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Pivotal decompositions of functions Marichal, Jean-Luc ; Teheux, Bruno in Discrete Applied Mathematics (2014), 174 We extend the well-known Shannon decomposition of Boolean functions to more general classes of functions. Such decompositions, which we call pivotal decompositions, express the fact that every unary ... [more ▼] We extend the well-known Shannon decomposition of Boolean functions to more general classes of functions. Such decompositions, which we call pivotal decompositions, express the fact that every unary section of a function only depends upon its values at two given elements. Pivotal decompositions appear to hold for various function classes, such as the class of lattice polynomial functions or the class of multilinear polynomial functions. We also define function classes characterized by pivotal decompositions and function classes characterized by their unary members and investigate links between these two concepts. [less ▲] Detailed reference viewed: 140 (9 UL)Reasoning about coalitional effectivity in modal extension of Lukasiewicz logic ; Teheux, Bruno Scientific Conference (2014, July 29) Detailed reference viewed: 38 (3 UL)Preassociative aggregation functions Marichal, Jean-Luc ; Teheux, Bruno in Laurent, Anne; Strauss, Olivier; Bouchon-Meunier, Bernadette (Eds.) et al 15th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2014, Montpellier, France, July 15-19, 2014. Proceedings, Part III (2014, July 22) We investigate the associativity property for varying-arity aggregation functions and introduce the more general property of preassociativity, a natural extension of associativity. We discuss this new ... [more ▼] We investigate the associativity property for varying-arity aggregation functions and introduce the more general property of preassociativity, a natural extension of associativity. We discuss this new property and describe certain classes of preassociative functions. [less ▲] Detailed reference viewed: 80 (7 UL)Associative string functions Lehtonen, Erkko ; Marichal, Jean-Luc ; Teheux, Bruno Scientific Conference (2014, June 24) Detailed reference viewed: 98 (15 UL)Associativity, preassociativity, and string functions Lehtonen, Erkko ; Marichal, Jean-Luc ; Teheux, Bruno Scientific Conference (2014, June 20) Detailed reference viewed: 54 (9 UL)Preassociativity for aggregation functions Marichal, Jean-Luc ; Teheux, Bruno Scientific Conference (2014, June 16) Detailed reference viewed: 70 (5 UL)Goldblatt-Thomason Theorem for Łukasiewicz finitely-valued modal language Teheux, Bruno in Flaminio, Tommaso; Godo, Lluis; Gottwald, Siegfried (Eds.) et al Graded Logical Approaches and their Applications - Abstracts (2014) Detailed reference viewed: 54 (2 UL)An Arrow-like theorem over median algebras ; Teheux, Bruno Poster (2014) We present an Arrow-like theorem for aggregation functions over convervative median algebras. In doing so, we give a characterization of conservative median algebras by means of forbidden substructures ... [more ▼] We present an Arrow-like theorem for aggregation functions over convervative median algebras. In doing so, we give a characterization of conservative median algebras by means of forbidden substructures and by providing their representation as chains. [less ▲] Detailed reference viewed: 76 (6 UL)Propositional Dynamic Logic for Searching Games with Errors Teheux, Bruno in Journal of Applied Logic (2014), 12(4), 377-394 We investigate some finitely-valued generalizations of propositional dynamic logic with tests. We start by introducing the n+1-valued Kripke models and a corresponding language based on a modal extension ... [more ▼] We investigate some finitely-valued generalizations of propositional dynamic logic with tests. We start by introducing the n+1-valued Kripke models and a corresponding language based on a modal extension of Łukasiewicz many-valued logic. We illustrate the definitions by providing a framework for an analysis of the Rényi - Ulam searching game with errors. Our main result is the axiomatization of the theory of the n+1-valued Kripke models. This result is obtained through filtration of the canonical model of the smallest n+1-valued propositional dynamic logic. [less ▲] Detailed reference viewed: 140 (8 UL)Fonctions associatives et préassociatives Marichal, Jean-Luc ; Teheux, Bruno Scientific Conference (2013, October 18) We investigate the associativity property for functions of multiple arities and introduce the more general property of preassociativity, an extension of associativity which does not involve any ... [more ▼] We investigate the associativity property for functions of multiple arities and introduce the more general property of preassociativity, an extension of associativity which does not involve any composition of functions. We discuss this new property and describe certain classes of preassociative functions. We also show how axiomatizations of several function classes can be extended by relaxing associativity to preassociativity. [less ▲] Detailed reference viewed: 53 (9 UL)Fonctions d’agrégation barycentriquement associatives Marichal, Jean-Luc ; Teheux, Bruno 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 (2013, October) We investigate the algebraic property of barycentric associativity for aggregation functions. This property, well-known in Kolmogoroff-Nagumo’s axiomatization of the quasi-arithmetic means, is often ... [more ▼] We investigate the algebraic property of barycentric associativity for aggregation functions. This property, well-known in Kolmogoroff-Nagumo’s axiomatization of the quasi-arithmetic means, is often considered as very natural whenever the aggregation process is of an (arithmetic, geometric, harmonic...) mean type. We recall the definition of this property and propose some extensions. We also present some results, some rather surprising, related to these properties. [less ▲] Detailed reference viewed: 133 (11 UL)Pivotal decompositions of aggregation functions Marichal, Jean-Luc ; Teheux, Bruno in Mesiar, Radko; Pap, Endre; Klement, Erich Peter (Eds.) 34th Linz Seminar on Fuzzy Set Theory (LINZ 2013) - Non-Classical Measures and Integrals (2013) Detailed reference viewed: 43 (11 UL)Dynamic many-valued logics for searching games with errors Teheux, Bruno Scientific Conference (2013) Detailed reference viewed: 33 (2 UL)Extending Łukasiewicz Logics with a Modality: Algebraic Approach to Relational Semantics ; Teheux, Bruno in Studia Logica (2013), 101(3), 505-545 Detailed reference viewed: 164 (11 UL)Extending functions to natural extensions Teheux, Bruno ; E-print/Working paper (2013) Detailed reference viewed: 43 (1 UL)Natural extension of median algebras Teheux, Bruno Scientific Conference (2013) Detailed reference viewed: 38 (4 UL)Algebraic approach to modal extensions of Łukasiewicz logics Teheux, Bruno Doctoral thesis (2009) Detailed reference viewed: 113 (11 UL)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 Detailed reference viewed: 45 (7 UL)A Duality for the Algebras of a Łukasiewicz n + 1-valued Modal System Teheux, Bruno in Studia Logica (2007), 87(1), 13-36 n this paper, we develop a duality for the varieties of a Łukasiewicz n + 1-valued modal system. This duality is an extension of Stone duality for modal algebras. Some logical consequences (such as ... [more ▼] n this paper, we develop a duality for the varieties of a Łukasiewicz 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 then derived and we propose some ideas for future research. [less ▲] Detailed reference viewed: 113 (7 UL)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: 70 (4 UL) |
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