Hauptsatz holds only for prenex formulae, though
it is extendable to intuitionistic logic; both give cut elimination; Herbrand’s theorem is
perhaps more informative on the Mittelsequenz
ailalogica.it/archive/preprint

#ProofTheory

Last updated 1 year ago

Yoriyuki Yamagata · @yoriyuki
3 followers · 3 posts · Server mathstodon.xyz
Jon Awbrey · @Inquiry
165 followers · 970 posts · Server mathstodon.xyz

Propositions As Types • 1
inquiryintoinquiry.com/2013/01

One of my favorite mathematical tricks — it almost seems too tricky to be true — is the . Moreover, I see hints the 2-part analogy can be extended to a 3-part analogy, as follows.

\[\text{proof hint : proof : proposition ~::~ untyped term : typed term : type}\]

See my notes on for more information.
oeis.org/wiki/Propositions_As_

#typetheory #ProofTheory #lambdacalculus #CurryHowardIsomorphism #propositionsastypes #propositionsastypesanalogy

Last updated 2 years ago

nilesh · @nilesh
1 followers · 8 posts · Server mathstodon.xyz

I stumbled upon one guy proposing a new foundation for computer mathematics called "Abstraction logic". As a newbie, I found it far more more comprehensible than usual any material on intuitionistic type theory versions.

But there's no social proof of it.

Any of people who are willing to have a look to weight on it?

Links:
arxiv.org/pdf/2207.05610.pdf
youtu.be/LbFKSaPhBSA
obua.com/publications/philosop

#ProofTheory #automatedreasoning #mathematics #foundation #lambdacalculus #typetheory #logic

Last updated 2 years ago

Jon Awbrey · @Inquiry
129 followers · 624 posts · Server mathstodon.xyz
Jon Awbrey · @Inquiry
109 followers · 499 posts · Server mathstodon.xyz
Richard Zach · @rrrichardzach
776 followers · 357 posts · Server mathstodon.xyz
Richard Zach · @rrrichardzach
776 followers · 357 posts · Server mathstodon.xyz
Richard Zach · @rrrichardzach
776 followers · 354 posts · Server mathstodon.xyz

Mon livre sur la théorie de la démonstration avec Paolo Mancosu et Sergio Galvan est disponible en français à partir d'aujourd'hui vrin.fr/livre/9782711630912/in

#ProofTheory #logique #logic

Last updated 2 years ago

Jon Awbrey · @Inquiry
97 followers · 425 posts · Server mathstodon.xyz

• 14
oeis.org/w/index.php?title=Log

• Logical and Topological

The procedure just described is called “traversing” the tree and the string read off is called the “” of the tree. The reverse operation of going from the string to the tree is called “parsing” the string and the tree constructed is called the “ParseGraph” of the string.



#ProofTheory #modeltheory #graphtheory #BooleanFunctions #PropositionalCalculus #lawsofform #spencerbrown #Peirce #logic #traversalstring #duality #LogicalGraphs

Last updated 2 years ago

Jon Awbrey · @Inquiry
96 followers · 414 posts · Server mathstodon.xyz
Jon Awbrey · @Inquiry
96 followers · 408 posts · Server mathstodon.xyz
Jon Awbrey · @Inquiry
94 followers · 376 posts · Server mathstodon.xyz
Jon Awbrey · @Inquiry
94 followers · 375 posts · Server mathstodon.xyz

• 5
oeis.org/w/index.php?title=Log

(cont.)

In particular, though we may note in passing such historical details as the circumstance that Charles Sanders used a symbol where George used a marker, the theme of principal interest at the abstract level of form is neutral with regard to variations of that order.


#ProofTheory #modeltheory #graphtheory #lawsofform #BooleanFunctions #PropositionalCalculus #logic #carpenterssquare #spencerbrown #streamercross #Peirce #abstractpointofview #LogicalGraphs

Last updated 2 years ago

Jon Awbrey · @Inquiry
90 followers · 359 posts · Server mathstodon.xyz

• 3
oeis.org/w/index.php?title=Log

We begin on a low but expansive plateau of mapped out in his system of \((\alpha),\) a platform so abstract in its mathematical forms as to support at least two interpretations for use in the conduct of logical reasoning. Along the way, we incorporate the later contributions of George , who revived and augmented Peirce's system in his book .

#ProofTheory #modeltheory #graphtheory #logic #lawsofform #spencerbrown #alphagraphs #Peirce #formalsystems #LogicalGraphs

Last updated 2 years ago

Jon Awbrey · @Inquiry
89 followers · 338 posts · Server mathstodon.xyz

• 1
oeis.org/w/index.php?title=Log

A is a graph-theoretic structure in one of the systems of graphical syntax Charles Sanders developed for .

In his papers on , , and , Peirce developed several versions of a graphical formalism, or a graph-theoretic formal language, designed to be interpreted for logic.


#ProofTheory #modeltheory #graphtheory #BooleanFunctions #PropositionalCalculus #ExistentialGraphs #EntitativeGraphs #QualitativeLogic #logic #Peirce #logicalgraph #LogicalGraphs

Last updated 2 years ago

Jon Awbrey · @Inquiry
81 followers · 259 posts · Server mathstodon.xyz
Jon Awbrey · @Inquiry
81 followers · 258 posts · Server mathstodon.xyz
Jon Awbrey · @Inquiry
80 followers · 256 posts · Server mathstodon.xyz