Relevant bibliographies by topics / Intensional-extensional

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Academic literature on the topic 'Intensional-extensional'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Intensional-extensional"

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Bourdier, Tony, Horatiu Cirstea, Daniel Dougherty, and Hélène Kirchner. "Extensional and Intensional Strategies." Electronic Proceedings in Theoretical Computer Science 15 (January 26, 2010): 1–19. http://dx.doi.org/10.4204/eptcs.15.1.

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Pitt, Eduardo Antônio. "Considerações acerca dos critérios de Identidade Intensional e Extensional na Conceitografia de Frege/Considerations on extensional and intensional identity criteria in Frege’s Begriffsschrift." Pensando - Revista de Filosofia 5, no. 10 (March 28, 2015): 123. http://dx.doi.org/10.26694/pensando.v5i10.2894.

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Neste artigo daremos principal atenção aos dois critérios de identidade de conteúdo conceitual que estão presentes nos §§ 3 e 8 da Conceitografia de Gottlob Frege. Nosso propósito é analisar as características destes critérios da notação conceitual de Frege porque pretendemos delimitar a discussão em torno dos problemas relacionados às noções de identidade intensional e extensional. Dessa forma, pretendemos: (i) analisar os critérios de identidade de conteúdo conceitual presentes nos §§ 3 e 8 da Conceitografia com o objetivo de mostrar que Frege apresentou uma caracterização híbrida da noção de conteúdo conceitual (valor semântico) e (ii) fazer considerações a respeito de relações que podemos estabelecer entre os critérios intensionais e extensionais de Frege e Richard Kirkham presentes no livro Teorias da Verdade: Uma Introdução Crítica. Com tais comparações pretendemos averiguar: (iii) se o critério de identidade do § 8 da Conceitografia é idêntico ao critério extensional de equivalência material de Kirkham e (iv) se o critério de identidade do § 3 da Conceitografia é mais forte, mais fraco ou idêntico aos critérios intensionais de equivalência essencial e de equivalência de sinonímia de Kirkham.Abstract: In this paper we will give primary attention to two identity criteria of conceptual content that are present in §§ 3 and 8 of Gottlob Frege's Begriffsschrift. Our purpose is to analyze the characteristics of these criteria of conceptual notation of Frege because we want to delimit the discussion around problems related to the notions of intensional and extensional identity. Thus, we intend to: (i) analyze the identity criteria of conceptual content present in §§ 3 and 8 of Begriffsschrift aiming to show that Frege introduced a hybrid characterization of the notion of conceptual content (semantic value) and (ii) make considerations about the relationships that we establish between intensional and extensional criteria of Frege and Richard Kirkham present in the book Theories of Truth: A Critical Introduction. With such comparisons we intend to investigate: (iii) if the identity criterion of § 8 of Begriffsschrift is identical to the extensional criterion of material equivalence in Kirkham and (iv) if the identity criterion of § 3 of Begriffsschrift is stronger, weaker or identical to intensional criteria of essential equivalence and of synonyms equivalence of Kirkham. Key words: Identity, Intensional Criterion, Extensional Criterion.
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Park, Seungbae. "Extensional scientific realism vs. intensional scientific realism." Studies in History and Philosophy of Science Part A 59 (October 2016): 46–52. http://dx.doi.org/10.1016/j.shpsa.2016.06.001.

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Gay, Simon, and Rajagopal Nagarajan. "Intensional and Extensional Semantics of Dataflow Programs." Formal Aspects of Computing 15, no. 4 (December 1, 2003): 299–318. http://dx.doi.org/10.1007/s00165-003-0018-1.

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Смирнова, Е. Д. "An approach to the interpretation on intensional contexts." Logical Investigations 19 (April 9, 2013): 238–45. http://dx.doi.org/10.21146/2074-1472-2013-19-0-238-245.

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The paper introduces a non-standard analysis of intensional contexts on the ground of generalized approach to semantics construction. The principles of building such kind semantics are consider. As far as I can see it is an idea on domains and anti-domains that lays in the ground a semantics of intensional contexts. Intensional contexts differ from extensional by ascription of specific values to intensional predicates (operators) and, what is more important, by a way of their combination with arguments. Thus constructing operations play the leading role in proposed analysis. The peculiarities of IPL: any expression including intensional predicates and operators has an intension as well as an extension.
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VAN DEN BERG, BENNO. "Three extensional models of type theory." Mathematical Structures in Computer Science 19, no. 2 (April 2009): 417–34. http://dx.doi.org/10.1017/s0960129509007440.

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We compare three categorical models of type theory with extensional constructs: setoids over extensional type theory; setoids over intensional type theory and a certain free exact category (the free ‘ΠW-pretopos’). By studying the amount of choice available in these categories, we are able show that they are distinct.
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Majkić, Zoran. "Conservative Intensional Extension of Tarski's Semantics." Advances in Artificial Intelligence 2013 (February 26, 2013): 1–10. http://dx.doi.org/10.1155/2013/920157.

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We considered an extension of the first-order logic (FOL) by Bealer's intensional abstraction operator. Contemporary use of the term “intension” derives from the traditional logical Frege-Russell doctrine that an idea (logic formula) has both an extension and an intension. Although there is divergence in formulation, it is accepted that the “extension” of an idea consists of the subjects to which the idea applies, and the “intension” consists of the attributes implied by the idea. From the Montague's point of view, the meaning of an idea can be considered as particular extensions in different possible worlds. In the case of standard FOL, we obtain a commutative homomorphic diagram, which is valid in each given possible world of an intensional FOL: from a free algebra of the FOL syntax, into its intensional algebra of concepts, and, successively, into an extensional relational algebra (different from Cylindric algebras). Then we show that this composition corresponds to the Tarski's interpretation of the standard extensional FOL in this possible world.
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Duží, Marie, and Aleš Horák. "Hyperintensional Reasoning Based on Natural Language Knowledge Base." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 28, no. 03 (May 21, 2020): 443–68. http://dx.doi.org/10.1142/s021848852050018x.

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The success of automated reasoning techniques over large natural-language texts heavily relies on a fine-grained analysis of natural language assumptions. While there is a common agreement that the analysis should be hyperintensional, most of the automatic reasoning systems are still based on an intensional logic, at the best. In this paper, we introduce the system of reasoning based on a fine-grained, hyperintensional analysis. To this end we apply Tichy’s Transparent Intensional Logic (TIL) with its procedural semantics. TIL is a higher-order, hyperintensional logic of partial functions, in particular apt for a fine-grained natural-language analysis. Within TIL we recognise three kinds of context, namely extensional, intensional and hyperintensional, in which a particular natural-language term, or rather its meaning, can occur. Having defined the three kinds of context and implemented an algorithm of context recognition, we are in a position to develop and implement an extensional logic of hyperintensions with the inference machine that should neither over-infer nor under-infer.
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Palopoli, Luigi, Luigi Pontieri, Giorgio Terracina, and Domenico Ursino. "Intensional and extensional integration and abstraction of heterogeneous databases." Data & Knowledge Engineering 35, no. 3 (December 2000): 201–37. http://dx.doi.org/10.1016/s0169-023x(00)00028-8.

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Tselishchev, Vitaliy V., and Alexander V. Khlebalin. "The Gap between the Intensional and Extensional in Mathematics." Siberian Journal of Philosophy 18, no. 2 (2020): 48–58. http://dx.doi.org/10.25205/2541-7517-2020-18-2-48-58.

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The paper is devoted to the study of the divergence of the intensionalist and extensionalist traditions in the foundations of mathematics. One of the important manifestations of this discrepancy was the debate on the status of the Axiom of Choice. In particular, we argue that Russell's challenging Axioms of the Choice is connected with his intensionalist philosophy of mathematics and the extensionalist approach of Zermelo. It is shown that the opposition of the intensionalist and extensionalist approaches includes such key problems of the philosophy of mathematics as the epistemological features of theorems and axioms, the nature of logical-philosophical analysis, and the role of logic in mathematics.
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Dissertations / Theses on the topic "Intensional-extensional"

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Hofmann, Martin. "Extensional concepts in intensional type theory." Thesis, University of Edinburgh, 1995. http://hdl.handle.net/1842/399.

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Theories of dependent types have been proposed as a foundation of constructive mathematics and as a framework in which to construct certified programs. In these applications an important role is played by identity types which internalise equality and therefore are essential for accommodating proofs and programs in the same formal system. This thesis attempts to reconcile the two different ways that type theories deal with identity types. In extensional type theory the propositional equality induced by the identity types is identified with definitional equality, i.e. conversion. This renders type-checking and well-formedness of propositions undecidable and leads to non-termination in the presence of universes. In intensional type theory propositional equality is coarser than definitional equality, the latter being confined to definitional expansion and normalisation. Then type-checking and well-formedness are decidable, and this variant is therefore adopted by most implementations. However, the identity type in intensional type theory is not powerful enough for formalisation of mathematics and program development. Notably, it does not identify pointwise equal functions (functional extensionality) and provides no means of redefining equality on a type as a given relation, i.e. quotient types. We call such capabilities extensional concepts. Other extensional concepts of interest are uniqueness of proofs and more specifically of equality proofs, subset types, and propositional extensionality---the identification of equivalent propositions. In this work we investigate to what extent these extensional concepts may be added to intensional type theory without sacrificing decidability and existence of canonical forms. The method we use is the translation of identity types into equivalence relations defined by induction on the type structure. In this way type theory with extensional concepts can be understood as a high-level language for working with equivalence relations instead of equality. Such translations of type theory into itself turn out to be best described using categorical models of type theory. We thus begin with a thorough treatment of categorical models with particular emphasis on the interpretation of type-theoretic syntax in such models. We then show how pairs of types and predicates can be organised into a model of type theory in which subset types are available and in which any two proofs of a proposition are equal. This model has applications in the areas of program extraction from proofs and modules for functional programs. For us its main purpose is to clarify the idea of syntactic translations via categorical model constructions. The main result of the thesis consists of the construction of two models in which functional extensionality and quotient types are available. In the first one types are modelled by types together with proposition-valued partial equivalence relations. This model is rather simple and in addition provides subset types and propositional extensionality. However, it does not furnish proper dependent types such as vectors or matrices. We try to overcome this disadvantage by using another model based on families of type-valued equivalence relations which is however much more complicated and validates certain conversion rules only up to propositional equality. We illustrate the use of these models by several small examples taken from both formalised mathematics and program development. We also establish various syntactic properties of propositional equality including a proof of the undecidability of typing in extensional type theory and a correspondence between derivations in extensional type theory and terms in intensional type theory with extensional concepts added. Furthermore we settle affirmatively the hitherto open question of the independence of unicity of equality proofs in intensional type theory which implies that the addition of pattern matching to intensional type theory does not yield a conservative extension.
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Silva, Isabel Cristina Siqueira da. "Visualization of intensional and extensional levels of ontologies." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2014. http://hdl.handle.net/10183/96976.

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Técnicas de visualização de informaçoes têm sido usadas para a representação de ontologias visando permitir a compreensão de conceitos e propriedades em domínios específicos. A visualização de ontologias deve ser baseada em representaccões gráficas efetivas e téquinas de interação que auxiliem tarefas de usuários relacionadas a diferentes entidades e aspectos. Ontologias podem ser complexas devido tanto à grande quantidade de níveis da hierarquia de classes como também aos diferentes atributos. Neste trabalho, propo˜e-se uma abordagem baseada no uso de múltiplas e coordenadas visualizações para explorar ambos os níceis intensional e extensional de uma ontologia. Para tanto, são empregadas estruturas visuais baseadas em árvores que capturam a característica hierárquiva de partes da ontologia enquanto preservam as diferentes categorias de classes. Além desta contribuição, propõe-se um inovador emprego do conceito "Degree of Interest" de modo a reduzir a complexidade da representação da ontologia ao mesmo tempo que procura direcionar a atenção do usuádio para os principais conceitos de uma determinada tarefa. Através da análise automáfica dos diferentes aspectos da ontologia, o principal conceito é colocado em foco, distinguindo-o, assim, da informação desnecessária e facilitando a análise e o entendimento de dados correlatos. De modo a sincronizar as visualizações propostas, que se adaptam facilmente às tarefas de usuários, e implementar esta nova proposta de c´calculo baseado em "Degree of Interest", foi desenvolvida uma ferramenta de visualização de ontologias interativa chamada OntoViewer, cujo desenvolvimento seguiu um ciclo interativo baseado na coleta de requisitos e avaliações junto a usuários em potencial. Por fim, uma última contribuição deste trabalho é a proposta de um conjunto de "guidelines"visando auxiliar no projeto e na avaliação de téncimas de visualização para os níceis intensional e extensional de ontologias.
Visualization techniques have been used for the representation of ontologies to allow the comprehension of concepts and properties in specific domains. Techniques for visualizing ontologies should be based on effective graphical representations and interaction techniques that support users tasks related to different entities and aspects. Ontologies can be very large and complex due to many levels of classes’ hierarchy as well as diverse attributes. In this work we propose a multiple, coordinated views approach for exploring the intensional and extensional levels of an ontology. We use linked tree structures that capture the hierarchical feature of parts of the ontology while preserving the different categories of classes. We also present a novel use of the Degree of Interest notion in order to reduce the complexity of the representation itself while drawing the user attention to the main concepts for a given task. Through an automatic analysis of ontology aspects, we place the main concept in focus, distinguishing it from the unnecessary information and facilitating the analysis and understanding of correlated data. In order to synchronize the proposed views, which can be easily adapted to different user tasks, and implement this new Degree of Interest calculation, we developed an interactive ontology visualization tool called OntoViewer. OntoViewer was developed following an iterative cycle of refining designs and getting user feedback, and the final version was again evaluated by ten experts. As another contribution, we devised a set of guidelines to help the design and evaluation of visualization techniques for both the intensional and extensional levels of ontologies.
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Fonseca, Rogério Ferreira da. "A complementaridade entre os aspectos intensional e extensional na conceituação de número real proposta por John Horton Conway." Pontifícia Universidade Católica de São Paulo, 2010. https://tede2.pucsp.br/handle/handle/10843.

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Made available in DSpace on 2016-04-27T16:57:02Z (GMT). No. of bitstreams: 1 Rogerio Ferreira da Fonseca.pdf: 1033862 bytes, checksum: 7874e284aff29ac820ecbd35113c89ae (MD5) Previous issue date: 2010-11-26
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This research is theoretical and has the goal of studying the concept of the real number. Epistemological issues are discussed surrounding the concept of number in general, and in particular the concept of real numbers. The discussions are based on the concept of complementarity as regards the analysis of cognitive and epistemological aspects of mathematical concepts. The focus of the research is to investigate a new proposal for the concept of numbers presented by the British mathematician John Horton Conway of Princeton University, which allows one to uniquely answer the question, What is a number? , which has long mobilized Mathematics philosophers and epistemologists. In addition, for this theory, a class of games is presented as a model for interpretation or application of the theory, thereby conceptualizing number as a game. Moreover, the game has assisted in learning Mathematics. We can conclude with this research that Conway s theory, in a complementary manner, can add new elements to the classical approaches to the concept of number, can indicate some of its weaknesses, and can highlight the importance of epistemological questioning in the evolution of mathematical knowledge. Another result of this research is to indicate the fertility of the concept of number that opens new frontiers for Mathematics. It is our opinion that Mathematics Education needs to be and should be close to advances in Mathematics
Esta pesquisa é de cunho teórico e tem por alvo o estudo do conceito de número real. Nela são discutidas questões de ordem epistemológicas que cercam o conceito de número, em geral, e em particular o conceito de número real. As discussões estão fundamentadas no conceito de complementaridade no que concerne à análise de aspectos cognitivos e epistemológicos de conceitos matemáticos. O foco da pesquisa é investigar uma nova proposta de conceituação de número apresentada pelo matemático inglês John Horton Conway, da Universidade de Princeton, a qual possibilita responder, de forma única, à questão: o que é número?, indagação que mobilizou filósofos e epistemólogos da Matemática por muito tempo. Além disso, para esta teoria uma classe de jogos se apresenta como um modelo de interpretação ou aplicação da teoria, conceituando então número como um jogo. Aliás, o jogo tem sido um auxiliar na aprendizagem da Matemática. Podemos inferir com esta pesquisa que a teoria de Conway de forma complementar pode acrescentar novos elementos às abordagens clássicas da conceituação de número, apontar algumas de suas fragilidades e destacar a importância dos questionamentos epistemológicos para a evolução do conhecimento matemático. Outro resultado desta pesquisa é indicar a fertilidade do conceito de número que ainda abre novas fronteiras para a Matemática. É nosso julgamento que a Educação Matemática precisa e deve estar próxima dos avanços da Matemática
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Vargas, Francisco [Verfasser], Laura [Akademischer Betreuer] Martignon, Keith [Akademischer Betreuer] Stenning, Timo [Gutachter] Leuders, Joachim [Gutachter] Engel, Laura [Gutachter] Martignon, and Keith [Gutachter] Stenning. "Intensional and extensional reasoning: Implications for Mathematics Education / Francisco Vargas ; Gutachter: Timo Leuders, Joachim Engel, Laura Martignon, Keith Stenning ; Laura Martignon, Keith Stenning." Ludwigsburg : Pädagogische Hochschule Ludwigsburg, 2021. http://d-nb.info/1234658666/34.

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Godoy, Evandro C. "O juízo como subordinação intensional e a Analítica Transcendental da Crítica da Razão Pura." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2014. http://hdl.handle.net/10183/96150.

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Interpretações com diferentes nuances têm sido oferecidas para a concepção de juízo enunciada na Crítica da Razão Pura, mas, grosso modo, pode-se classificálas sob duas linhas gerais, a interpretação analítica e a interpretação a partir de Port-Royal. Ambas as linhas interpretativas, entretanto, se identificam na tese de que no juízo são também subordinadas representações singulares. Esta concepção, designada de interpretação extensional do juízo, leva de modo geral a uma leitura pouco caridosa da obra. A finalidade deste texto é propor e esboçar a defesa de outro modo de conceber o juízo pautado pelas seguintes teses: i) intuições e conceitos não se relacionam no ou pelo juízo; ii) a relação extensional não é suficiente para a determinação de qual conceito é superior ou inferior (gênero ou espécie) e iii) a relação que estabelece a série intensional do conceito determina a hierarquia superior/inferior e por isto é a relação de maior relevância cognitiva. Fazendo frente à concepção extensional, a proposta aqui defendida é designada de interpretação intensional e demanda que a distinção entre intuições e conceitos seja levada às últimas consequências. A potência elucidativa e a conformidade com o texto desta abordagem do juízo mostram-se pela possibilidade de compatibilização das diferentes partes da Analítica transcendental, mesmo aquelas que a literatura secundária tende a descartar ou atribuir pouco significado. Na esteira da elaboração desta compatibilização, após a apresentação e defesa da concepção intensional do juízo, o texto trata em sequência da Dedução metafísica, da Dedução transcendental, do Esquematismo e dos Princípios, procurando ressaltar a interconexão e articulação destas partes, que é calcada na mediação da relação entre os produtos do entendimento e da sensibilidade pela imaginação. Assim, apesar de partir da concepção de juízo, o objetivo do texto é buscar uma leitura da obra magna de Kant que prioriza a consistência. A compatibilização da concepção de juízo com as partes mais relevantes da Analítica – principalmente para o que pesa para o problema da possibilidade de juízos sintéticos a priori – é uma conquista considerável, mas este estudo representa passos, que embora sejam fundamentais, são apenas iniciais na compreensão do idealismo transcendental.
Interpretations with different nuances have been offered for the conception of judgment set out in the Critique of Pure Reason, but, roughly speaking, one can classify them under two broad lines, named, analytic interpretation and interpretation from Port-Royal. However, both lines identify itself under the thesis that in judgments are also subordinate singular representations. This conception, designated here extensional interpretation of judgment, commonly leads to an uncharitable reading of the work. The objective of this text is to propose and outline the defense of another conception of judgment, guided by the following theses: i) intuitions and concepts do not relate in or by means of judgment, ii) the extensional relation is not sufficient to determine which concept is higher or lower (genus or species) and iii) the relation which establishes the intensional series of concept is that one which determines the higher/lower hierarchy and that is the relationship of more cognitive relevance. Contrasting to extensional conception, the proposal advocated here is named of intensional interpretation and demands to take the distinction between intuitions and concepts until its ultimate consequences. The explanatory power and accordance with text of this approach of judgment shows itself by reconciling different parts of the Transcendental Analytic, even those that secondary literature tends to dismiss or assign little significance. In the development of this compatibility, after the presentation and defense of intensional conception of judgment, the text addresses sequentially the Metaphysical Deduction, the Transcendental Deduction, the Schematism and the Principles, seeking to emphasize the linkage and interconnection of these parts, which is modeled on mediation of imagination in the relationship between the products of understanding and sensibility. Therefore, although starting from the conception of judgment, the purpose of the text is to seek a reading of Kant's greatest work that prioritizes consistency. Presenting the compatibility of conception of judgment with the most relevant parts of Analytic – mainly for the concern of the possibility of synthetic a priori judgments – is a considerable achievement, but this study represents steps that, although fundamentals, are just initials to the understanding of transcendental idealism.
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Στεργίου, Βιργινία. "Ιστορική εξέλιξη, ερμηνείες και διδακτικές προσεγγίσεις της έννοιας του απειροστού." Thesis, 2009. http://nemertes.lis.upatras.gr/jspui/handle/10889/1932.

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Στόχος της παρούσας Διατριβής είναι να ερευνήσει τη διαμόρφωση των αντιλήψεων γύρω από τα απειροστά και τις σχετικές μ’ αυτά επ’ άπειρον διαδικασίες σε δύο κατευθύνσεις: 1. Την ιστορική εξέλιξη και ερμηνεία της έννοιας του απειροστού και 2. Την ανάλυση των σχετικών αντιλήψεων των φοιτητών-αυριανών καθηγητών των μαθηματικών. Στο πρώτο μέρος της διατριβής γίνεται ανάλυση και ερμηνεία των αντιλήψεων για τα απειροστά που εκφράστηκαν από την Αρχαία μέχρι τη σύγχρονη εποχή. Η μελέτη αυτή οδηγεί στην κατασκευή ενός ερμηνευτικού πλαισίου που διακρίνει τα ιστορικά ερμηνευτικά πρότυπα (μοντέλα) των απειροστών σε τρία αντιθετικά ζεύγη ως εξής: Ι. Εντασιακά-Εκτασιακά πρότυπα απειροστών. ΙΙ. Ομογενή-Μη ομογενή πρότυπα απειροστών. ΙΙΙ. Μηδενοδύναμα-μη μηδενοδύναμα πρότυπα απειροστών. Το παραπάνω πλαίσιο χρησιμοποιείται στο δεύτερο μέρος της διατριβής ως μεθοδολογικό εργαλείο για το σχεδιασμό διδακτικών πειραμάτων και την ανάλυση των εμπειρικών δεδομένων. Ειδικότερα, έγιναν τρία διδακτικά πειράματα με φοιτητές του Τμήματος των Μαθηματικών. Στο πρώτο πείραμα ερευνήθηκε η έννοια της ταχύτητας σύγκλισης ακολουθίας ως μια διαισθητική προσέγγιση στα απειροστά. Στο δεύτερο πείραμα, ερευνήθηκε η δυνατότητα προσέγγισης στα απειροστά μέσα από κλασσικά θέματα των διακριτών Μαθηματικών, όπως ο υπολογισμός του αθροίσματος των δυνάμεων φυσικών αριθμών. Στο τρίτο πείραμα έγινε διδασκαλία ενός συγκεκριμένου μοντέλου των υπερ-πραγματικών αριθμών και αναλύθηκαν τα αποτελέσματα. Τα κυριότερα συμπεράσματα της διατριβής είναι: 1. Η σημασία της κατασκευής μαθηματικών οντοτήτων που ικανοποιούν τα αξιώματα της Πραγματικής Ανάλυσης, 2. Η σημασία της διαισθητικής προσέγγισης και τα όριά της και 3. Η καταλληλότητα των προτεινόμενων μοντέλων και θεμάτων, ως διδακτικού υλικού.
The aim of this Ph.D thesis is the conceptions regarding infinitesimals and infinitesimal processes in two directions: 1. The historical evolution and interpretation of the concept of infinitesimal and 2. The analysis of the conception of the students–prospective teachers of Mathematics. The first part of the thesis contains a study and an analysis of infinitesimals that appeared in History from Antiquity to our era. This study leads to the construction of a framework of interpretation which distinguishes the interpretative models into three pairs of opposites: I. Homogenous-Nonhomogenous, models of infinitesimals II. Intensional-Extensional, models of infinitesimals III. Nilpotent-Non nilpotent, models of infinitesimals The above framework is applied in the second part of the thesis, as a methodological tool for the design of didactical experiments with students of Mathematics. The first experiment concerns a research study on the notion of the rate of convergence, as an intuitive approach to infinitesimals. The second experiment is referred to the emergence of infinitesimals through classical themes (issues) of discrete mathematics, such as the computation of sums of powers of integers. The third experiment concerns the teaching of a specific model of Hyper-Real numbers and the analysis of its empirical outcomes. The main conclusions of this thesis are: 1. The significance of the construction of mathematical entities, which satisfy the axioms of Real Analysis. 2. The significance of the intuitive approach, as well with a focus on its foreseen limitations. 3. The relevance of the proposed models and themes as potential didactical material.
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Books on the topic "Intensional-extensional"

1

Hofmann, Martin. Extensional Constructs in Intensional Type Theory. London: Springer London, 1997.

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Hofmann, Martin. Extensional Constructs in Intensional Type Theory. London: Springer London, 1997. http://dx.doi.org/10.1007/978-1-4471-0963-1.

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3

Hofmann, Martin. Extensional constructs in intensional type theory. Berlin: Springer, 1997.

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4

Ruzsa, Imre. Introduction to metalogic: With an appendix on type-theoretical extensional and intensional logic. Budapest: Áron Publishers, 1997.

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5

Talcott, Carolyn L. The essence of Rum: A theory of the intensional and extensional aspects of Lisp-type computation. Stanford, Calif: Dept. of Computer Science, Stanford University, 1985.

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6

Extensional Constructs in Intensional Type Theory. Springer, 2011.

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7

Hájek, Alan. Philosophical Heuristics and Philosophical Methodology. Edited by Herman Cappelen, Tamar Szabó Gendler, and John Hawthorne. Oxford University Press, 2016. http://dx.doi.org/10.1093/oxfordhb/9780199668779.013.3.

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Philosophy has a wealth of heuristics—philosophical heuristics—although they have not been well documented or studied. Sometimes they draw attention to a problem with a philosophical position—for example, it involves a problematic definite description, or it has to make a choice that seems arbitrary. Sometimes they provide solutions to a problem—for example, there are many techniques for handling arbitrariness. Sometimes they suggest ways of replacing hard problems with easier ones, with strategies for approaching the latter—for example, replacing intensional notions with extensional surrogates, and then perhaps diagramming the latter. Sometimes they appeal to fertile modes of thinking more generally—for example, continuity reasoning. Philosophers have been becoming increasingly self-conscious of their methodology, yet I believe that the study of such heuristics has been surprisingly neglected. This chapter highlights the importance of philosophical heuristics to philosophical methodology. It considers especially a cluster involving the notion of resemblance.
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8

Millikan, Ruth Garrett. Beyond Concepts. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198717195.001.0001.

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This book weaves together themes from natural ontology, philosophy of mind, philosophy of language and information, areas of inquiry that have not recently been treated together. The sprawling topic is Kant’s how is knowledge possible? but viewed from a contemporary naturalist standpoint. The assumption is that we are evolved creatures that use cognition as a guide in dealing with the natural world, and that the natural world is roughly as natural science has tried to describe it. Very unlike Kant, then, we must begin with ontology, with a rough understanding of what the world is like prior to cognition, only later developing theories about the nature of cognition within that world and how it manages to reflect the rest of nature. And in trying to get from ontology to cognition we must traverse another non-Kantian domain: questions about the transmission of information both through natural signs and through purposeful signs including, especially, language. Novelties are the introduction of unitrackers and unicepts whose job is to recognize the same again as manifested through the jargon of experience, a direct reference theory for common nouns and other extensional terms, a naturalist sketch of uniceptual—roughly conceptual— development, a theory of natural information and of language function that shows how properly functioning language carries natural information, a novel description of the semantics/pragmatics distinction, a discussion of perception as translation from natural informational signs, new descriptions of indexicals and demonstratives and of intensional contexts and a new analysis of the reference of incomplete descriptions.
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Book chapters on the topic "Intensional-extensional"

1

Hofmann, Martin. "Introduction." In Extensional Constructs in Intensional Type Theory, 1–12. London: Springer London, 1997. http://dx.doi.org/10.1007/978-1-4471-0963-1_1.

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Hofmann, Martin. "Syntax and semantics of dependent types." In Extensional Constructs in Intensional Type Theory, 13–54. London: Springer London, 1997. http://dx.doi.org/10.1007/978-1-4471-0963-1_2.

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Hofmann, Martin. "Syntactic properties of propositional equality." In Extensional Constructs in Intensional Type Theory, 55–87. London: Springer London, 1997. http://dx.doi.org/10.1007/978-1-4471-0963-1_3.

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Hofmann, Martin. "Proof irrelevance and subset types." In Extensional Constructs in Intensional Type Theory, 89–113. London: Springer London, 1997. http://dx.doi.org/10.1007/978-1-4471-0963-1_4.

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Hofmann, Martin. "Extensionality and quotient types." In Extensional Constructs in Intensional Type Theory, 115–62. London: Springer London, 1997. http://dx.doi.org/10.1007/978-1-4471-0963-1_5.

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Hofmann, Martin. "Applications." In Extensional Constructs in Intensional Type Theory, 163–87. London: Springer London, 1997. http://dx.doi.org/10.1007/978-1-4471-0963-1_6.

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Hofmann, Martin. "Conclusions and further work." In Extensional Constructs in Intensional Type Theory, 189–90. London: Springer London, 1997. http://dx.doi.org/10.1007/978-1-4471-0963-1_7.

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Flach, Peter A. "Inductive logic databases: From extensional to intensional knowledge." In Deductive and Object-Oriented Databases, 3. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/3-540-63792-3_2.

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Phan, Viet Binh, Eric Pardede, and J. Wenny Rahayu. "From Extensional Data to Intensional Data: AXML for XML." In Studies in Computational Intelligence, 273–310. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-17551-0_10.

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Prado, Hércules A., Stephen C. Hirtle, and Paulo M. Engel. "Scalable Model for Extensional and Intensional Descriptions of Unclassified Data." In Lecture Notes in Computer Science, 407–14. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-45591-4_53.

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Conference papers on the topic "Intensional-extensional"

1

Blot, Valentin, and Jim Laird. "Extensional and Intensional Semantic Universes." In LICS '18: 33rd Annual ACM/IEEE Symposium on Logic in Computer Science. New York, NY, USA: ACM, 2018. http://dx.doi.org/10.1145/3209108.3209206.

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Fong, A. C. M., and Guanyue Hong. "Ontology-Powered Hybrid Extensional-Intensional Learning." In the 2019 International Conference. New York, New York, USA: ACM Press, 2019. http://dx.doi.org/10.1145/3355402.3355406.

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Console, Marco, Giuseppe De Giacomo, Maurizio Lenzerini, and Manuel Namici. "Intensional and Extensional Views in DL-Lite Ontologies." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/251.

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The use of virtual collections of data is often essential in several data and knowledge management tasks. In the literature, the standard way to define virtual data collections is via views, i.e., virtual relations defined using queries. In data and knowledge bases, the notion of views is a staple of data access, data integration and exchange, query optimization, and data privacy. In this work, we study views in Ontology-Based Data Access (OBDA) systems. OBDA is a powerful paradigm for accessing data through an ontology, i.e., a conceptual specification of the domain of interest written using logical axioms. Intuitively, users of an OBDA system interact with the data only through the ontology's conceptual lens. We present a novel framework to express natural and sophisticated forms of views in OBDA systems and introduce fundamental reasoning tasks for these views. We study the computational complexity of these tasks and present classes of views for which these tasks are tractable or at least decidable.
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"The Role of Intensional and Extensional Interpretation in Semantic Representations – The Intensional and Preextensional Layers in MultiNet." In The 4th International Workshop on Natural Language Understanding and Cognitive Science. SciTePress - Science and and Technology Publications, 2007. http://dx.doi.org/10.5220/0002415900920105.

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Jha, Abhay, Dan Olteanu, and Dan Suciu. "Bridging the gap between intensional and extensional query evaluation in probabilistic databases." In the 13th International Conference. New York, New York, USA: ACM Press, 2010. http://dx.doi.org/10.1145/1739041.1739082.

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Monet, Mikaël. "Solving a Special Case of the Intensional vs Extensional Conjecture in Probabilistic Databases." In SIGMOD/PODS '20: International Conference on Management of Data. New York, NY, USA: ACM, 2020. http://dx.doi.org/10.1145/3375395.3387642.

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da Silva, Isabel Cristina Siqueira, Carla Maria Dal Sasso Freitas, and Giuseppe Santucci. "An integrated approach for evaluating the visualization of intensional and extensional levels of ontologies." In the 2012 BELIV Workshop. New York, New York, USA: ACM Press, 2012. http://dx.doi.org/10.1145/2442576.2442578.

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Reports on the topic "Intensional-extensional"

1

Taylor, Carolyn L. The Essence of Rum: A Theory of the Intensional and Extensional Aspects of Lisp-Type Computation,. Fort Belvoir, VA: Defense Technical Information Center, August 1985. http://dx.doi.org/10.21236/ada327435.

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