723 research outputs found

    Recognisable languages over monads

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    The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of composing structures into bigger structures. It so happens that category theory has an abstract concept for this, namely a monad. The goal of this paper is to propose monads as a unifying framework for discussing existing algebras and designing new algebras

    Dual Space of a Lattice as the Completion of a Pervin Space

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    16th International Conference, RAMiCS 2017, Lyon, France, May 15-18, 2017, ProceedingsInternational audienceThis survey paper presents well-known results from a new angle. A Pervin space is a set X equipped with a set of subsets,called the blocks of the Pervin space. Blocks are closed under finite intersections and finite unions and hence form a lattice of subsets of X. Pervin spaces are thus easier to define than topological spaces or (quasi)-uniform spaces. As a consequence, most of the standard topological notions, like convergence and cluster points, specialisation order, filtersand Cauchy filters, complete spaces and completion are much easier to define for Pervin spaces. In particular, the completion of a Pervin space turns out to be the dual space (in the sense of Stone) of the original lattice.We show that any lattice of subsets can be described by a set of inequations of the form u ≀ v, where u and v are elements of its dual space. Applications to formal languages and complexity classes are given.Cet article de synthĂšse prĂ©sente des rĂ©sultats bien connus sous un nouvel angle. Un espace de Pervin est unensemble X Ă©quipĂ© d'un ensemble de parties, appelĂ© les blocs de l'espace de Pervin. Les blocs sont fermĂ©s par intersection finie et union finie et forment ainsi un treillis de parties de X. Les espaces de Pervin sont doncplus faciles Ă  dĂ©finir que les espaces topologiques ou les espaces (quasi-)uniformes. Par consĂ©quent, la plupart des notions topologiques, comme la convergence et les points d'adhĂ©rence, l'ordre de spĂ©cialisation, les filtres de Cauchy, les espaces complets et la complĂ©tion sont beaucoup plus faciles Ă  dĂ©finir pour les espaces Pervin. En particulier, la complĂ©tion d'un espace Pervin s'avĂšre ĂȘtre l'espace dual (au sens de Stone) du treillis de dĂ©part.Nous montrons que tout treillis de parties peut ĂȘtre dĂ©crit par un ensemble d'inĂ©quations de la forme u ≀ v, oĂč u et v sont des Ă©lĂ©ments de son espace dual. On donne des applications aux langages formels et aux classes de complexitĂ©

    Changing a semantics: opportunism or courage?

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    The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201

    Laboratory coupling approach

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    This chapter deals with the coupling of smart grid laboratories for joint experiments. Therefore, various possibilities are outlined and a reference implementation is introduced. Finally, the vision of a distributed, virtual research infrastructure is presented

    Reinventing grounded theory: some questions about theory, ground and discovery

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    Grounded theory’s popularity persists after three decades of broad-ranging critique. In this article three problematic notions are discussed—‘theory,’ ‘ground’ and ‘discovery’—which linger in the continuing use and development of grounded theory procedures. It is argued that far from providing the epistemic security promised by grounded theory, these notions—embodied in continuing reinventions of grounded theory—constrain and distort qualitative inquiry, and that what is contrived is not in fact theory in any meaningful sense, that ‘ground’ is a misnomer when talking about interpretation and that what ultimately materializes following grounded theory procedures is less like discovery and more akin to invention. The procedures admittedly provide signposts for qualitative inquirers, but educational researchers should be wary, for the significance of interpretation, narrative and reflection can be undermined in the procedures of grounded theory

    The Ontology of Biological Attributes (OBA)-computational traits for the life sciences.

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    Existing phenotype ontologies were originally developed to represent phenotypes that manifest as a character state in relation to a wild-type or other reference. However, these do not include the phenotypic trait or attribute categories required for the annotation of genome-wide association studies (GWAS), Quantitative Trait Loci (QTL) mappings or any population-focussed measurable trait data. The integration of trait and biological attribute information with an ever increasing body of chemical, environmental and biological data greatly facilitates computational analyses and it is also highly relevant to biomedical and clinical applications. The Ontology of Biological Attributes (OBA) is a formalised, species-independent collection of interoperable phenotypic trait categories that is intended to fulfil a data integration role. OBA is a standardised representational framework for observable attributes that are characteristics of biological entities, organisms, or parts of organisms. OBA has a modular design which provides several benefits for users and data integrators, including an automated and meaningful classification of trait terms computed on the basis of logical inferences drawn from domain-specific ontologies for cells, anatomical and other relevant entities. The logical axioms in OBA also provide a previously missing bridge that can computationally link Mendelian phenotypes with GWAS and quantitative traits. The term components in OBA provide semantic links and enable knowledge and data integration across specialised research community boundaries, thereby breaking silos
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