On the existence of right adjoints for surjective mappings between fuzzy structures0

En este trabajo los autores continúan su estudio de la caracterización de la existencia de adjunciones (conexiones de Galois isótonas) cuyo codominio no está dotado de estructura en principio. En este artículo se considera el caso difuso en el que se tiene un orden difuso R definido en un conjunto A y una aplicación sobreyectiva f:A-> B compatible respecto de dos relaciones de similaridad definidas en el dominio A y en el condominio B, respectivamente. Concretamente, el problema es encontrar un orden difuso S en B y una aplicación g:B-> A compatible también con las correspondientes similaridades definidas en A y en B, de tal forma que el par (f,g) constituya un adjunción

Consensus theories: an oriented survey

This article surveys seven directions of consensus theories: Arrowian results, federation consensus rules, metric consensus rules, tournament solutions, restricted domains, abstract consensus theories, algorithmic and complexity issues. This survey is oriented in the sense that it is mainly – but not exclusively – concentrated on the most significant results obtained, sometimes with other searchers, by a team of French searchers who are or were full or associate members of the Centre d'Analyse et de Mathématique Sociale (CAMS).Consensus theories ; Arrowian results ; aggregation rules ; metric consensus rules ; median ; tournament solutions ; restricted domains ; lower valuations ; median semilattice ; complexity

On the relation between the probabilistic characterization of the common cause and Bell's notion of local causality

In the paper the relation between the standard probabilistic characterization of the common cause (used for the derivation of the Bell inequalities) and Bell's notion of local causality will be investigated. It will be shown that the probabilistic common cause follows from local causality if one accepts, as Bell did, two assumptions concerning the common cause: first, the common cause is localized in the intersection of the past of the correlating events; second, it provides a complete specification of the `beables' of this intersection. However, neither assumptions are a priori requirements. In the paper the logical role of these assumptions will be studied and it will be shown that only the second assumption is necessary for the derivation of the probabilistic common cause from local causality

Aggregation of Weak Fuzzy Norms

[EN] Aggregation is a mathematical process consisting in the fusion of a set of values into a unique one and representing them in some sense. Aggregation functions have demonstrated to be very important in many problems related to the fusion of information. This has resulted in the extended use of these functions not only to combine a family of numbers but also a family of certain mathematical structures such as metrics or norms, in the classical context, or indistinguishability operators or fuzzy metrics in the fuzzy context. In this paper, we study and characterize the functions through which we can obtain a single weak fuzzy (quasi-)norm from an arbitrary family of weak fuzzy (quasi-)norms in two different senses: when each weak fuzzy (quasi-)norm is defined on a possibly different vector space or when all of them are defined on the same vector space. We will show that, contrary to the crisp case, weak fuzzy (quasi-)norm aggregation functions are equivalent to fuzzy (quasi-)metric aggregation functions.J.R.-L. acknowledges financial support from the research project PGC2018-095709-B-C21 funded by MCIN/AEI/10.13039/501100011033 and FEDER Una manera de hacer Europa.Pedraza Aguilera, T.; Ramos-Canós, J.; Rodríguez López, J. (2021). Aggregation of Weak Fuzzy Norms. Symmetry (Basel). 13(10):1-16. https://doi.org/10.3390/sym13101908116131

On the concept of Bell's local causality in local classical and quantum theory

The aim of this paper is to give a sharp definition of Bell's notion of local causality. To this end, first we unfold a framework, called local physical theory, integrating probabilistic and spatiotemporal concepts. Formulating local causality within this framework and classifying local physical theories by whether they obey local primitive causality --- a property rendering the dynamics of the theory causal, we then investigate what is needed for a local physical theory, with or without local primitive causality, to be locally causal. Finally, comparing Bell's local causality with the Common Cause Principles and relating both to the Bell inequalities we find a nice parallelism: Bell inequalities cannot be derived neither from local causality nor from a common cause unless the local physical theory is classical or the common cause is commuting, respectively.Comment: 24 pages, 5 figure

Automated verification of refinement laws

Demonic refinement algebras are variants of Kleene algebras. Introduced by von Wright as a light-weight variant of the refinement calculus, their intended semantics are positively disjunctive predicate transformers, and their calculus is entirely within first-order equational logic. So, for the first time, off-the-shelf automated theorem proving (ATP) becomes available for refinement proofs. We used ATP to verify a toolkit of basic refinement laws. Based on this toolkit, we then verified two classical complex refinement laws for action systems by ATP: a data refinement law and Back's atomicity refinement law. We also present a refinement law for infinite loops that has been discovered through automated analysis. Our proof experiments not only demonstrate that refinement can effectively be automated, they also compare eleven different ATP systems and suggest that program verification with variants of Kleene algebras yields interesting theorem proving benchmarks. Finally, we apply hypothesis learning techniques that seem indispensable for automating more complex proofs

Consensus theories: an oriented survey

URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/cesdp2010.htmlDocuments de travail du Centre d'Economie de la Sorbonne 2010.57 - ISSN : 1955-611XThis article surveys seven directions of consensus theories: Arrowian results, federation consensus rules, metric consensus rules, tournament solutions, restricted domains, abstract consensus theories, algorithmic and complexity issues. This survey is oriented in the sense that it is mainly – but not exclusively – concentrated on the most significant results obtained, sometimes with other searchers, by a team of French searchers who are or were full or associate members of the Centre d'Analyse et de Mathématique Sociale (CAMS).Cet article présente une vue d'ensemble de sept directions de recherche en théorie du consensus : résultats arrowiens, règles d'agrégation définies au moyen de fédérations, règles définies au moyen de distances, solutions de tournoi, domaines restreints, théories abstraites du consensus, questions de complexité et d'algorithmique. Ce panorama est orienté dans la mesure où il présente principalement – mais non exclusivement – les travaux les plus significatifs obtenus – quelquefois avec d'autres chercheurs – par une équipe de chercheurs français qui sont – ou ont été – membres pléniers ou associés du Centre d'Analyse et de Mathématique Sociale (CAMS)

Aggregation functions of topological structures

[ES] Las funciones de agregación son un tipo especial de funciones que permiten combinar un número finito de entradas en una única salida que debe resumir de algún modo la información de todas las entradas. Como ejemplo paradigmático de estas funciones podemos destacar la media aritmética aunque el abanico disponible es muy amplio. El estudio de este tipo de funciones se ha convertido en un área muy activa de las matemáticas debido a su utilidad tanto en matemática pura (ecuaciones funcionales, teoría de integración, ...) como en matemática aplicada (toma de decisiones, inteligencia artificial). Además de aglutinar valores, las funciones de agregación permiten también fusionar estructuras topológicas. Por ejemplo, Dobos y sus colaboradores han estudiado el problema de determinar aquellas funciones que permiten obtener, a partir de una familia arbitraria de espacios métricos, una métrica en el producto cartesiano de dichos espacios. Este problema también se ha analizado en el caso de casi-métricas, es decir, métricas que no satisfacen necesariamente el axioma de simetría. Un problema muy interesante relacionado con este es el de caracterizar las funciones que no solo permiten hacer esta agregación de métricas sino que también conservan la topología producto, es decir, caracterizar las funciones que al agregar métricas devuelven una métrica compatible con la topología producto. Aparte del estudio de agregación de estructuras topológicas clásicas, también existen resultados sobre cómo agregar estructuras difusas. Por otra parte, también se ha investigado la agregación de otras estructuras topológicas como las normas y las normas asimétricas pero no existen resultados sobre la agregación de su correspondiente estructura difusa. Así, en este trabajo se propone al estudiante que haga un análisis de los diferentes resultados que existen sobre funciones que agregan estructuras topológicas tanto en el contexto clásico como en el difuso. Además, también se abordará el problema de obtener la caracterización de aquellas funciones que agregan normas difusas débiles. De este modo, los objetivos principales de este trabajo son: revisar el concepto de función de agregación y sus propiedades fundamentales; revisar los resultados existentes en la literatura sobre la agregación de métricas y casi-métricas; estudiar las caracterizaciones que existen sobre funciones que agregan normas y normas asimétricas; revisar algunos conceptos de la topología difusa; caracterizar las funciones que permitan agregar normas difusas y establecer una relación adecuada con las funciones que agregan métricas difusas.[EN] Aggregation functions are a type of functions that allow us to combine a finite number of inputs into one output that in some way summarize de information of all the inputs. An example of this functions is the arithmetic mean, but there are lots of different possibilities. The study of these functions has become in an important area of mathematics because of their utility in pure mathematics (funcional equations, integration theory) and in applies mathematics (making decisions, artificial intelligence). Moreover, we can use aggregation functions to combine topological structures. For example, Dobos and his collaborators have solved the problem of when a function allow us to obtain from a family of metric spaces, a new metric in the Cartesian product of that spaces. This problem has been analyzed in the case of quasi-metrics, i. e. metrics that don't hold the axiom of symmetry. An interesting problem related to this one is characterizing functions that aggregate metrics and preserve the product topology. That is to say, characterize functions that when they aggregate metrics, the output is a metric compatible with the product topology. In addition to the results of functions that aggregate topological structures in the classic sense, there exist results of fuzzy structures. Moreover, there are papers about norms and asymmetric norms, but there are not results about aggregation of norms and quasi-norms in the fuzzy context. So, in this paper there is an analysis of the existing literature about functions that aggregate topological structures in the classic sense and in the fuzzy context. Moreover, we solve the problem of characterize weak fuzzy norm agrgegation functions. So the principal objectives of this paper are: Make a review of the concept of an aggregation function and its principal properties. Make a review of the existing results in the literature about aggregation functions of metrics and quasi-metrics. Study the existing characterizations about norms and asymmetric norms. Make a review about some concepts of fuzzy topology. Characterize fuzzy norm aggregation function and establish a relation between these functions and fuzzy metric aggregation functions.Ramos Canos, J. (2021). Aggregation functions of topological structures. Universitat Politècnica de València. http://hdl.handle.net/10251/175057TFG