User:Lord Farin/Sandbox

This page exists for me to be able to test features I am developing. Also, incomplete proofs may appear here.

Feel free to comment.

Over time, stuff may move to User:Lord_Farin/Sandbox/Archive.

Subpages of this one may exist; they are listed at this PW special page.

Also see Module:Sandbox/Lord_Farin for my Lua sandbox.

Proof Rules / Rules of Inference
The pages in Category:Proof Rules are currently focused on PropLog. As I cover more ground in PredLog, most of the proof rules transfer.

Not all systems have equivalent rules of inference and derived rules.

To accommodate for further coverage of these subjects we ought to design these pages in a way that we can easily add the references to new proof systems having these rules.

This includes the proof of being a derived rule if necessary. Those pages will look like Deduction Theorem.

Applications will mostly lie in deriving stuff like Completeness Theorems, but once we get to deeper parts of proof theory it is going to be very convenient to have this solid foundation.

Expect a proposal on the subpages here, including an explanation/motivation on Talk:Main Page. &mdash; Lord_Farin (talk) 09:13, 17 June 2022 (UTC)


 * A daunting prospect. IIRC it took quite some time to come up with the current structure, and even now I'm not sure if I got it the way it should be.


 * I look forward to the proposal. --prime mover (talk) 09:28, 17 June 2022 (UTC)


 * Progress/structure to be at User:Lord_Farin/Sandbox/Proof Rules. &mdash; Lord_Farin (talk) 19:15, 17 June 2022 (UTC)


 * Completed. Took longer than anticipated. Some source review tasks remain but they are not many and should be straightforward. &mdash; Lord_Farin (talk) 12:43, 4 September 2022 (UTC)

Resolving Definition:Propositional Tableau
I rediscovered a rewrite of Definition:Propositional Tableau in my sandbox. It is a transcript of what can be found in the "second edition" of Keisler-Robbin. Since I now managed to also find the true, first edition, I can set up the transition proper. User:Lord_Farin/Sandbox/PT will record the progress. &mdash; Lord_Farin (talk) 16:57, 20 September 2017 (EDT)


 * The consolidation is done. There are some loose ends but they are either not critical (in that they are part of the usual discourse of the refactor category) or tied into the approach to Basson-O'Connor:
 * which serves to resolve the problems with Definition:Consistent (Logic). Screw thoroughness and consistency.
 * which serves to resolve the problems with Definition:Consistent (Logic). Screw thoroughness and consistency.


 * The residue is below. I will proceed with Basson-O'Connor. &mdash; Lord_Farin (talk) 15:09, 9 October 2017 (EDT)


 * The progress of revisiting Basson-O'Connor is on User:Lord_Farin/Sandbox/BOC. &mdash; Lord_Farin (talk) 15:54, 9 October 2017 (EDT)

Integrated approach

 * Equivalence of Semantic Consequence and Logical Implication
 * Equivalence of Definitions of Logical Consistence

Loose ends
(This list is also on my user page)


 * Definition:Used WFF / Definition:Unused WFF
 * Fix inline definition on Tableau Extension Lemma
 * Models for Propositional Logic
 * Strongly Sound Proof System is Sound
 * Strongly Complete Proof System is Complete