Let’s agree in calling “classical demonstration” a deduction that enables us to know the rational necessity that something is the case and cannot be otherwise. I propose to take seriously actual instances of this notion, e.g. some mathematical proofs, and explore certain discoursive and epistemic implications of their existence. Then I will look at questions about characterizing, rigorizing and acknowledging this kind of conclusive proof. Finally, some remarks on the meaning of Provability Logic in this context will be made.

My purpose in this paper is to show the evolution of the relationship between nonmonotonic logic and logic programming. I think that there are two periods in the evolution of this relationship. The first one isthe point of contact between these two fields that had been developed independently. In the second period, as I will show, the motivation to propose three-valued nonmonotonic logic comes from the study of the relationship between these two fields, and not from the study of nonmonotonic logic itself.

La argumentación es un aspecto publico y comunicativo, quizás no el único, de los procesos cognitivos inferenciales en la especie humana. Aunque los propios procesos cognitivos inferenciales no son exclusivos de los seres humanos, su expresión a través de la comunicación lingüística, su utilización en los procesos sociales para la conformación y cambio de las creencias y la conducta es propiamente humana. Una explicación correcta del concepto de argumentación es por tanto importante para captar nuestro concepto de racionalidad, de uso de la razón. EI trabajo explora la forma que tiene el concepto de argumentación en la cultura occidental utilizando las herramientas de teorías cognitivas recientes sobre la naturaleza de los conceptos, sugiriendo sus consecuencias para el concepto de razón.The argumentation is a public and communicative aspect, maybe not the only one, of inferential cognitive processes in the human species. While the very inferential, cognitive processes are not exclusive of the human beings, their expression through the linguistic communication, their use in social processes to shape and change beliefs and behaviour is properly human. An accurate description of the concept of argumentation is important then to grasp our concept of rationality, of the use of the reason. This paper explores the form of the concept of argumentation in western culture using the tools of recent cognitive theories on the nature of concepts, suggesting its consequences for the concept of reason.