search

prathyvsh / morphisms-of-computational-structures

A visual catalogue + story of morphisms displayed across computational structures.
https://patternatlas.com/
122 stars 6 forks source link

Investigate the link between CPS, Peirce’s Law, Intuitionistic Logic, and Classical Logic #21

Open prathyvsh opened 4 years ago

prathyvsh commented 4 years ago

A brief of the idea I glimpsed is that using Peirce’s law you can translate classical proofs into intuitionistic ones by Continuation Passing Style.

References: https://www.cs.uoregon.edu/research/summerschool/summer02/lectures/classical_read.ps https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.30.1334&rep=rep1&type=pdf

prathyvsh commented 3 years ago

Aristotle’s Syllogistic and Core Logic: http://u.osu.edu/tennant.9/files/2014/07/tennant_hpl2014-pqsi5u.pdf

I think the Corcoran-Smiley interpretation of Aristotle’s logic as many-sorted logic is linked to this.

prathyvsh commented 3 years ago

This looks like a pretty interesting document that gives a computational grounding for the dialectica interpretation. The introduction draws links between Aristotle’s work and also contains reference to call/cc. A Materialist Dialectica: https://hal.archives-ouvertes.fr/tel-01247085/document

prathyvsh commented 3 years ago

Interesting set of slides on studying semantics here: https://staff.fnwi.uva.nl/d.j.n.vaneijck2/courses/09/pdfs/CSWFP.pdf

prathyvsh commented 3 years ago

This article tries to show a link between Aristotle’s hylomorphism and recursion schemes: https://blog.sumtypeofway.com/posts/recursion-schemes-part-5.html

prathyvsh commented 3 years ago

Link between abduction and continuations here: https://tel.archives-ouvertes.fr/tel-00783245/document

prathyvsh commented 3 years ago

This topic is touched upon by Henry Story on his second year PhD report: https://co-operating.systems/2019/04/01/PhD_second_year_report.pdf