Interpretationen der Heyting-Arithmetik endlicher Typen.
Interpreting number theory in nilpotent groups.
Interpreting reflexive theories in finitely many axioms
For finitely axiomatized sequential theories F and reflexive theories R, we give a characterization of the relation ’F interprets R’ in terms of provability of restricted consistency statements on cuts. This characterization is used in a proof that the set of (as well as ) sentences π such that GB interprets ZF+π is -complete.
Interpreting set theory in the endomorphism semi-group of a free algebra or in a category
Interrelation of algebraic, semantical and logical properties for superintuitionistic and modal logics
We consider the families 𝓛 of propositional superintuitionistic logics (s.i.l.) and NE(K) of normal modal logics (n.m.l.). It is well known that there is a duality between 𝓛 and the lattice of varieties of pseudo-boolean algebras (or Heyting algebras), and also NE(K) is dually isomorphic to the lattice of varieties of modal algebras. Many important properties of logics, for instance, Craig's interpolation property (CIP), the disjunction property (DP), the Beth property (BP), Hallden-completeness...
Intersection preserving and global expansions of subalgebras and filters in lattice implication algebras.
Intersection properties of partitions of a cardinal
Intersection Types for lambda^{gtz}-calculus
Intersections of prescribed power, type, or measure
Intrinsic Stochastic Processes.
Introducing FDSA (Fuzzy Dictionary of Synonyms and Antonyms): applications on information retrieval and stand-alone use.
We start by analyzing the role of imprecision in information retrieval in the Web, some theoretical contributions for managing this problem and its presence in search engines, with special emphasis on the use of thesaurus in order to increase the relevance of the documents retrieved. We then present FDSA, a Spanish electronic dictionary of synonyms that compute degrees of synonymy, and an eflicient implementation of it by using deterministic acyclic finite-state automata. We conclude by conjecturing...
Introduction à l'analyse algébrique
Introduction de quelques formes générales des fonctions pseudo-booléennes.
Introduction : la théorie de l’homotopie en perspective
Introduction to Diophantine Approximation
In this article we formalize some results of Diophantine approximation, i.e. the approximation of an irrational number by rationals. A typical example is finding an integer solution (x, y) of the inequality |xθ − y| ≤ 1/x, where 0 is a real number. First, we formalize some lemmas about continued fractions. Then we prove that the inequality has infinitely many solutions by continued fractions. Finally, we formalize Dirichlet’s proof (1842) of existence of the solution [12], [1].
Introduction to Formal Preference Spaces
In the article the formal characterization of preference spaces [1] is given. As the preference relation is one of the very basic notions of mathematical economics [9], it prepares some ground for a more thorough formalization of consumer theory (although some work has already been done - see [17]). There was an attempt to formalize similar results in Mizar, but this work seems still unfinished [18]. There are many approaches to preferences in literature. We modelled them in a rather illustrative...
Introduction to Liouville Numbers
The article defines Liouville numbers, originally introduced by Joseph Liouville in 1844 [17] as an example of an object which can be approximated “quite closely” by a sequence of rational numbers. A real number x is a Liouville number iff for every positive integer n, there exist integers p and q such that q > 1 and [...] It is easy to show that all Liouville numbers are irrational. Liouville constant, which is also defined formally, is the first transcendental (not algebraic) number. It is...
Introduzione delle variabili nel quadro delle teorie base dei Fondamenti della Matematica
Introduciamo la nozione di variabile nel quadro assiomatico delle teorie base dei Fondamenti della Matematica [9]. In tale quadro le variabili sono inserite come oggetti «unari», assumono valori di varie specie, possono essere connesse da correlazioni (o corrispondenze) e ammettono rappresentazioni funzionali locali. Gli assiomi sulle variabili sono scelti tenendo presenti gli usi più frequenti del termine «variabile» in Analisi Matematica, Fisica Matematica, Algebra, Geometria, Logica e in molte...
Intuitionistic double negation as a necessity operator.
Intuitionistic Frege systems are polynomially equivalent.