1,721,288 research outputs found
Logical Foundations of Qantitative Equality
No full textIn quantitative reasoning one compares objects by distances, instead
of equivalence relations, so that one can measure how much they
are similar, rather than just saying whether they are equivalent or
not. In this paper we aim at providing a logical ground to quantitative reasoning with distances in Linear Logic, using the categorical
language of Lawvere’s doctrines. The key idea is to see distances
as equality predicates in Linear Logic. We use graded modalities to
write a resource sensitive substitution rule for equality, which allows us to give it a quantitative meaning by distances. We introduce
a deductive calculus for (Graded) Linear Logic with quantitative
equality and the notion of Lipschitz doctrine to give it a sound and
complete categorical semantics. We also describe a universal con-
struction of Lipschitz doctrines, which generates examples based
for instance on metric spaces and quantitative realisability
CAUCHY COMPLETIONS AND THE RULE OF UNIQUE CHOICE IN RELATIONAL DOCTRINES
No full textLawvere’s generalized the notion of complete metric space to the field of enriched categories: an enriched category is said to be Cauchy-complete if every left adjoint bimodule into it is represented by an enriched functor. Looking at this definition from a logical standpoint, regarding bimodules as an abstraction of relations and functors as an abstraction of functions, Cauchy-completeness resembles a formulation of the rule of unique choice. In this paper, we make this analogy precise, using the language of relational doctrines, a categorical tool that provides a functorial description of the calculus of relations, in the same way Lawvere’s hyperdoctrines give a functorial description of predicate logic. Given a relational doctrine, we define Cauchy-complete objects as those objects of the domain category satisfying the rule of unique choice. Then, we present a universal construction that completes a relational doctrine with the rule of unique choice, that is, producing a new relational doctrine where all objects are Cauchy-complete. We also introduce relational doctrines with singleton objects and show that these have the minimal structure needed to build the reflector of the full subcategory of its domain on Cauchy-complete objects. The main result is that this reflector exists if and only if the relational doctrine has singleton objects and this happens if and only if its restriction to Cauchy-complete objects is equivalent to its completion with the rule of unique choice. We support our results with many examples, also falling outside the scope of standard doctrines, such as complete metric spaces, Banach spaces and compact Hausdorff spaces in the general context of monoidal topology, which are all shown to be Cauchy-complete objects for appropriate relational doctrines
QUANTITATIVE EQUALITY IN SUBSTRUCTURAL LOGIC VIA LIPSCHITZ DOCTRINES
No full textSubstructural logics naturally support a quantitative interpretation of formulas, as they are seen as consumable resources. Distances are the quantitative counterpart of equivalence relations: they measure how much two objects are similar, rather than just saying whether they are equivalent or not. Hence, they provide the natural choice for modelling equality in a substructural setting. In this paper, we develop this idea, using the categorical language of Lawvere’s doctrines. We work in a minimal fragment of Linear Logic enriched by graded modalities, which are needed to write a resource sensitive substitution rule for equality, enabling its quantitative interpretation as a distance. We introduce both a deductive calculus and the notion of Lipschitz doctrine to give it a sound and complete categorical semantics. The study of 2-categorical properties of Lipschitz doctrines provides us with a universal construction, which generates examples based for instance on metric spaces and quantitative realisability. Finally, we show how to smoothly extend our results to richer substructural logics, up to full Linear Logic with quantifiers
E, Danesino C, Pasquali F, Nicolis E, Cesaro S, Perobelli S. The Italian SDS registry (RI-SDS): evolution form 1999.Proceedings of 8th International Congress on Shwachman-Diamond Syndrome, page 44. Verona 17-20 April 2016
No full textSurvival Analysis of italian registry of SDS patient
Elementary fibrations of enriched groupoids
No full textThe present paper aims at stressing the importance of the Hofmann-Streicher groupoid model for Martin Löf Type Theory as a link with the first-order equality and its semantics via adjunctions. The groupoid model was introduced by Martin Hofmann in his Ph.D. thesis and later analysed in collaboration with Thomas Streicher. In this paper, after describing an algebraic weak factorisation system (L, R) on the category C-Gpd of C-enriched groupoids, we prove that its fibration of algebras is elementary (in the sense of Lawvere) and use this fact to produce the factorisation of diagonals for (L, R) needed to interpret identity types
'My Friends are my Audience': Mass-mediation of Personal Content and Relations in Facebook
No full textFacebook identity management implies a selective front and backstage: users perform multiple social roles for a multiple spectator audience (boyd 2008). But as friend lists increase and the discussion about sensitive topics becomes more critical, people tend to protect their image by dealing only with content that may be interesting to all their contacts (Hogan, 2010).
Starting from field research on Italian users (40 in-depth interviews with Facebook users aged 14-55), this paper discusses the idea of Facebook as a place where people are engaged in building their social relations and their self-representation by managing their online presence in a way that can be both intriguing and acceptable for most of their contacts.
The paper will highlight the strategies of content homogenization and the online behavior adopted by users according to their perceptions of their «imagined audience» (Litt, 2012).
The article aims at underlining that Facebook use is surprisingly consistent with mass-media and generalist-media cultural models: users seem to apply models of television spectatoriality, not only in terms of passivity (lurking), but also in terms of consumption (skipping uninteresting content) and content production performed for a generalist audience (developing a distinctive and acceptable style of interaction)
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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