Incertidumbre y lógica en el razonamiento con opiniones parcialmente inconsistentes

En este trabajo consideramos dos actitudes posibles para tratar la inferencia con afirmaciones parcialmente inconsistentes. Por una parte, nos ocupamos de la lógica paraconsistente de Jaskowski, según la presentación de Da Costa y Doria, como marco para este tipo de inferencias. Por la otra, planteamos el problema en el contexto de la lógica posibilista, desarrollada fundamentalmente por Dubois y Prade, a partir de la teoría de conjuntos difusos de Zadeh. Tratamos de mostrar finalmente, que para el manejo de opiniones parcialmente inconsistentes, una lógica tiene que dejar lugar para la existencia de "grados de certeza", a fin de dar sentido a la presencia de "opiniones" parcialmente inconsistentes, diferenciando la opinión de la ignorancia total

Negations in the adjunctive discursive logic

In the logical literature, Discursive (or Discussive) Logic introduced by Stanislaw Jaskowski is seen as one of the earliest examples of the so-called paraconsistent logic. Nevertheless, there is some confusion over what discursive logic actually is. One of the possible sources of the confusion may be easily discerned; it comes from the fact that Jaskowski published his two papers in Polish and their English translations appeared many years later.1 Up till 1999, no one but a Polish reader was able to read Jaskowski's paper on the discursive conjunction and, consequently some authors took discursive logic to be a foremost example of a non-adjunctive logic. The situation became even more complicated when da Costa, Dubikajtis and Kotas presented an axiomatization with discursive connectives as primitive symbols. It turned out that a connective of the discursive conjunction they considered did not correspond to any of Jaskowski's connectives. Thus, their axiomatization contained some axiom schemata that were not generally valid in Jaskowski's logic. The purpose of this paper is to clarify the confusion surrounding the discursive logic. We will present a direct semantics and axiomatization of Jaskowski's adjunctive discursive logic and show how to define and axiomatize two additional connectives of negation