arXiv subjects
Publications and source records attributed to Bruno Teheux.
We investigate the barycentric associativity property for functions with indefinite arities and discuss the more general property of barycentric preassociativity, a generalization of barycentric associativity which does not involve any composition of functions. We also provide a generalization of Kolmogoroff-Nagumo's characterization of the quasi-arithmetic mean functions to barycentrically preassociative functions.
The classical property of associativity is very often considered in aggregation function theory and fuzzy logic. In this paper we provide axiomatizations of various classes of preassociative functions, where preassociativity is a generalization of associativity recently introduced by the authors. These axiomatizations are based on existing characterizations of some noteworthy classes of associative operations, such as the class of Aczélian semigroups and the class of t-norms.
We introduce the concept of associativity for string functions, where a string function is a unary operation on the set of strings over a given alphabet. We discuss this new property and describe certain classes of associative string functions. We also characterize the recently introduced preassociative functions as compositions of associative string functions with injective unary maps. Finally, we provide descriptions of the classes of associative and preassociative functions which depend only on the length of the input.
We investigate the associativity property for functions of indefinite arities and introduce and discuss the more general property of preassociativity, a generalization of associativity which does not involve any composition of functions.
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.
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.
The paper is dedicated to the problem of adding a modality to the \Lukasiewicz many-valued logics in the purpose of obtaining completeness results for Kripke semantics. We define a class of modal many-valued logics and their corresponding Kripke models and modal many-valued algebras. Completeness results are considered through the construction of a canonical model. Completeness is obtained for modal finitely-valued logics but also for a modal many-valued system with an infinitary deduction rule. We introduce two classes of frames for the finitely-valued logics and show that they define two distinct classes of Kripke-complete logics.