• Corpus ID: 211677686

Computing the density of tautologies in propositional logic by solving system of quadratic equations of generating functions

@article{Eom2020ComputingTD,
  title={Computing the density of tautologies in propositional logic by solving system of quadratic equations of generating functions},
  author={Taehyun Eom},
  journal={arXiv: Logic},
  year={2020}
}
  • Taehyun Eom
  • Published 1 March 2020
  • Computer Science
  • arXiv: Logic
In this paper, we will provide a method to compute the density of tautologies among the set of well-formed formulae consisting of $m$ variables, a negation symbol and an implication symbol, which has a possibility to be applied for other logical systems. This paper contains computational numerical values of the density of tautologies for two, three, and four variable cases. Also, for certain quadratic systems, we will introduce the $s$-cut concept to make a better approximation when we compute… 

References

SHOWING 1-6 OF 6 REFERENCES

On the Asymptotic Density of Tautologies in Logic of Implication and Negation

The paper solves the problem of finding the asymptotic probability of the set of tautologies of classical logic with one propositional variable, implication and negation and proves the existence of this limit for classical (and at the same time intuitionistic) logic of implication built with exactly one variable.

Probability distribution for simple tautologies

Density of Tautologies in Logics with One Variable

The ratio of the number of tautologies and thenumber of formulae of length n is estimated by determining the asymptotic density of tauts in different kinds of logics with one variable.

Tautologies over implication with negative literals

It is proved that asymptotically, when the number of variables becomes large, all tautologies have the following simple structure: either a premise equal to the goal, or two premises which are opposite literals.

Analytic Combinatorics

This text can be used as the basis for an advanced undergraduate or a graduate course on the subject, or for self-study, and is certain to become the definitive reference on the topic.

Analytic Combinatorics (Cambridge

  • 2009