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Some order dualities in logic, games and choices

Bernard Monjardet

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Abstract: We first present the concept of duality appearing in order theory, i.e. the notions of dual isomorphism and of Galois connection. Then, we describe two fundamental dualities, the duality extension/intention associated with a binary relation between two sets, and the duality between implicational systems and closure systems. Finally, we present two "concrete" dualities occuring in social choice and in choice functions theories.

Keywords: antiexchange closure operator; simple game; Galois connection; implicational system; path-independent choice function; simple game.; analyse des concepts; correspondance de Galois; fermeture anti-échange; fonction de choix chemin-indépendante; jeu simple; système implicatif (search for similar items in EconPapers)
Date: 2007-03
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Published in International Game Theory Review, 2007, 9 (1), pp.1-12. ⟨10.1142/S0219198907001242⟩

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Working Paper: Some order dualities in logic, games and choices (2007) Downloads
Working Paper: Some order dualities in logic, games and choices (2004) Downloads
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DOI: 10.1142/S0219198907001242

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