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Axiomatic Set Theory à la Dijkstra and Scholten

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Acosta, Ernesto
Aldana, Bernarda
Bohórquez, Jaime
Rocha, Camilo
Abstract (Spanish)
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 demostradas, principalmente, mediante la sustitución de "igual por igual". 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 documento 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 de matemáticas e informática con el enfoque algebraico de Dijkstra y Scholten.
Abstract (English)
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.
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17 páginas.
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© Springer Nature Switzerland AG 2018

URI: https://repositorio.escuelaing.edu.co/handle/001/1836
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References

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