Open Access
2004 A Simple Embedding of T into Double S5
Steven Kuhn
Notre Dame J. Formal Logic 45(1): 13-18 (2004). DOI: 10.1305/ndjfl/1094155276


The system obtained by adding full propositional quantification to S5 is known to be decidable, while that obtained by doing so for T is known to be recursively intertranslatable with full second-order logic. Recently it was shown that the system with two S5 operators and full propositional quantification is also recursively intertranslatable with second-order logic. This note establishes that the map assigning [1][2]p to \squarep provides a validity and satisfaction preserving translation between the T system and the double S5 system, thus providing an easier proof of the recent result.


Download Citation

Steven Kuhn. "A Simple Embedding of T into Double S5." Notre Dame J. Formal Logic 45 (1) 13 - 18, 2004.


Published: 2004
First available in Project Euclid: 2 September 2004

zbMATH: 1088.03020
MathSciNet: MR2133081
Digital Object Identifier: 10.1305/ndjfl/1094155276

Primary: 03B45

Keywords: 2S5 , propositional quantifier

Rights: Copyright © 2004 University of Notre Dame

Vol.45 • No. 1 • 2004
Back to Top