On the cardinality of some families of discrete connectives

The computation of a closed formula for the cardinality of some discrete connectives has received the interest of the research community since the beginning of this class of oper-ators. This paper constitutes a substantial progress in this topic. First, monotonicities and other properties of discrete connectives are related to plane partitions, a concept deeply studied in the field of combinatorics. Second, the already known expressions on the cardi-nality of plane partitions are adapted to the concrete properties of discrete connectives. With this, we establish closed formulas for discrete negations and some binary discrete connectives; concretely, discrete conjunctions, disjunctions and implications. As well, we establish formulas for the cardinality of some sets of implications satisfying several addi-tional properties known in the literature.(c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CCBY license (http://creativecommons.org/licenses/by/4.0/).