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
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7 Citations
Background Citations
6
Results Citations
1

7 Citations

Asymptotic Properties of Logics

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…

Asymptotic Density for Equivalence

The fraction of large random trees representing a given Boolean function in implicational logic

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”.

Complexity and Limiting Ratio of Boolean Functions over Implication

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.

Analysis of Algorithms DMTCS proc . AD , 2005 , 139 – 146 And / or tree probabilities of Boolean functions

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.

And/or tree probabilities of Boolean functions

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.

Random Boolean expressions

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.

References

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Statistics of Intuitionistic versus Classical Logics

This paper shows the exact density of intuitionistic logic and demonstrates that it covers a substantial part of classical prepositional calculus and may have a philosophical impact on understanding how much the phenomenon of truth is sporadic or frequent in random mathematics sentences.

Advanced Combinatorics: The Art of Finite and Infinite Expansions

I. Vocabulary of Combinatorial Analysis.- 1.1. Subsets of a Set Operations.- 1.2. Product Sets.- 1.3. Maps.- 1.4. Arrangements, Permutations.- 1.5. Combinations (without repetitions) or Blocks.- 1.6.…

Orthogonal Polynomials

In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discussed.

Statistical properties of simple types

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.

A remark on Stirling formula , Ammer

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