1,720,955 research outputs found
Around the Minimalist Foundation: (Co)Induction and Equiconsistency
Get PDFWe study extensions and meta-mathematical properties of the Minimalist Foundation. The first chapter is introductory: we recall the systems of the Minimalist Foundation, reviewing their philosophical cores and main meta-mathematical results, together with a thorough exposition on how to work in them. The second chapter is devoted to considering two dual extensions of the Minimalist Foundation and their topological interpretations: with inductive predicates, adapted from the joint work with M.E. Maietti in [1], and with coinductive predicates, adapted from the preprint [2]. The last two chapters, taken from joint works with M.E. Maietti, focus on the level tower of the Minimalist Foundation, showing in particular the overall equiconsistency between the intensional level, the intuitionistic extensional level, and the classical extensional level.
Bibliography
[1] 2022. A topological counterpart of well-founded trees in dependent type theory. With M. E. Maietti. Electronic Notes in Theoretical Informatics and Computer Science, Volume 3. Proceedings of MFPS XXXIX. DOI: 10.46298/entics.11755
[2] 2024. A topological reading of inductive and coinductive definitions in Dependent Type Theory. arXiv preprint arXiv:2404.0349
Equiconsistency of the Minimalist Foundation with its classical version
Get PDFThe Minimalist Foundation, for short MF, was conceived by the first author with G. Sambin in 2005, and fully formalized in 2009, as a common core among the most relevant constructive and classical foundations for mathematics. To better accomplish its minimality, MF was designed as a two-level type theory, with an intensional level mTT, an extensional one emTT, and an interpretation of the latter into the first.
Here, we first show that the two levels of MF are indeed equiconsistent by interpreting mTT into emTT. Then, we show that the classical extension
is equiconsistent with emTT by suitably extending the Gödel-Gentzen double-negation translation of classical logic in the intuitionistic one. As a consequence, MF turns out to be compatible with classical predicative mathematics à la Weyl, contrary to the most relevant foundations for constructive mathematics.
Finally, we show that the chain of equiconsistency results for MF can be straightforwardly extended to its impredicative version to deduce that Coquand-Huet's Calculus of Constructions equipped with basic inductive types is equiconsistent with its extensional and classical versions too
A topological counterpart of well-founded trees in dependent type theory
Get PDFWithin dependent type theory, we provide a topological counterpart of
well-founded trees (for short, W-types) by using a proof-relevant version of
the notion of inductively generated suplattices introduced in the context of
formal topology under the name of inductively generated basic covers. In more
detail, we show, firstly, that in Homotopy Type Theory, W-types and proof
relevant inductively generated basic covers are propositionally mutually
encodable. Secondly, we prove they are definitionally mutually encodable in the
Agda implementation of intensional Martin-Loef's type theory. Finally, we
reframe the equivalence in the Minimalist Foundation framework by introducing
well-founded predicates as the logical counterpart for predicates of dependent
W-types. All the results have been checked in the Agda proof-assistant.Comment: To be published in the post-proceedings of the 39th Conference on
Mathematical Foundations of Programming Semantic
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe 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
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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