Paper Info
Title
Statistics of implicational logic
Abstract
In this paper we investigate the size of the fraction of tautologies of the given length n against the number of all formulas of length n for implicational logic. We are specially interested in asymptotic behavior of this fraction. We demonstrate the relation between a number of premises of implicational formula and asymptotic probability of finding formula with this number of premises. Furthermore we investigate the distribution of this asymptotic probabilities. Distribution for all formulas is contrasted with the same distribution for tautologies only. We prove those distributions to be so different that enable us to estimate likelihood of truth for a given long formula. Despite of the fact that all discussed problems and methods in this paper are solved by mathematical means, the paper may have some philosophical impact on the understanding how much the phenomenon of truth is sporadic or frequent in random logical sentences.
Year
DOI
Venue
2003
10.1016/S1571-0661(04)80856-9
Electronic Notes in Theoretical Computer Science
DocType
Volume
ISSN
Journal
84
1571-0661
Citations 
PageRank 
References 
3
0.56
1
Authors
1
Name
Order
Citations
PageRank
Marek Zaionc111117.27