User:Lord Farin/Sandbox/BOC

Basson - O'Connor - Introduction to Symbolic Logic
This page describes my working through the following source:



I will stop once the coverage has allowed for proving completeness and soundness results for Propositional Logic as covered in this book.

Later

 * Actually rewrite Definition:Consistent; separate "consistent set of formulas" and "consistent axiom system"
 * Cover definition 1 of consistent axiom system (p.75 BOC) as a theorem of equivalence between consistency and soundness. Sequentially before Definition:Consistent/Proof System/Propositional Logic/Definition 2. Compare Equivalence of Definitions of Consistent.
 * Reconsider Definition:Natural Deduction?

Current

 * 20171027: Actually Axiom System as a concept deserves to remain separate from Proof System, because of its use in analysis of independence of axioms etc. For it is common that the rules of inference are fixed but the set of axioms is up for discussion. I will get to this.
 * 20171019: The integration of the two pages mentioned below and their subpages is going to take a lot more effort, due to proper linking left and right. Slow, steady progression should establish the following migrations (consistent with observations made upon the introduction of axiom systems in 2016, according to my talk page):
 * 20171018: Started working on integrating Definition:Axiom System and Definition:Proof System as the two are intimately related, and will coincide for the purposes of . A first step is to move the axiomatic treatment of Basson-O'Connor to the scope of Definition:Hilbert Proof System. See User:Lord_Farin/Sandbox/Definition:Hilbert Proof System/Instance 2 etc.. &mdash; Lord_Farin (talk) 16:31, 18 October 2017 (EDT)
 * 20171016: Started working on replacing the current mess of definitions and theorems from different areas on substitution in PropLog and PredLog. The page User:Lord_Farin/Sandbox/Definition:Substitution (Formal Systems) intends to integrate and replace the following:


 * 20171011: Refactored coverage of formal grammar by introducing Definition:Language of Propositional Logic/Basson-O'Connor. Definition:Natural Deduction is still to do. Current page is Definition:Metalanguage. &mdash; Lord_Farin (talk) 16:21, 11 October 2017 (EDT)
 * 20171009: Got to Definition:Natural Deduction. The hard part starts here. It should be considered to split the axiomatic/theorem status for every tautology for every source. This is painstaking but may be necessary for consistent coverage. &mdash; Lord_Farin (talk) 17:15, 9 October 2017 (EDT)
 * 20171009: Made a start. Got to $\S 3.5$, Definition:Tautology before having to change anything. &mdash; Lord_Farin (talk) 15:56, 9 October 2017 (EDT)