# Statistics of implicational logic

@inproceedings{Zaionc2003StatisticsOI,
title={Statistics of implicational logic},
author={Marek Zaionc},
booktitle={Workshop on Logic, Language, Information and Computation},
year={2003}
}
• M. Zaionc
• Published in
Workshop on Logic, Language…
1 September 2003
• Mathematics
7 Citations
This paper presents the number of results concerning problems of asymptotic densities in the variety of propositional logics. We investigate, for propositional formulas, the proportion of tautologies
• Computer Science, Mathematics
Random Struct. Algorithms
• 2012
The relation between the probability of a function and its complexity is obtained when random expressions are drawn according to a critical branching process and it is proved that most expressions computing any given function in this system are “simple”.
• Computer Science, Mathematics
MFCS
• 2008
It is shown how to approximate the probability of a function f when the number of variables grows to infinity, and that this asymptotic probability has a simple expression in terms of the complexity of f.
• Computer Science, Mathematics
• 2005
Two probability distributions on Boolean functions defined in terms of their representations by a d/or trees (or formulas) are considered, with special attention being paid to the constant function True and read-once functions in a fixed number of variables.
• Computer Science, Mathematics
• 2005
Two probability distributions on Boolean functions defined in terms of their representations by $\texttt{and/or}$ trees (or formulas) are considered, with special attention being paid to the constant function $\textit{True}$ and read-once functions in a fixed number of variables.
This work examines how to define several probability distributions on the set of Boolean functions on a fixed number of variables, starting from a representation of Boolean expressions by trees and considers the relations between the probability of a Boolean function and its complexity.

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From the lower and upper bounds presented, it is deduced that at least 1/3 of classical tautologies are intuitionistic, or the density or asymptotic probability of provable intuitionistic propositional formulas in the set of all formulas.

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