Relevant bibliographies by topics / Axiomatic set theory

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Axiomatic set theory'

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Published: 4 June 2021
Last updated: 28 July 2024

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Journal articles on the topic "Axiomatic set theory"

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Lovyagin, Yuri N., and Nikita Yu Lovyagin. "Finite Arithmetic Axiomatization for the Basis of Hyperrational Non-Standard Analysis." Axioms 10, no. 4 (October 19, 2021): 263. http://dx.doi.org/10.3390/axioms10040263.

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The standard elementary number theory is not a finite axiomatic system due to the presence of the induction axiom scheme. Absence of a finite axiomatic system is not an obstacle for most tasks, but may be considered as imperfect since the induction is strongly associated with the presence of set theory external to the axiomatic system. Also in the case of logic approach to the artificial intelligence problems presence of a finite number of basic axioms and states is important. Axiomatic hyperrational analysis is the axiomatic system of hyperrational number field. The properties of hyperrational numbers and functions allow them to be used to model real numbers and functions of classical elementary mathematical analysis. However hyperrational analysis is based on well-known non-finite hyperarithmetic axiomatics. In the article we present a new finite first-order arithmetic theory designed to be the basis of the axiomatic hyperrational analysis and, as a consequence, mathematical analysis in general as a basis for all mathematical application including AI problems. It is shown that this axiomatics meet the requirements, i.e., it could be used as the basis of an axiomatic hyperrational analysis. The article in effect completes the foundation of axiomatic hyperrational analysis without calling in an arithmetic extension, since in the framework of the presented theory infinite numbers arise without invoking any new constants. The proposed system describes a class of numbers in which infinite numbers exist as natural objects of the theory itself. We also do not appeal to any “enveloping” set theory.
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Jiang, Jingying. "From Set Theory to the Axiomatization of Set Theory." Highlights in Science, Engineering and Technology 88 (March 29, 2024): 243–47. http://dx.doi.org/10.54097/nbmg4652.

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Axiomatic set theory was created by German mathematician Zermelo as a strategy for addressing and resolving paradoxes in the field of mathematical study. By adopting this strategy, the axiomatic technique will be applied to set theory. The person argues that Cantor's failure to impose restrictions on the idea of a set is the cause of the dilemma. They also claim that Cantor's definition of a set is unclear. Both of these arguments are predicated on the idea that Cantor neglected to place limitations on the idea of a set. Zermelo hypothesized that the condensed version of the axioms would make it easier to define a set and elaborate on its properties, and he was correct in his prediction. The creation of an axiomatization for set theory is the first of this research's main goals. Second, the investigation of various set theory development methods in comparison to one another. Even though there are intriguing puzzles in the field of set theory that have not yet been solved, the axiomatization of set theory is widely regarded as a significant accomplishment in the field.
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Cutolo, Raffaella, Ulderico Dardano, and Virginia Vaccaro. "Axiomatic set theory and unincreasable infinity." Applied Mathematical Sciences 8 (2014): 6725–32. http://dx.doi.org/10.12988/ams.2014.49687.

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Boichenko, Victor A., Alexey A. Belov, and Olga G. Andrianova. "Axiomatic Foundations of Anisotropy-Based and Spectral Entropy Analysis: A Comparative Study." Mathematics 11, no. 12 (June 17, 2023): 2751. http://dx.doi.org/10.3390/math11122751.

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An axiomatic development of control systems theory can systematize important concepts. The current research article is dedicated to the investigation and comparison of two axiomatic approaches to the analysis of discrete linear time-invariant systems affected by external random disturbances. The main goal of this paper is to explore axiomatics of an anisotropy-based theory in comparison with axiomatics of a spectral entropy approach in detail. It is demonstrated that the use of the spectral entropy approach is mathematically rigorous, which allows one to prove that the minimal disturbance attenuation level in terms of an anisotropy-based control theory provides the desired performance that is not only for ergodic signals. As a result, axiomatics of the spectral entropy approach allows one to rigorously prove that anisotropy-based controllers can be used to guarantee the desired disturbance attenuation level, not only for stationary random sequences, but also for a wider set of input random signals.
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Vdovin, A. M. "FOUNDATIONS OF A NEW AXIOMATIC SET THEORY." Mathematics of the USSR-Izvestiya 37, no. 2 (April 30, 1991): 467–73. http://dx.doi.org/10.1070/im1991v037n02abeh002074.

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Vdovin, A. M. "EXTENSION OF A NEW AXIOMATIC SET THEORY." Russian Academy of Sciences. Izvestiya Mathematics 42, no. 3 (June 30, 1994): 615–19. http://dx.doi.org/10.1070/im1994v042n03abeh001548.

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Tamir, Dan E., Cao Zhi-Qiang, Abraham Kandel, and Joe L. Mott. "An axiomatic approach to fuzzy set theory." Information Sciences 52, no. 1 (October 1990): 75–83. http://dx.doi.org/10.1016/0020-0255(90)90036-a.

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Hintikka, Jaakko. "Independence-friendly logic and axiomatic set theory." Annals of Pure and Applied Logic 126, no. 1-3 (April 2004): 313–33. http://dx.doi.org/10.1016/j.apal.2003.11.006.

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Anacona, Maribel, Luis Carlos Arboleda, and F. Javier Pérez-Fernández. "On Bourbaki’s axiomatic system for set theory." Synthese 191, no. 17 (July 26, 2014): 4069–98. http://dx.doi.org/10.1007/s11229-014-0515-1.

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DEISER, OLIVER. "AN AXIOMATIC THEORY OF WELL-ORDERINGS." Review of Symbolic Logic 4, no. 2 (March 4, 2011): 186–204. http://dx.doi.org/10.1017/s1755020310000390.

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We introduce a new simple first-order framework for theories whose objects are well-orderings (lists). A system ALT (axiomatic list theory) is presented and shown to be equiconsistent with ZFC (Zermelo Fraenkel Set Theory with the Axiom of Choice). The theory sheds new light on the power set axiom and on Gödel’s axiom of constructibility. In list theory there are strong arguments favoring Gödel’s axiom, while a bare analogon of the set theoretic power set axiom looks artificial. In fact, there is a natural and attractive modification of ALT where every object is constructible and countable. In order to substantiate our foundational interest in lists, we also compare sets and lists from the perspective of finite objects, arguing that lists are, from a certain point of view, conceptually simpler than sets.
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Dissertations / Theses on the topic "Axiomatic set theory"

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Alakhrass, Mohammad. "Superharmonic and multiply superharmonic functions and Jensen measures in axiomatic Brelot spaces." Thesis, McGill University, 2009. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=115846.

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We study quasi superharmonic functions in Brelot spaces and the relationship between a reduced function, and harmonic and Jensen measures. We introduce the concept of quasi multiply superharmonic functions on a product of two Brelot spaces and study their properties. A main result obtained is characterizing the quasi superharmonic functions in terms of harmonic, finely harmonic and Jensen measures. Then we prove that a quasi multiply superharmonic function on a product of Brelot spaces equals its lower semicontinuous regularization out side of a 2-negligible set. Further we give a sufficient condition on a Brelot space O under which O becomes an extension space for superharmonic functions. As a result we characterize the extreme Jensen measures in such spaces. Finally we study extreme Jensen measures relative to several classes of multiply superharmonic functions.
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Sotkowitz, Michael. "Logic and mathematics unsettled." Thesis, Boston University, 2008. https://hdl.handle.net/2144/28586.

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Boston University. University Professors Program Senior theses.
PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you.
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Zeng, Yong. "Axiomatic approach to the modeling of product conceptual design processes using set theory." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq64894.pdf.

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Weydert, Emil. "How to approximate the naive comprehension scheme inside of classical logic." Bonn : [s.n.], 1989. http://catalog.hathitrust.org/api/volumes/oclc/19990751.html.

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Brill, Markus [Verfasser], Felix [Akademischer Betreuer] Brandt, and Jérôme [Akademischer Betreuer] Lang. "Set-Valued Solution Concepts in Social Choice and Game Theory : Axiomatic and Computational Aspects / Markus Brill. Gutachter: Felix Brandt ; Jérôme Lang. Betreuer: Felix Brandt." München : Universitätsbibliothek der TU München, 2012. http://d-nb.info/1031512683/34.

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Batista, Márcio Venâncio. "Proposta de um método de aplicação da teoria de projeto axiomático ao desenvolvimento de software PON-POR." Universidade Tecnológica Federal do Paraná, 2013. http://repositorio.utfpr.edu.br/jspui/handle/1/613.

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Esta pesquisa propõe um método que aplica a Teoria de Projeto Axiomático (PA) ao processo de desenvolvimento de software que se orientam por regras. Nesse âmbito, salienta-se que não foi encontrada na literatura, durante os esforços de pesquisa deste trabalho, a aplicação da Teoria de Projeto Axiomático a sistemas orientados a Regras. Entretanto, a Teoria de Projeto Axiomático já sim foi foco de pesquisa e aplicação no processo de desenvolvimento de software orientado a objeto, servindo de inspiração ao presente trabalho. Dito isso, este trabalho propõe o método Projeto Axiomático aplicado ao Paradigma Orientado a Notificações e ao Paradigma Orientado a Regras (PA-PON-POR) desde que as regras sigam o modelo de estruturação dado pelo PON. O método PA-PON-POR propõe a decomposição funcional de requisitos do sistema em quatro níveis que são: Casos de Uso, Subcasos de Uso Independentes de Características Técnicas, Subcasos de Uso Dependentes de Características Técnicas e Serviços Técnicos. Além disso, o método PA-PON-POR aplica o Axioma da Independência do PA em cada um dos quatro níveis de decomposição por meio das matrizes de projeto e métricas de cálculo da reangularidade e semangularidade do próprio PA. As matrizes de projeto ainda auxiliam na identificação das Premissas exclusivas, elementos esses importantes quando um sistema PON-POR possui Regras que possuem Ações que instigam a geração de fatos conflitantes. O Axioma da Informação do Projeto Axiomático também é aplicado em cada nível de decomposição avaliando as soluções de projeto quanto a sua quantidade de informação. Ainda, o método PA-PON-POR apresenta um conjunto de métricas especificas para avaliação da qualidade estrutural da composição de Regras do sistema, fornecendo critérios para tomada de decisão sobre a qualidade do projeto especificado. Além disso, o método PA-PON-POR é passível de aplicação simultânea com o método existente de projeto de software baseado em desenvolvimento de aplicações PON-POR chamado de Desenvolvimento Orientado a Notificações e Orientado a Regras (DON-DOR), auxiliando na obtenção e validação de artefatos do mesmo. O método PA-PON-POR foi aplicado no desenvolvimento de dois softwares, o primeiro software refere-se um simulador de portão eletrônico e o segundo software refere-se a um sistema de vendas. Em ambas as aplicações, o método PA-PON-POR demonstrou ser eficiente no que se propõe, auxiliando no processo de criação de Regras e de sistemas PON-POR com alguma garantia de qualidade.
This research proposes a method to apply the Axiomatic Design Theory (ADT) in the Rule-oriented software development process. In this context, it was not found in the literature, by the efforts of this work research, the application of ADT in Rule-oriented software development. However, the ADT was focus on research in Object-Oriented software development in a previous work, which was used as inspiration in this current research work. This current research proposes the method Axiomatic Design for Notification-Oriented Paradigm and Rule-Oriented Paradigm (AD-NOP-ROP) since the rules follow the NOP structural model. This method proposes a functional decomposition of system requirements in four levels which are: Use Cases, Use Subcases that are Technical Feature Independent, Use Subcases that are Technical Feature Dependent, and Technical Service . Furthermore, the method AD-NOP-ROP applies the ADT Independence Axiom in each one of the decomposition levels by means of design matrixes and metrics which calculates reangularity and semangularity from ADT. The design matrixes still aids in the identification of Exclusive Premises, which are important elements of NOP-ROP systems with Rules whose Actions instigate the creation of conflicting facts. The Information Axiom from ADT is also applied in each decomposition level in order to evaluate design solutions in terms of its amount of information. Still, the method AD-NOP-ROP presents a set of metrics which are specific for evaluation of structural quality of Rule composition, thereby providing criteria for decision making with respect to design quality. Besides, the method AD-NOP-ROP can be used in a simultaneous way with the existent method used for software design based on NOP-ROP application development, so called Notification-Oriented and Rule-Oriented Application Development (NO-RO-AD), in order to assist in the achievement and validation of artifacts. The method AD-NOP-ROP was applied during the development of two software systems, the first one refers to an Electronic Gate and the second one refers to a Sales System. In both applications the method displayed efficiency in its purposes, assisting in the Rule creation process and also in the creation of NOP-ROP software with some quality assurance.
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Schön, Michaela Costa. "Número: reflexões sobre as conceituações de Russell e Peano." Pontifícia Universidade Católica de São Paulo, 2006. https://tede2.pucsp.br/handle/handle/11104.

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Made available in DSpace on 2016-04-27T16:57:50Z (GMT). No. of bitstreams: 1 EDM - Michaela C Schon.pdf: 1931458 bytes, checksum: 5cde0886ff87d5dafb588e52ab96ed50 (MD5) Previous issue date: 2006-11-06
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This paper aimed the realization of a study concerning the philosophical epistemology of the concept of number, in which it still makes sense to ask: What is number? In this perspective, we have assumed as problematic the philosophical duality of the conceptualizations of numbers, according to Axiomatic (proposed by Peano) e by the Set Theory and Logics (proposed by Russell), being the Conceptualization of Number the problem of this research, concerning the possibility of introducing an ultimate definition to this concept. The focus of this research is in the polemics that exists about the number introduced by Russell (1872-1970) contrary to Piano s (1858-1932), taking as a basis Otte s criticism, introduced in the article: B. Russell Introduction to Mathematical Philosophy , 2001. The research was developed using, as a reference, the sense of Complementarity, as well as using proper qualitative methodological research procedures. As a conclusion, we are able to claim that numbers are: on one hand, characteristics of certain classes and, on the other hand, operative concepts. This way, the existence of polemics between philosophers like Frege and Russell, who have favored predicative aspects, that is, they define number in terms of cardinality and, others like Grassmann, Dedekind and Peano who have highlighted the ordinal numbers, justify Otto s proposition of complementarity between the approaches. The possibility of having cognitive and didactical consequences on the teaching in the use of one or another approach of conceptualization of the number or both, as Otte intends, makes this study a contribution to Mathematical Education
Este trabalho objetivou realizar um estudo sobre a epistemologia filosófica do conceito de número, na qual ainda faz sentido o questionamento: O que é número? Nesta perspectiva, assumiu-se como problemática a dualidade filosófica das conceituações de número, sustentadas pela Axiomática (proposta por Peano) e pela Teoria dos Conjuntos e Lógica (proposta por Russell), sendo o problema de pesquisa a Conceituação de Número frente a essa dualidade e à possibilidade de ser apresentada uma definição em definitivo ao conceito de número. O foco da presente pesquisa está na polêmica existente entre a concepção de número apresentada por Russell (1872-1970) contraposta à de Peano (1858-1932), tomando-se por base as críticas de Otte, apresentadas no artigo: B. Russell Introduction to Mathematical Philosophy , de 2001. A pesquisa desenvolveu-se tendo por referência a noção de Complementaridade, tendo sido utilizados procedimentos metodológicos adequados às pesquisas qualitativas. Como conclusão pode-se afirmar que os números são: por um lado, características de certas classes e, por outro, conceitos operativos. Deste modo, a existência da polêmica entre filósofos como Frege e Russell, que favoreceram os aspectos predicativos, isto é, definem os números em termos de cardinalidade e, outros como Grassmann, Dedekind e Peano que destacam os números ordinais, justifica a proposição de Otte da complementaridade entre as abordagens. A possibilidade de existirem conseqüências cognitivas e didáticas na utilização no ensino de uma ou outra abordagem da conceituação de número ou de ambas como pretende Otte torna, este estudo, uma contribuição para a Educação Matemática
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Pereira, Ana Maria. "Abordagem de especificação de requisitos baseada em projeto axiomático." Universidade Tecnológica Federal do Paraná, 2011. http://repositorio.utfpr.edu.br/jspui/handle/1/361.

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Esta dissertação apresenta uma abordagem que aplica a Teoria de Projeto Axiomático à especificação de requisitos de sistemas de software visando melhorar a qualidade da solução de projeto desde a análise do problema até identificação dos requisitos efetivamente. O objetivo da abordagem desenvolvida é propor e integrar métodos que permitam o uso de Projeto Axiomático em um processo de Engenharia de Requisitos. A abordagem de especificação de requisitos proposta estabelece a aplicação do Axioma da Independência no estudo de problemas e necessidades do cliente. Desta forma, incluem-se no processo de engenharia de requisitos novos domínios de estudo, o domínio do problema e o domínio do cliente. É estabelecido um modelo de hierarquia para a decomposição de Problemas, Necessidades e Requisitos. Um processo de ziguezagueamento é sugerido para que se possa aplicar a abordagem proposta em conjunto com um processo de desenvolvimento interativo e incremental como o Processo Unificado. Apresenta-se um estudo de caso de um sistema de teste de equipamentos em uma linha de produção. O estudo de caso tem por objetivo demonstrar a aplicação prática da abordagem de especificação de requisitos proposta nesta dissertação. Além disso, apresentam-se os experimentos realizados durante o trabalho de pesquisa e seus resultados. Para exemplificar a execução dos experimentos é demonstrado o processo de especificação de requisitos para um sistema de relatórios de visitas a clientes. Este exemplo ajuda a ilustrar como a abordagem apresentada pode ser utilizada para aumentar a consistência e a qualidade dos requisitos de projetos de software.
This dissertation presents an approach that applies the Axiomatic Design Theory to the specification of software systems requirements. This Approach intends to improve the quality of design solution since its inception, which involves from the problem analysis to the requirements identification. The purpose of the proposed approach is to offer methods that allow the use of axiomatic design in a process of requirements engineering. The proposed requirements specification approach establishes the application of the Axiom of Independence in the study of problems and costumer needs. In this way, new domains, the problem domain and the costumer domain, are included in the requirements engineering process. It is established a hierarchical model for the decomposition of Problems, Needs and Requirements. A zig-zag process is suggested in order to use the propose approach in conjunction with a development process as the Unified Process. It is presented a case study of a system for equipment testing in a production line. The case study aims to demonstrate the practical application of the requirements specification approach proposed in this dissertation. In addition, the results of the experiments performed during the research are presented. The requirements specification process for a reporting system is shown to illustrate the experiments. This example helps billustrate how the proposed approach can be used to increase the consistency and quality of software requirements.
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Souza, Rafael Gorski Moreno. "Problem-Based SRS: método para especificação de requisitos de software baseado em problemas." Universidade Tecnológica Federal do Paraná, 2016. http://repositorio.utfpr.edu.br/jspui/handle/1/1811.

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Especificação de requisitos é reconhecida como como uma atividade critica nos processos de desenvolvimento de software por causa de seu impacto nos riscos do projeto quando mal executada. Um grande conjunto de estudos discute aspectos teóricos, proposições de técnicas e práticas recomendadas para a Engenharia de Requisitos (ER). Para ter sucesso, ER tem que assegurar que requisitos especificados são completos e corretos, o que significa que todas as intenções dos stakeholders são cobertas pelos requisitos e que não existem requisitos desnecessários. Entretanto, a captura precisa das intenções stakeholders continua sendo um desafio e é o maior fator para falhas em projetos de software. Esta dissertação apresenta um novo método denominado “Problem-Based SRS” que tem como objetivo melhorar a qualidade da especificação de requisitos de software (SRS – Software Requirements Specification) no sentido de que os requisitos especificados forneçam uma resposta adequada para os problemas dos clientes reais. Neste método, o conhecimento sobre os requisitos de software é construído a partir do conhecimento sobre os problemas do cliente. O Problem-Based SRS consiste de uma organização de atividades e resultados através de um processo que contem cinco etapas. O método fornece suporte ao time de engenharia de requisitos para analisar sistematicamente o contexto de negócio e especificar os requisitos de software, considerando o vislumbre e a visão do software. Os aspectos de qualidade das especificações são avaliados utilizando técnicas de rastreabilidade e princípios do axiomatic design. Os casos de estudo realizados e apresentados nesta dissertação apontam que o método proposto pode contribuir de forma significativa para uma melhor especificação de requisitos de software.
Requirements specification has long been recognized as critical activity in software development processes because of its impact on project risks when poorly performed. A large amount of studies addresses theoretical aspects, propositions of techniques, and recommended practices for Requirements Engineering (RE). To be successful, RE have to ensure that the specified requirements are complete and correct what means that all intents of the stakeholders in a given business context are covered by the requirements and that no unnecessary requirement was introduced. However, the accurate capture the business intents of the stakeholders remains a challenge and it is a major factor of software project failures. This master’s dissertation presents a novel method referred to as “Problem-Based SRS” aiming at improving the quality of the Software Requirements Specification (SRS) in the sense that the stated requirements provide suitable answers to real customer ́s businesses issues. In this approach, the knowledge about the software requirements is constructed from the knowledge about the customer ́s problems. Problem-Based SRS consists in an organization of activities and outcome objects through a process that contains five main steps. It aims at supporting the software requirements engineering team to systematically analyze the business context and specify the software requirements, taking also into account a first glance and vision of the software. The quality aspects of the specifications are evaluated using traceability techniques and axiomatic design principles. The cases studies conducted and presented in this document point out that the proposed method can contribute significantly to improve the software requirements specification.
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"An axiomatization of common-sense geometry /." Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3008317.

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Books on the topic "Axiomatic set theory"

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Bernays, Paul. Axiomatic set theory. New York: Dover Publications, 1991.

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Bernays, Paul. Axiomatic set theory. New York: Dover, 1991.

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Aguilar, Victor. Axiomatic theory of economics. Commack, NY: Nova Science Publishers, Inc., 1999.

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Peters, H. J. M. Axiomatic bargaining game theory. Dordrecht: Kluwer Academic Publishers, 1992.

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Liu, Xiaodong, and Witold Pedrycz. Axiomatic Fuzzy Set Theory and Its Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-00402-5.

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Roland Hinnion and Thierry Libert (eds). ONE HUNDRED YEARS OF AXIOMATIC SET THEORY. Paris: Academia, 2012.

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Bellotti, Luca. What is a model of axiomatic set theory? Pisa: ETS, 2012.

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Aczel, Peter. Non-well-founded sets. Stanford, CA: Center for the Study of Language and Information, 1988.

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Fiore, Marcelo P. First steps on the representation of domains (extended abstract). Edinburgh: LFCS, Dept. of Computer Science, University of Edinburgh, 1995.

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Bernard, Grofman, Blais André 1947-, and Bowler Shaun 1958-, eds. Duverger's law of plurality voting: The logic of party competition in Canada, India, the United Kingdom and the United States. New York: Springer, 2009.

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Book chapters on the topic "Axiomatic set theory"

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Schindler, Ralf. "Axiomatic Set Theory." In Set Theory, 9–21. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06725-4_2.

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Jech, Thomas. "Axiomatic Set Theory." In Set Theory, 1–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-662-22400-7_1.

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Vaught, Robert L. "Axiomatic Set Theory." In Set Theory, 65–69. Boston, MA: Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0835-8_7.

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Mendelson, Elliott. "Axiomatic Set Theory." In Introduction to Mathematical Logic, 176–230. Boston, MA: Springer US, 1987. http://dx.doi.org/10.1007/978-1-4615-7288-6_5.

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Cameron, Peter J. "Axiomatic set theory." In Springer Undergraduate Mathematics Series, 113–40. London: Springer London, 1998. http://dx.doi.org/10.1007/978-1-4471-0589-3_6.

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Cantone, Domenico, Eugenio Omodeo, and Alberto Policriti. "Axiomatic Views of Aggregates." In Set Theory for Computing, 61–86. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-3452-2_3.

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García, José Luis. "Classes." In Intuitive Axiomatic Set Theory, 41–56. Boca Raton: Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781003449911-3.

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García, José Luis. "Pure Sets." In Intuitive Axiomatic Set Theory, 129–44. Boca Raton: Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781003449911-7.

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García, José Luis. "ZF-Universes." In Intuitive Axiomatic Set Theory, 164–78. Boca Raton: Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781003449911-9.

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García, José Luis. "Objects, Collections, Sets." In Intuitive Axiomatic Set Theory, 19–40. Boca Raton: Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781003449911-2.

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Conference papers on the topic "Axiomatic set theory"

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Tian, Xiaojuan, Guangfei Hu, and Jing Li. "A new fuzzy associative classification based on axiomatic fuzzy set theory." In 2010 Seventh International Conference on Fuzzy Systems and Knowledge Discovery (FSKD). IEEE, 2010. http://dx.doi.org/10.1109/fskd.2010.5569158.

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Nordlund, Mats, Taesik Lee, and Sang-Gook Kim. "Axiomatic Design: 30 Years After." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-52893.

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In 1977, Nam P Suh proposed a different approach to design research. Suh’s approach was different in that it introduced the notions of domains and layers in a 2-D design thinking and stipulated a set of axioms that describes what is a good design. Following Suh’s 2-D reasoning structure in a zigzagging manner and applying these axioms through the design process should enable the designer to arrive at a good design. In this paper, we present our own experiences in applying Suh’s theories to software design, product design, organizational design, process design, and more in both academic and industrial settings. We also share our experience from teaching the Axiomatic Design theory to students at universities and engineers in industry, and draw conclusions on how best to teach and use this approach, and what results one can expect. The merits of the design axioms are discussed based on the practical experiences that the authors have had in their application. The process developed around the axioms to derive maximum value (solution neutral environment, design domains, what-how relationship, zig-zag process, decomposition, and design matrices) is also discussed and some updates are proposed.
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Dimarogonas, Andrew D. "On the Axiomatic Foundation of Design." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0027.

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Abstract Mechanical design methodology has its origins in the writings of ancient Greek and Alexandrine authors between 300 BC and 100 AD when also the first aesthetic theory was proposed. German authors of the middle of 19th Century have introduced the foundation for Mechanical Design on basic Design Principles, modernized the machine element methodology and introduced the parallel development of the function with the form. F. Redtenbacher introduced a set of design principles. Reuleaux (1852) introduced two fundamental Design Principles (Ground Rules), re-introduced recently in axiomatic form by Suh et al. The paper discusses the merits of establishing Design Principles or Design Axioms as the fundamental Rules of design and the implications of these Rules on the design and manufacturing methodology. The relation of the Design Rules with the principles of the total quality engineering in the Taguchi sense is also investigated.
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Zhou, Chunlai, Biao Qin, and Xiaoyong Du. "A Savage-style Utility Theory for Belief Functions." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/712.

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In this paper, we provide an axiomatic justification for decision making with belief functions by studying the belief-function counterpart of Savage's Theorem where the state space is finite and the consequence set is a continuum [l, M] (l<M). We propose six axioms for a preference relation over acts, and then show that this axiomatization admits a definition of qualitative belief functions comparing preferences over events that guarantees the existence of a belief function on the state space. The key axioms are uniformity and an analogue of the independence axiom. The uniformity axiom is used to ensure that all acts with the same maximal and minimal consequences must be equivalent. And our independence axiom shows the existence of a utility function and implies the uniqueness of the belief function on the state space. Moreover, we prove without the independence axiom the neutrality theorem that two acts are indifferent whenever they generate the same belief functions over consequences. At the end of the paper, we compare our approach with other related decision theories for belief functions.
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Novaro, Arianna, Umberto Grandi, Dominique Longin, and Emiliano Lorini. "Goal-Based Collective Decisions: Axiomatics and Computational Complexity." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/65.

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We study agents expressing propositional goals over a set of binary issues to reach a collective decision. We adapt properties and rules from the literature on Social Choice Theory to our setting, providing an axiomatic characterisation of a majority rule for goal-based voting. We study the computational complexity of finding the outcome of our rules (i.e., winner determination), showing that it ranges from Nondeterministic Polynomial Time (NP) to Probabilistic Polynomial Time (PP).
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Iannotti, P. "Selection of best beam theories based on natural frequencies and dynamic response obtained through mode superposition method." In IV Aerospace PhD-Days. Materials Research Forum LLC, 2024. http://dx.doi.org/10.21741/9781644903193-2.

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Abstract. Simplified formulations, particularly 1D models, are fundamental for reducing the computational cost typically required by structural analyses. The use of a limited number of nodal degrees of freedom has inevitable implications for the model’s capabilities and accuracy. Furthermore, the performance of a reduced formulation is strictly problem-dependent, and the choice of a specific set of primary unknowns must be weighted considering their influence on the accuracy of the results of interest. In this work, a procedure for the selection of the best 1D models to adopt for time-response analyses is investigated. Through the Axiomatic/Asymptotic Method (AAM), the influence of single unknowns is evaluated for a specific structural configuration, which can be described as a combination of aspect ratio, material, geometry, and boundary conditions. The finite element governing equations for every considered set of variables are obtained through the Carrera Unified Formulation (CUF). The main indicator for the quality of a theory is based on the evaluation of a certain number of natural frequencies. Dynamic response analyses are then carried out using the modal superposition method to further asses the performance of the selected best theories.
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Petrolo, M. "Refinement of structural theories for composite shells through convolutional neural networks." In Aeronautics and Astronautics. Materials Research Forum LLC, 2023. http://dx.doi.org/10.21741/9781644902813-31.

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Abstract. This study examines the use of Convolutional Neural Networks (CNN) to determine the optimal structural theories to adopt for the modeling of composite shells, to combine accuracy and computational efficiency. The use of the Axiomatic/Asymptotic Method (AAM) on higher-order theories (HOT) based on polynomial expansions can be cumbersome due to the amount of Finite Element Models (FEM) virtually available and the problem-dependency of a theory’s performance. Adopting the Carrera Unified Formulation (CUF) can mitigate this obstacle through its procedural and lean derivation of the required structural results. At the same time, the CNN can act as a surrogate model to guide the selection process. The network can inform on the convenience of a specific set of generalized variables after being trained with just a small percentage of the results typically required by the AAM. The CNN capabilities are compared to the AAM through the Best Theory Diagram (BTD) obtained using different selection criteria: errors over natural frequencies or failure indexes.
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Petrolo, Marco, and Erasmo Carrera. "Best Structural Theories for Free Vibrations of Sandwich Composites via Machine Learning." In ASME 2019 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/imece2019-10296.

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Abstract This work presents a novel methodology for the development of refined structural theories for the modal analysis of sandwich composites. Such a methodology combines three well-established techniques, namely, the Carrera Unified Formulation (CUF), the Axiomatic/Asymptotic Method (AAM), and Artificial Neural Networks (NN). CUF generates structural theories and finite element arrays hierarchically. CUF provides the training set for the NN in which the structural theories are inputs and the natural frequencies targets. AAM evaluates the influence of each generalized displacement variable, and NN provides Best Theory Diagrams (BTD), i.e., curves providing the minimum number of nodal degrees of freedom required to satisfy a given accuracy requirement. The aim is to build BTD with far less computational cost than in previous works. The numerical results consider sandwich spherical shells with soft cores and different features, such as thickness and curvature to investigate their influence on the choice of generalized displacement variables. The numerical results show the importance of third-order generalized displacement variables and prove that the present framework can be of interest to evaluate the performance of any structural theory as typical design parameters change and provide guidelines to the analysts on the most convenient computational model to save computational cost without accuracy penalties.
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Malinin, Len. "Design Under Contradictory Requirements." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-65108.

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This article presents a design method aimed at addressing contradictory requirements during the conceptual design activities or new product development. Of several methods aimed at developing a “good design” (not necessarily solving a contradiction), a general formal method was proposed in the Axiomatic Design Theory (ADT) by NP Suh [1]. ADT views design as a process that translates a set of functional requirements into a set of design parameters through a design matrix. The goal of the axiomatic design is to force a designer to start from scratch and explore the relationship between functions of the product and its design characteristics. Because the design characteristics in this approach are determined from scratch, the contradictions theoretically will be eliminated at a high level, before the design is developed in more detail. The ADT, however, does not offer specific tools to address contradictory requirements. Hegel’s Logic claims that “there is absolutely nothing whatever in which we cannot and must not point to contradictions“[2]. In this paper, we argue that with the right focus, contradictions can be leveraged to develop a stronger design solution. While contradictory requirements to product characteristics arise in almost every project, most often they are addressed by searching for a useful compromise in a highly iterative procedure. A more efficient approach, presented in this paper, satisfies both sides of a contradictory requirement (at different moments of time, or for different parts of the object, or at different sections of its non-linear characteristic). It is shown that in many cases, the most important step is reframing of the initial problem, which can be done by listing contradictory requirements and indicating to which parts of the object / moments of time/ stages of its life cycle they apply. Once it is done, the solution can often transpire from the reformulated problem statement, or can be generated using a very limited set of separation principles. An additional option, which has not been previously recommended for resolving contradictions, is separation of contradictory requirements in the space of material or object parameters, by selecting non-linear material or device characteristics. For instance, a medical device needs to meet different requirements in different tests: high elasticity (for the kink test) and at the same time high strength (for the burst test). This means that the target material should meet contradictory requirements to a single characteristic, its stress-deformation curve. The contradiction can be resolved using the fact that high elasticity (the kink test) is required at relatively low deformations whereas high strength (the burst test) is required at large deformations. Generally, for selection of a non-linear characteristic, it is proposed to use a morphological table with non-linear characteristics of a material or of similar devices based on different operation principles (such as different I-V curves of a current limiting device). Several case studies dealing with different subject matter applications illustrate the proposed method. The case studies include medical devices (peripherally inserted central catheter, vena cava filter), aerodynamic tractor-trailer devices, current limiting devices. The case studies are based on real life projects that resulted in patented designs.
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Shi, Zhuochen, and Gregory Mocko. "Knowledge Base Representation for Axiomatic Design Through Ontologies." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13171.

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Axiomatic Design has been applied and developed as a tool, offering a scientific basis for design and improving design activities. Axiomatic Design has been used in various fields such as software system design, structure design, and product design. However, several challenges and limitations exist in Axiomatic Design including: the inconsistency in identifying design parameters, existence of coupled design, and multiple groups of functional requirements and design parameters. Aimed at using Axiomatic Design to generate conceptual solutions in engineering design while overcoming its limitations, a formal ontology is developed. The ontology defines functional requirements, design parameters, concepts, components and variables and their relationships. Axioms and rules of Axiomatic Design for the ontology are summarized. The Axiomatic Design ontology is applied to the design of a car seat as an example generating several concepts, and then compared and analyzed multiple groups of the concepts with the help of Axiomatic Design rules. More design ideas can be generated by combining detailed concepts as the higher level possible solutions.
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