A practical inference method with several implicative gradual rules and a fuzzy input: one and two dimensions

International audienceA general approach to practical inference with gradual implicative rules and fuzzy inputs is presented. Gradual rules represent constraints restricting outputs of a fuzzy system for each input. They are tailored for interpolative reasoning. Our approach to inference relies on the use of inferential independence. It is based on fuzzy output computation under an interval-valued input. A double decomposition of fuzzy inputs is done in terms of alpha-cuts and in terms of a partitioning of these cuts according to areas where only a few rules apply. The case of one and two dimensional inputs is consideredCet article présente une méthode d'inférence avec des règles implicatives graduelles pour une entrée floue. Les règles graduelles représentent des contraintes qui restreignent l'univers de sortie pour chacune des entrées. Elles sont conçues pour réaliser des interpolations. L'algorithme que nous proposons s'appuie sur le principe de indépendance inférentielle. Il met en oeuvre une double décomposition de l'ensemble flou d'entrée, par alpha-coupes et suivant le partitionnement de l'univers des variables d'entrée. Les cas étudiés correspondent à des systèmes à une et deux dimension

Vers une utilisation pratique des règles implicatives

International audienceLes règles implicatives, qui permettent de modéliser des contraintes, restent méconnues. Nous proposons dans cet article des lignes directrices pour la conception pratique de systèmes de règles implicatives : construction de partitions adaptées, interprétation des résultats de l'inférence, coopération de plusieurs systèmes de règles et sémantique. La méthodologie est appliquée à un procédé agroalimentaire. / Implicatives rules, which model constraints remain unknown. We propose in this article guidelines for building practical systems of implicative rules : design of suitable partitions, interpretation of inference results, system cooperation and semantics. The methodology is applied to a food process

Fuzzy interpolation and level 2 gradual rules

International audienceFunctional laws may be known only at a finite number of points, and then the function can be completed by interpolation techniques obeying some smoothness conditions. We rather propose here to specify constraints by means of gradual rules for delimiting areas where the function may lie between known points. Such an approach results in an imprecise interpolation graph whose shape is controlled by tuning the fuzziness attached to the reference points. However, the graph so-built is still crisp, which means that different possible paths between the interpolation points cannot be distinguished according to their plausibility. The paper discusses a method for introducing membership degrees inside the interpolation graph. The developed formalism relies on the use of weighted nested graphs. It amounts to handling level 2 gradual rules for specifying a family of flexible constraints on the reference points. The proposed approach is compared with the one of extending gradual rules for dealing with type2 fuzzy reference points

Characterising algorithmic thinking: A university study of unplugged activities

Algorithmic thinking is a type of thinking that occurs in the context of computational thinking. Given its importance in the current educational context, it seems pertinent to deepen into its conceptual and operational understanding for teaching. The exploration of research shows us that there are almost no studies at university level where algorithmic thinking is connected to mathematical thinking, and more importantly, to characterise it and be able to analyse and evaluate it better. The aim of this research is to characterise algorithmic thinking in a university context of the Bachelor's Degree in Mathematics by unplugged tasks, offering a model of analysis through categories that establish connections between mathematical and algorithmic working spaces in three dimensions, semiotic, instrumental and discursive. The results confirm the interaction between these dimensions and their predictive value for better programming performance. The study also adds novel considerations related to the role and interaction of mathematical and computational thinking categories involved in algorithmic thinking.Instituto de Matemática Interdisciplinar (IMI)Fac. de Ciencias MatemáticasTRUEUnión EuropeaMinisterio de Ciencia e Innovaciónpu

Thomas S. Schelling: game theory and indirect communication

In their recent work Thomas S. Schelling (2007, 2010), reiterating original arguments about game theory and its applications to social sciences. In particular, game theory helps to explore situations in which agents make decisions interdependent (strategic communication). Schelling's originality is to extend economic theory to social sciences. When a player can anticipate the options and influence the decisions of others. The strategy, indirect communication plays a crucial role. To illustrate, we investigate how to perform the payoff matrix in cases of bribery and threatSocial Science, Schelling, game theory, strategic communications, bribes, threats

Polymorphic set-theoretic types for functional languages

We study set-theoretic types: types that include union, intersection, and negation connectives. Set-theoretic types, coupled with a suitable subtyping relation, are useful to type several programming language constructs \u2013 including conditional branching, pattern matching, and function overloading \u2013 very precisely. We define subtyping following the semantic subtyping approach, which interprets types as sets and defines subtyping as set inclusion. Our set-theoretic types are polymorphic, that is, they contain type variables to allow parametric polymorphism. We extend previous work on set-theoretic types and semantic subtyping by showing how to adapt them to new settings and apply them to type various features of functional languages. More precisely, we integrate semantic subtyping with three important language features. In Part I we study implicitly typed languages with let-polymorphism and type inference (previous work on semantic subtyping focused on explicitly typed languages). We describe an implicitly typed lambda-calculus and a declarative type system for which we prove soundness. We study type inference and prove results of soundness and completeness. Then, we show how to make type inference more precise when programs are partially annotated with types. In Part II we study gradual typing. We describe a new approach to add gradual typing to a static type system; the novelty is that we give a declarative presentation of the type system, while previous work considered algorithmic presentations. We first illustrate the approach on a Hindley-Milner type system without subtyping. We describe declarative typing, compilation to a cast language, and sound and complete type inference. Then, we add set-theoretic types, defining a subtyping relation on set-theoretic gradual types, and we describe sound type inference for the extended system. In Part III we consider non-strict semantics. The existing semantic subtyping systems are designed for call-by-value languages and are unsound for non-strict semantics. We adapt them to obtain soundness for call-by-need. To do so, we introduce an explicit representation for divergence in the types, allowing the type system to distinguish the expressions that are already evaluated from those that are computations which might diverge.Cette th\ue8se porte sur l'\ue9tude des types ensemblistes : des types qui contiennent des connecteurs d'union, d'intersection et de n\ue9gation. Les types ensemblistes permettent de typer de mani\ue8re tr\ue8s pr\ue9cise plusieurs constructions des langages de programmation (comme par exemple les branches conditionnelles, le filtrage par motif et la surcharge des fonctions) lorsqu'ils sont utilis\ue9s avec une notion appropri\ue9e de sous-typage. Pour d\ue9finir celle-ci, nous utilisons l'approche du sous-typage s\ue9mantique, dans laquelle les types sont interpr\ue9t\ue9s comme des ensembles, et o\uf9 le sous-typage est d\ue9fini comme l'inclusion ensembliste. Dans la plupart de cette th\ue8se, les types ensemblistes sont polymorphes, dans le sens o\uf9 ils contiennent des variables de type pour permettre le polymorphisme param\ue9trique. La th\ue8se \ue9tend les travaux pr\ue9c\ue9dents sur les types ensemblistes et le sous-typage s\ue9mantique en montrant comment les adapter \ue0 des nouveaux contextes et comment les utiliser pour typer plusieurs aspects des langages fonctionnels. Elle se compose de trois parties. La premi\ue8re partie porte sur une \ue9tude des langages typ\ue9s de mani\ue8re implicite avec polymorphisme du "let" et inf\ue9rence de types (contrairement aux travaux pr\ue9c\ue9dents sur le sous-typage s\ue9mantique qui \ue9tudiaient des langages typ\ue9s explicitement). Nous y d\ue9crivons un lambda-calcul typ\ue9 implicitement avec un syst\ue8me de types dont nous d\ue9montrons la correction. De m\ueame, nous y \ue9tudions l'inf\ue9rence de types dont nous d\ue9montrons la correction et la compl\ue9tude. Enfin, nous montrons comment rendre l'inf\ue9rence plus pr\ue9cise quand les programmes sont partiellement annot\ue9s avec des types. La deuxi\ue8me partie d\ue9crit une nouvelle approche permettant d'\ue9tendre un syst\ue8me de types statique avec du typage graduel; l'originalit\ue9 venant du fait que nous d\ue9crivons le syst\ue8me de types de fa\ue7on d\ue9clarative, lorsque les syst\ue8mes existants proposent des descriptions algorithmiques. Nous illustrons cette approche en ajoutant le typage graduel \ue0 un syst\ue8me de types \ue0 la Hindley-Milner sans sous-typage. Nous d\ue9crivons pour cela un syst\ue8me de types d\ue9claratif, un processus de compilation vers un langage avec v\ue9rifications de type dynamiques (ou "casts"), et nous pr\ue9sentons un syst\ue8me d'inf\ue9rence de types correct et complet. Ensuite, nous y ajoutons les types ensemblistes, en d\ue9finissant une relation de sous-typage sur les types graduel ensemblistes, puis en pr\ue9sentant un syst\ue8me d'inf\ue9rence de types correct pour le syst\ue8me \ue9tendu. La troisi\ue8me partie porte sur l'\ue9tude des s\ue9mantiques non-strictes. Les syst\ue8mes existants qui utilisent le sous-typage s\ue9mantique ont \ue9t\ue9 d\ue9velopp\ue9s pour des langages avec appel par valeur et ne sont pas s\ufbrs pour des s\ue9mantiques non-strictes. Nous montrons ici comment les adapter pour garantir leur s\ufbret\ue9 en appel par n\ue9cessit\ue9. Pour faire \ue7a, nous introduisons dans les types une repr\ue9sentation explicite de la divergence, afin que le syst\ue8me des types puisse distinguer les expressions qui ne demandent pas d'\ue9valuation de celles qui la demandent et pourraient ainsi diverger

On the veridicality of perfective clause-embedding verbs in Polish

Die vorliegende Arbeit beschäftigt sich mit der wahrheitsbasierten Bedeutung perfektiver satzeinbettender Prädikate im Polnischen, i.e. mit dem Zusammenhang zwischen Aspekt und Wahrheitsinferenz. Den Kern meiner Dissertation bilden sogenannte ‚reveal-type predicates‘ wie ‘beweisen’, ‘zeigen’ oder ‘offenbaren [dass]’. In Abhängigkeit von deren aspektueller Markierung bringen sie entweder eine maximale (bei perfektiven Verben) oder eine partielle Evidenz (bei imperfektiven Verben) für die Wahrheit einer eingebetteten Proposition mit sich. Nur wenn die Evidenz maximal ist, wird der dass-Satz notwendigerweise als wahr interpretiert. Ich habe gezeigt, dass maximale Evidenz einer totalen Affiziertheit eines nominalen inkrementellen Themas (wie z. B. in ‘einen Schrank bauen.pfv’) entspricht (Maximalität von Evidenz = Maximalität vom Schrank). Somit sind reveal-type predicates inkrementell. Außerdem habe ich eine Akzeptabilitätsstudie mit 51 polnischen MuttersprachlerInnen geplant und durchgeführt, die die Veridikalität des Perfektivs und die Neutralität des Imperfektivs bestätigt hat. Die Interpretation der Ergebnisse wurde um eine Korpusuntersuchung ergänzt. Basierend auf den theoretischen Beobachtungen und den Studienergebnissen habe ich eine einheitliche Analyse für inkrementelle Verben vorgeschlagen, die entweder ein nominales oder ein propositionales Objekt verlangen. Die von mir für das Polnische entdeckten Korrelationen gelten auch für andere slawische (Tschechisch, Russisch) und einige nicht-slawische Sprachen (austronesische Sprachen, Französisch, Ungarisch).In my dissertation, I investigated a systematic interaction between the perfective aspect of a clause-embedding verb and a truth-oriented interpretation of embedded propositions in Polish. I demonstrated that the so-called reveal-type predicates (‘prove’, ‘reveal’, ‘show [that]’) are in complementary distribution with respect to triggering truth-related meaning of their sentential complements. Whereas perfective variants enforce embedded propositions to be true, imperfective counterparts are almost only compatible with false (or neutral) propositions. I further showed that clause-embedding reveal-type predicates exhibit an incremental structure and can therefore be treated by analogy to verbs that combine with nominal incremental themes. In the former case, we have a gradual creation of a proof, whereas in the latter case, we have a gradual creation of an object like ‘wardrobe’ (maximality of evidence = maximality of a wardrobe). I proposed a novel analysis of incremental theme verbs that combine with either nouns or clauses. According to my analysis, one possible realization of a partial-total affectedness of an incremental theme is a gradual creation of a proof for an embedded proposition. In order to obtain empirical evidence for the (non-)veridicality of (im)perfective reveal-type predicates in Polish, I conducted an acceptability judgement study with 51 Polish native speakers. I further conducted a corpus-based analysis of the frequency of investigated lexemes, which completed the interpretation of results. Apart from Polish, I provided evidence from other Slavic languages (Czech, Russian) and some non-Slavic languages (Austronesian languages, French, Hungarian)

Integrating Historical Operating Decisions and Expert Criteria into a DSS for the Management of a multireservoir System

[EN] This paper presents a collaborative framework to couple historical records with expert knowledge and criteria in order to define a Decision Support System (DSS) to support the seasonal operation of the reservoirs of the Jucar river system. The framework relies on the co-development of a DSS tool that is able to explicitly reproduce the decision-making processes and criteria considered by the system operators. Fuzzy logic is used to derive the implicit operating rules followed by the managers based on historical decisions and expert knowledge obtained in the co-development process, combining both sources of information. Fuzzy regression is used to forecast future inflows based on the meteorological and hydrological variables considered by the system operators in their decisions on reservoir operation. The DSS was validated against historical records. The developed framework and tools offer the system operators a way to predefine a set of feasible ex ante management decisions, as well as to explore the consequences associated with any single choice. In contrast with other approaches, the fuzzy-based method used is able to embed inflow uncertainty and its effects in the definition of the decisions on the system operation. Furthermore, the method is flexible enough to be applied to other water resource systems.The authors wish to acknowledge the Jucar River Basin Management Authority (Confederacion Hidrografica del Joecar, CHJ), especially its Operation Office's (Oficina de Explotacion) system operators Jose Maria Benlliure Moreno and Juan Fullana Montoro, for their contribution to the whole process, valuable suggestions, and provision of the necessary data to carry out the study. The study has been partially supported by the IMPADAPT project (CGL2013-48424-C2-1-R) with Spanish MINECO (Ministerio de Economia y Competitividad) and FEDER funds. It has also received funding from the European Union's Horizon 2020 research and innovation programme under the IMPREX project (GA 641.811).Macian-Sorribes, H.; Pulido-Velazquez, M. (2017). Integrating Historical Operating Decisions and Expert Criteria into a DSS for the Management of a multireservoir System. Journal of Water Resources Planning and Management. 143(1). https://doi.org/10.1061/(ASCE)WR.1943-5452.0000712S143