Undecidability of the problem of recognizing axiomatizations for implicative propositional calculi

Autor:	Bokov, Grigoriy V.
Rok vydání:	2014
Předmět:	Mathematics - Logic Computer Science - Logic in Computer Science
Zdroj:	Logic Journal of the IGPL (2015) 23 (2): 341-353
Druh dokumentu:	Working Paper
DOI:	10.1093/jigpal/jzu047
Popis:	In this paper we consider propositional calculi, which are finitely axiomatizable extensions of intuitionistic implicational propositional calculus together with the rules of modus ponens and substitution. We give a proof of undecidability of the following problem for these calculi: whether a given finite set of propositional formulas constitutes an adequate axiom system for a fixed propositional calculus. Moreover, we prove the same for the following restriction of this problem: whether a given finite set of theorems of a fixed propositional calculus derives all theorems of this calculus. The proof of these results is based on a reduction of the undecidable halting problem for the tag systems introduced by Post. Comment: 13 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1407.7010 Zobrazit plný text záznamu View this record from Arxiv