Density of tautologies in logics with one variable

Authors:
László Aszalós;Tamás Herendi
Affiliations:
University of Debrecen, Egyetem tér 1, Debrecen, Hungary;University of Debrecen, Egyetem tér 1, Debrecen, Hungary
Venue:
Acta Cybernetica
Year:
2012

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Abstract

In the present paper we estimate the ratio of the number of tautologies and the number of formulae of length n by determining the asymptotic density of tautologies in different kinds of logics with one variable. The logics under consideration are the ones with a single connective (nand or nor); negation with a connective (disjunction or conjunction); and several connectives.