Sur des classes de fonctions à seuil caractérisables par des contraintes relationnelles — On classes of threshold functions characterizable by relational constraints
Couceiro, Miguel; Lehtonen, Erkko; Schölzel, Karsten
Actes des 22èmes rencontres francophones sur la Logique Floue et ses Applications (LFA 2013), Université de Reims Champagne-Ardenne, (2013), 145-152
Motivated by modal semantics induced by majority games, we consider the class of threshold functions. It was shown by L. Hellerstein that this class is characterizable by relational constraints (or equivalently, by functional equations), but that there is no characterization by means of finitely many constraints. In this paper, we present a complete classification of classes of threshold functions induced by Boolean clones, into whether they are characterizable by finitely many relational constraints. Moreover we provide sets of constraints characterizing each of such classes.