On Logical Method for Counting Dedekind Numbers

  • Authors:

  • Mati Tombak;Ain Isotamm;Tõnu Tamme

  • Affiliations:

  • -;-;-

  • Venue:
  • FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
  • Year:
  • 2001

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Abstract

A description of the property of monotonicity of Boolean functions using propositional calculus is presented, which allows to use #SAT algorithms for computing Dedekind numbers. Using an obvious modification of Davis-Putnam satisfiability algorithm, Dedekind numbers until the seventh have been calculated. Standard arithmetization of propositional logic allows to deduce Kisielewicz's formula in more transparent way.