logic and completeness theorem
logic and Completeness Theorem
La créativité des définitions dans les systèmes para-euclidiens
Cet article considère trois sortes de calcul propositionnel (mais surtout la troisième), à la fois d'un point de vue logique et d'un point de vue épistémologique : (1) les systèmes classiques qui ont les propriétés suivantes : (a) chaque axiome doit contenir seulement (ou doit être compris comme contenant seulement) des termes primitifs, (b) chaque définition est métalinguistique, (c) chaque définition est non créatrice ; (2) les systèmes de Leśnieswski qui satisfont (a) mais ni (b) ni (c), une...
La fonction logique de Hilbert à travers les «Grundlagen der Mathematik»
La logique intensionnelle et les langues naturelles
La théorie d'un anneau de polynômes
Lambda-calcul, évaluation paresseuse et mise en mémoire
Langages à valeurs réelles et applications
Lattice of ℤ-module
In this article, we formalize the definition of lattice of ℤ-module and its properties in the Mizar system [5].We formally prove that scalar products in lattices are bilinear forms over the field of real numbers ℝ. We also formalize the definitions of positive definite and integral lattices and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [14], and cryptographic systems with lattices [15] and coding theory [9]....
L'axiomatisation de la syntaxe et le second theorem de Gödel
Le dimostrazioni di teoremi fondate sull’uso di calcolatori
Le fantôme de la modalité
Le lambda-calcul du second ordre
Le texte philosophique comme lieu d'étude sur la logique usuelle
Learning discrete categorial grammars from structures
We define the class of discrete classical categorial grammars, similar in the spirit to the notion of reversible class of languages introduced by Angluin and Sakakibara. We show that the class of discrete classical categorial grammars is identifiable from positive structured examples. For this, we provide an original algorithm, which runs in quadratic time in the size of the examples. This work extends the previous results of Kanazawa. Indeed, in our work, several types can be associated to a word...
Lebesgue's Convergence Theorem of Complex-Valued Function
In this article, we formalized Lebesgue's Convergence theorem of complex-valued function. We proved Lebesgue's Convergence Theorem of realvalued function using the theorem of extensional real-valued function. Then applying the former theorem to real part and imaginary part of complex-valued functional sequences, we proved Lebesgue's Convergence Theorem of complex-valued function. We also defined partial sums of real-valued functional sequences and complex-valued functional sequences and showed their...
Left and right semi-uninorms on a complete lattice
Uninorms are important generalizations of triangular norms and conorms, with a neutral element lying anywhere in the unit interval, and left (right) semi-uninorms are non-commutative and non-associative extensions of uninorms. In this paper, we firstly introduce the concepts of left and right semi-uninorms on a complete lattice and illustrate these notions by means of some examples. Then, we lay bare the formulas for calculating the upper and lower approximation left (right) semi-uninorms of a binary...
Leibniz Series forπ
In this article we prove the Leibniz series for π which states that π4=∑n=0∞(−1)n2⋅n+1. The formalization follows K. Knopp [8], [1] and [6]. Leibniz’s Series for Pi is item 26 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/.
Les -types du système
Nous démontrons dans ce papier que les types du système habités uniquement par des -termes (les -types) sont à quantificateur positif. Nous présentons ensuite des conséquenses de ce résultat et quelques exemples.
Les I-types du système
We prove in this paper that the types of system inhabited uniquely by λI-terms (the I-types) have a positive quantifier. We give also consequences of this result and some examples.