Artículos con la etiqueta ‘lógica matemática’

Rational Lukasiewicz logic and DMV-algebras

Por • 4 dic, 2012 • Category: Filosofía

In this paper we present some results on the variety of divisible MV-algebras. Any free divisible MV-algebra is an algebra of continuous piecewise linear functions with rational coefficients. Correspondingly, Rational {\L}ukasiewicz logic is defined and its tautology problem is shown to be co-NP-complete.

Axiomatic Method and Category Theory

Por • 5 oct, 2012 • Category: Filosofía

Lawvere’s axiomatization of topos theory and Voevodsky’s axiomatization of heigher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hibert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in Categorical logic opens new possibilities for using this method in physics and other natural sciences.

Stabilité et simplicité positive

Por • 4 may, 2012 • Category: Crítica

We study extensions universal positive model theory. And we continue the study of stability and simplicity already initiated by Ben Yaacov.

Forcing consequences of PFA together with the continuum large

Por • 12 mar, 2012 • Category: Crítica

We develop a new method for building forcing iterations with symmetric systems of structures as side conditions. Using our method we prove that the forcing axiom for the class of all the small finitely proper posets is compatible with a large continuum.

Très courte enquête sur l’extension non-triviale de la logique de propositions à la logique du premier et deuxième ordre

Por • 16 feb, 2012 • Category: Filosofía

The formal construction of the second-order logic or predicate calculus essentially adds quantifiers to propositional logic. Why second-order logic cannot be reduced to that of the first order? How to demonstrate that certain predicates are of higher-order? What type of order matches the natural language? Is there a philosophical position behind every logic, even for classical ones? What philosophical position for what logic in connection to its expressive power? These are the questions we ask and that we very briefly sketch as a first reflection. (paper in French)

Reasoning about constructive concepts

Por • 6 ene, 2012 • Category: Ambiente

We find that second order quantification is problematic when a quantified concept variable is supposed to function predicatively. This issue is analyzed and it is shown that a constructive interpretation of the falling under relation suffices to resolve the difficulty. We are then able to present a formal system for reasoning about concepts. We prove that this system is consistent and we investigate the extent to which it is able to interpret set theoretic and number theoretic systems of a more standard type.

Kinds of concepts

Por • 6 ene, 2012 • Category: Crítica

The central focus is on clarifying the distinction between sets and proper classes. To this end we identify several categories of concepts (surveyable, definite, indefinite), and we attribute the classical set theoretic paradoxes to a failure to appreciate the distinction between surveyability and definiteness.