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Algebraic approach to modal extensions of Łukasiewicz logics Teheux, Bruno Doctoral thesis (2009) Detailed reference viewed: 119 (7 ULg)A Duality for the Algebras of a Lukasiewicz n + 1-valued Modal System Teheux, Bruno in Studia Logica (2007), 87(1), 13-36 We develop a duality for the varieties of a Lukasiewicz n + 1-valued modal system. This duality is an extension of Stone duality for modal algebras. Some logical consequences (such as completeness results ... [more ▼] We develop a duality for the varieties of a Lukasiewicz n + 1-valued modal system. This duality is an extension of Stone duality for modal algebras. Some logical consequences (such as completeness results, correspondence theory. . . ) are the derived and we propose some ideas for future research. [less ▲] Detailed reference viewed: 42 (9 ULg)Lattice of subalgebras in the finitely generated varieties of MV-algebras Teheux, Bruno in Discrete Mathematics (2007), 307(17-18), 2261-2275 In this paper, we use the theory of natural duality to study subalgebra lattices in the finitely generated varieties of MV-algebras, With this tool, we obtain the dual atomicity of these lattices, and ... [more ▼] In this paper, we use the theory of natural duality to study subalgebra lattices in the finitely generated varieties of MV-algebras, With this tool, we obtain the dual atomicity of these lattices, and characterize the members of these varieties in which every subalgebra is an intersection of maximal subalgebras. Then, we determine the algebras that have a modular or distributive lattice of subalgebras. [less ▲] Detailed reference viewed: 42 (8 ULg)Natural dualities for varieties generated by a set of subalgebras of a semi-primal algebra Mathonet, Pierre ; ; Teheux, Bruno in Algebra and Discrete Mathematics (2007), (1), 67--85 The main contribution of this paper is the construction of a strong duality for the varieties generated by a set of subalgebras of a semi-primal algebra. We also obtain an axiomatization of the objects of ... [more ▼] The main contribution of this paper is the construction of a strong duality for the varieties generated by a set of subalgebras of a semi-primal algebra. We also obtain an axiomatization of the objects of the dual category and develop some algebraic consequences (description of the dual of the finite structures and algebras, construction of finitely generated free algebras,. . . ). Eventually, we illustrate this work for the finitely generated varieties of MV-algebras. [less ▲] Detailed reference viewed: 50 (6 ULg)Treillis des sous-algèbres et opérateurs sur les MV-algèbres Teheux, Bruno Master of advanced studies dissertation (2004) Detailed reference viewed: 44 (4 ULg) |
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