morphisms-of-computational-structures
morphisms-of-computational-structures copied to clipboard
prathyvsh
Investigate the link between CPS, Peirce’s Law, Intuitionistic Logic, and Classical Logic
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
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.
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
Interesting set of slides on studying semantics here: https://staff.fnwi.uva.nl/d.j.n.vaneijck2/courses/09/pdfs/CSWFP.pdf
This article tries to show a link between Aristotle’s hylomorphism and recursion schemes: https://blog.sumtypeofway.com/posts/recursion-schemes-part-5.html
Link between abduction and continuations here: https://tel.archives-ouvertes.fr/tel-00783245/document
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