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On the Significance of Self-Justifying Axiom Systems from the Perspective of Analytic Tableaux

2013/06/29 by Dan E. Willard, Willard, Dan E.
Computer Science · Mathematics · #03B52 #03F25 #03F45 #03H13 #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO) #cs.LO #math.LO #msc:03B52 #msc:03F25 #msc:03F45 #msc:03H13

paper · pdf · doi:10.48550/arxiv.1307.0150

Cover page + 33 pages of text. All the theorems in this January 2014 manuscript also had appeared in the earlier "Version 1" June 2013 draft. The main difference between these two drafts is that I substantially spiced up the accompanying narrative, so as to better explain the motivation for this research endeavor

arxiv created 2014/01/13 · arxiv updated 2014/01/14

Abstract

This article will be a continuation of our research into self-justifying systems. It will introduce several new theorems and their applications. (One of these results will transform our previous infinite-sized self-verifying formalisms into tighter systems, with only a finite number of axioms.) It will explain how self-justification is useful, even when the Incompleteness Theorem limits its reach.

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