Generating functionology
Counting Satisfiable k-CNF Formulas
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Statistical properties of simple types
Mathematical Structures in Computer Science
Intuitionistic vs. classical tautologies, quantitative comparison
TYPES'07 Proceedings of the 2007 international conference on Types for proofs and programs
Classical and intuitionistic logic are asymptotically identical
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
On counting untyped lambda terms
Theoretical Computer Science
Density of tautologies in logics with one variable
Acta Cybernetica
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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 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.