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.

Model Theory WIP

 * $\checkmark$ Definition:Theory and Definition:Theory (Logic)
 * $\checkmark$ Sort out relation between Definition:Formal Semantics and Definition:Model Theory
 * Formal Semantics is currently more general.
 * But in principle a Formal Semantics is just a definition, and Model Theory is a branch of mathematics
 * Therefore Formal Semantics should stand to Model Theory as Definition:Proof System stands to Definition:Proof Theory
 * Idea, restructure current Model Theory results to Definition:Model Theory for Predicate Logic, which is then the branch of maths dealing with the Definition:Formal Semantics of Structures for Predicate Logic
 * Then explain on Model Theory page that Model Theory for Predicate Logic is the most prominent.
 * $\checkmark$ Following this reorganisation, clean up the structure of Category:Mathematical Logic to make sense. Update: A lot of restructuring done. It should be sufficient for now, except aforementioned change for Model Theory and Formal Semantics
 * $\checkmark$ Clean up the Bourbaki track into the general pages as described on Definition talk:Formal Language/Alphabet/Letter

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

Predicate logic
This stuff has been nagging me for a long time now. I will start working on a new page to replace Definition:Predicate Calculus. See User:Lord_Farin/Sandbox/Definition:Language of Predicate Logic. &mdash; Lord_Farin (talk) 12:14, 25 March 2016 (UTC)


 * The move is complete. See Definition:Language of Predicate Logic for the result. More polishing is to be done, but the primary move is out of the way. &mdash; Lord_Farin (talk) 19:58, 24 July 2016 (UTC)


 * Good job! --prime mover (talk) 20:00, 24 July 2016 (UTC)

Thanks! I will get to refactoring the pages and setting up nice transclusions once the improved extension is available (which I'm in the process of improving the dev environment of with Joe). And then my hands will finally be untied from big outstanding redesigns. &mdash; Lord_Farin (talk) 20:10, 24 July 2016 (UTC)

To do:
 * Refactor Definition:Language of Predicate Logic c.s.
 * Rewrite Definition:Substitution, Definition:Substitution Instance and everything tied to it in a universal language and framework.
 * Includes "Notation II.8.11" of Kunen on substitution notation
 * Split up Category:Predicate Logic and Category:Definitions/Predicate Logic