Majority digraphs

Tri Lai, Jörg Endrullis, Lawrence S. Moss

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

A majority digraph is a finite simple digraph G = (V,→) such that there exist finite sets Av for the vertices v ∈ V with the following property: u → v if and only if “more than half of the Au are Av”. That is, u → v if and only if (formula presented). We characterize the majority digraphs as the digraphs with the property that every directed cycle has a reversal. If we change to any real number α ∈ (0, 1), we obtain the same class of digraphs. We apply the characterization result to obtain a result on the logic of assertions “most X are Y ” and the standard connectives of propositional logic.

Original language English 3701-3715 15 Proceedings of the American Mathematical Society 144 9 https://doi.org/10.1090/proc/13038 Published - 2016

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Digraph
If and only if
Propositional Logic
Reversal
Assertion
Finite Set
Logic
Cycle

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Lai, Tri ; Endrullis, Jörg ; Moss, Lawrence S. / Majority digraphs. In: Proceedings of the American Mathematical Society. 2016 ; Vol. 144, No. 9. pp. 3701-3715.
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Majority digraphs. / Lai, Tri; Endrullis, Jörg; Moss, Lawrence S.

In: Proceedings of the American Mathematical Society, Vol. 144, No. 9, 2016, p. 3701-3715.

Research output: Contribution to JournalArticleAcademicpeer-review

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