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Trames, classifications, définitions

Daniel Parrochia (1991)

Mathématiques et Sciences Humaines

L'article part d'une analogie entre trames et partitions, définitions conceptuelles et optiques. On montre que les divisions d'un espace de concepts ressemblent souvent à celles de l'espace réel. On étudie alors quelques exemples de pavage d'un espace conceptuel (Aristote) et on compare les processus dichotomiques platoniciens (générateurs de définitions) aux filtres d'une algèbre booléenne. Par la suite, on généralise ces modèles, considérant des structures floues et des «ensembles approximatifs»...

Two Axiomatizations of Nelson Algebras

Adam Grabowski (2015)

Formalized Mathematics

Nelson algebras were first studied by Rasiowa and Białynicki- Birula [1] under the name N-lattices or quasi-pseudo-Boolean algebras. Later, in investigations by Monteiro and Brignole [3, 4], and [2] the name “Nelson algebras” was adopted - which is now commonly used to show the correspondence with Nelson’s paper [14] on constructive logic with strong negation. By a Nelson algebra we mean an abstract algebra 〈L, T, -, ¬, →, ⇒, ⊔, ⊓〉 where L is the carrier, − is a quasi-complementation (Rasiowa used...

Two extensions of system F with (co)iteration and primitive (co)recursion principles

Favio Ezequiel Miranda-Perea (2009)

RAIRO - Theoretical Informatics and Applications

This paper presents two extensions of the second order polymorphic lambda calculus, system F, with monotone (co)inductive types supporting (co)iteration, primitive (co)recursion and inversion principles as primitives. One extension is inspired by the usual categorical approach to programming by means of initial algebras and final coalgebras; whereas the other models dialgebras, and can be seen as an extension of Hagino's categorical lambda calculus within the framework of parametric polymorphism....

Una lógica modal para la geometría esférica de incidencia.

Alfonso Ríder Moyano, Rafael María Rubio Ruiz (2005)

RACSAM

Habitualmente, las geometrías de incidencia están basadas en estructuras bisurtidas formadas por puntos y rectas, y conectadas por una relación entre ambas clases. En lo que sigue, introducimos una estructura monosurtida, que llamamos Marco Esférico de Incidencia, la cual resulta adecuada, para construir una base semántica que permita su consideración en el lenguaje modal. Construiremos así un sistema axiomático para dicho lenguaje, que estaría determinado por la estructura creada, es decir probaremos...

Una proposta di teorie base dei Fondamenti della Matematica

Ennio De Giorgi, Marco Forti, Giacomo Lenzi (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Vengono proposte alcune teorie base dei Fondamenti della Matematica che assumono come concetti primitivi i concetti di numero naturale, collezione, qualità, operazione e relazione; le operazioni e le relazioni considerate possono essere più o meno complesse: il numero naturale che indica il grado di complessità è detto arietà. Nelle teorie considerate è raggiunto un alto grado di autoreferenza.

Una teoria-quadro per i fondamenti della matematica

Ennio De Giorgi, Marco Forti (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We propose a "natural" axiomatic theory of the Foundations of Mathematics (Theory Q) where, in addition to the membership relation (between elements and classes), pairs, sets, natural numbers, n-tuples and operations are also introduced as primitives by means of suitable ground classes. Moreover, the theory Q allows an easy introduction of other mathematical and logical entities. The theory Q is finitely axiomatized in § 2, using a first-order language with a binary relation (membership) and five...

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