2013 • In Marichal, Jean-Luc; Essounbouli, Najib; Guelton, Kevin (Eds.) Actes des 22èmes rencontres francophones sur la Logique Floue et ses Applications, 10-11 octobre 2013, Reims, France
Boolean function; relational constraint; functional equation; threshold function; clone; characterization; fonction à seuil; caractérisation; Fonction booléenne; contrainte relationnelle; équation fonctionnelle
Abstract :
[en] 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.
Disciplines :
Mathematics Quantitative methods in economics & management
Author, co-author :
Couceiro, Miguel; Université Paris Dauphine > LAMSADE
Lehtonen, Erkko ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC)
Schölzel, Karsten ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
Sur des classes de fonctions à seuil caractérisables par des contraintes relationnelles
Alternative titles :
[en] On classes of threshold functions characterizable by relational constraints
Publication date :
October 2013
Event name :
Rencontres francophones sur la logique floue et ses applications 2013 (LFA 2013)
Event organizer :
Najib Essounbouli (co-président du comité d’organisation) Kevin Guelton (co-président du comité d’organisation) Jean-Luc Marichal (président du comité de programme)
Event place :
Reims, France
Event date :
from 10-10-2013 to 11-10-2013
Audience :
International
Main work title :
Actes des 22èmes rencontres francophones sur la Logique Floue et ses Applications, 10-11 octobre 2013, Reims, France
