Pivotal decompositions of functions

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 ▲]

Preassociative aggregation functions

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 ▲]

Associativity, preassociativity, and string functions

Scientific Conference (2014, June 20)

Goldblatt-Thomason Theorem for Łukasiewicz finitely-valued modal language

in Flaminio, Tommaso; Godo, Lluis; Gottwald, Siegfried (Eds.) et al Graded Logical Approaches and their Applications - Abstracts (2014)

Propositional Dynamic Logic for Searching Games with Errors

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 ▲]

Fonctions d’agrégation barycentriquement associatives

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 ▲]

Dynamic many-valued logics for searching games with errors

Scientific Conference (2013)

Extending functions to natural extensions

E-print/Working paper (2013)

Algebraic approach to modal extensions of Łukasiewicz logics

Doctoral thesis (2009)

A Duality for the Algebras of a Łukasiewicz n + 1-valued Modal System

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 ▲]