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Axiomatic Set Theory à la Dijkstra and Scholten
dc.contributor.author | Acosta, Ernesto | |
dc.contributor.author | Aldana, Bernarda | |
dc.contributor.author | Bohórquez, Jaime | |
dc.contributor.author | Rocha, Camilo | |
dc.date.accessioned | 2021-05-24T23:13:38Z | |
dc.date.accessioned | 2021-10-01T17:22:44Z | |
dc.date.available | 2021-05-24T23:13:38Z | |
dc.date.available | 2021-10-01T17:22:44Z | |
dc.date.issued | 2017 | |
dc.identifier.isbn | 978-3-319-66561-0 | |
dc.identifier.isbn | 978-3-319-66562-7 | |
dc.identifier.uri | https://repositorio.escuelaing.edu.co/handle/001/1480 | |
dc.description.abstract | The algebraic approach by E.W. Dijkstra and C.S. Scholten to formal logic is a proof calculus, where the notion of proof is a sequence of equivalences proved – mainly – by using substitution of ‘equals for equals’. This paper presents Set , a first-order logic axiomatization for set theory using the approach of Dijkstra and Scholten. What is novel about the approach presented in this paper is that symbolic manipulation of formulas is an effective tool for teaching an axiomatic set theory course to sophomore-year undergraduate students in mathematics. This paper contains many examples on how argumentative proofs can be easily expressed in Set and points out how the rigorous approach of Set can enrich the learning experience of students. The results presented in this paper are part of a larger effort to formally study and mechanize topics in mathematics and computer science with the algebraic approach of Dijkstra and Scholten. | spa |
dc.description.abstract | El enfoque algebraico de E.W. Dijkstra y C.S. Scholten a la lógica formal es un cálculo de prueba, donde la noción de prueba es una secuencia de equivalencias probadas, principalmente, mediante la sustitución de "iguales por iguales". Este artículo presenta Set, una axiomatización lógica de primer orden para la teoría de conjuntos utilizando el enfoque de Dijkstra y Scholten. Lo novedoso del enfoque presentado en este artículo es que la manipulación simbólica de fórmulas es una herramienta eficaz para enseñar un curso de teoría axiomática de conjuntos a estudiantes de segundo año de pregrado en matemáticas. Este artículo contiene muchos ejemplos sobre cómo las pruebas argumentativas se pueden expresar fácilmente en Set y señala cómo el enfoque riguroso de Set puede enriquecer la experiencia de aprendizaje de los estudiantes. Los resultados presentados en este artículo son parte de un esfuerzo mayor para estudiar y mecanizar formalmente temas en matemáticas e informática con el enfoque algebraico de Dijkstra y Scholten. | spa |
dc.format.extent | 12 páginas | spa |
dc.format.mimetype | application/pdf | spa |
dc.language.iso | eng | spa |
dc.publisher | Springer Nature | spa |
dc.relation.ispartofseries | Communications in Computer and Information Science book series (CCIS, volume 735); | |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | spa |
dc.source | https://link.springer.com/chapter/10.1007%2F978-3-319-66562-7_55 | spa |
dc.title | Axiomatic Set Theory à la Dijkstra and Scholten | spa |
dc.type | Artículo de revista | spa |
dc.description.notes | Colombian Conference on Computing | spa |
dc.type.version | info:eu-repo/semantics/publishedVersion | spa |
oaire.accessrights | http://purl.org/coar/access_right/c_14cb | spa |
oaire.version | http://purl.org/coar/version/c_970fb48d4fbd8a85 | spa |
dc.contributor.researchgroup | CTG-Informática | spa |
dc.identifier.doi | doi.org/10.1007/978-3-319-66562-7_55 | |
dc.identifier.url | https://link.springer.com/chapter/10.1007%2F978-3-319-66562-7_55 | |
dc.publisher.place | Suiza | spa |
dc.relation.citationedition | CCC 2017 | spa |
dc.relation.citationendpage | 791 | spa |
dc.relation.citationstartpage | 775 | spa |
dc.relation.indexed | N/A | spa |
dc.relation.ispartofbook | Advances in Computing | spa |
dc.relation.references | Dijkstra, E.W., Scholten, C.S.: Predicate Calculus and Program Semantics. Texts and Monographs in Computer Science. Springer, New York (1990) | spa |
dc.relation.references | Halmos, P.R.: Naive Set Theory. Undergraduate Texts in Mathematics. Springer, New York (1974) | spa |
dc.relation.references | Hodel, R.E.: An Introduction to Mathematical Logic. Dover Publications Inc., New York (2013) | spa |
dc.relation.references | Hrbacek, K., Jech, T.J.: Introduction to Set Theory. Monographs and Textbooks in Pure and Applied Mathematics, vol. 220, 3rd edn. M. Dekker, New York (1999). Rev. and expanded edition | spa |
dc.relation.references | Hsiang, J.: Refutational theorem proving using term-rewriting systems. Artif. Intell. 25(3), 255–300 (1985) | spa |
dc.relation.references | Jech, T.J.: Set Theory. Pure and Applied Mathematics, a Series of Monographs and Textbooks, vol. 79. Academic Press, New York (1978) | spa |
dc.relation.references | Kunen, K.: Set Theory. Studies in Logic, vol. 34. College Publications, London (2013). Revised edition | spa |
dc.relation.references | Meseguer, J.: General logics. In: Logic Colloquium 1987: Proceedings. Studies in Logic and the Foundations of Mathematics, 1st edn., vol. 129, pp. 275–330. Elsevier, Granada, August 1989 | spa |
dc.relation.references | Meseguer, J.: Conditional rewriting logic as a unified model of concurrency. Theor. Comput. Sci. 96(1), 73–155 (1992) | spa |
dc.relation.references | Rocha, C.: The formal system of Dijkstra and Scholten. In: Martí-Oliet, N., Ölveczky, P.C., Talcott, C. (eds.) Logic, Rewriting, and Concurrency. LNCS, vol. 9200, pp. 580–597. Springer, Cham (2015). doi: 10.1007/978-3-319-23165-5_27 | spa |
dc.relation.references | Rocha, C., Meseguer, J.: A rewriting decision procedure for Dijkstra-Scholten’s syllogistic logic with complements. Revista Colombiana de Computación 8(2), 101–130 (2007) | spa |
dc.relation.references | Rocha, C., Meseguer, J.: Theorem proving modulo based on boolean equational procedures. In: Berghammer, R., Möller, B., Struth, G. (eds.) RelMiCS 2008. LNCS, vol. 4988, pp. 337–351. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-78913-0_25 | spa |
dc.relation.references | Tourlakis, G.J.: Lectures in Logic and Set Theory. Cambridge Studies in Advanced Mathematics, vol. 82–83. Cambridge University Press, Cambridge (2003) | spa |
dc.rights.accessrights | info:eu-repo/semantics/closedAccess | spa |
dc.rights.creativecommons | Atribución 4.0 Internacional (CC BY 4.0) | spa |
dc.subject.armarc | Teoría axiomática de conjuntos | SPA |
dc.subject.armarc | Lógica de Dijkstra-Scholten | SPA |
dc.subject.armarc | SET | ENG |
dc.subject.armarc | Manipulación simbólica | SPA |
dc.subject.proposal | Axiomatic set theory | spa |
dc.subject.proposal | Dijkstra-Scholten logic | spa |
dc.subject.proposal | Derivation | spa |
dc.subject.proposal | Formal system | spa |
dc.subject.proposal | Zermelo-Fraenkel (ZF) | spa |
dc.subject.proposal | Symbolic manipulation | spa |
dc.subject.proposal | Undergraduate-level course | spa |
dc.type.coar | http://purl.org/coar/resource_type/c_3248 | spa |
dc.type.content | Text | spa |
dc.type.driver | info:eu-repo/semantics/bookPart | spa |
dc.type.redcol | https://purl.org/redcol/resource_type/CAP_LIB | spa |
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