The propositional calculus AoC, “Algebra of Classes”,and the extended propositional calculus EAC, “Extended Algebra ofClasses” are introduced in this paper. They are extensions, by additionalpropositional functions which are not invariant under the biconditional,of the corresponding classical propositional systems. Theirorigin lies in an analysis, motivated by Cantor’s concept of the cardinalnumbers, of A. P. Morse’s impredicative, polysynthetic set theory.

An extension of the Quantified Propositional Calculus1 obtained by the addition of two binary propositional functions is put forward as an inheritor of E. Schröder's “Algebra der Logik”. The formal system is itself not new, in fact it forms part of A. P. Morse's “A Theory of Sets”; although the latter is considered as a first-order system. Since the additional propositional functions are not invariant under the logical biconditional, this system–and many others naturally obtained from it–give us a collection of (...) examples of non-standard, but mathematically meaningful, propositional systems. (shrink)

In Logical Forms Part II, Chateaubriand begins the Chapter on “Propositional Logic” by considering the reading of the ‘conditional’ by ‘implies’; in fact he states that:There is a confusion, as a matter of fact, and it runs deep, but it is a confusion in propositional logic itself, and the mathematician’s reading is a rather sensible one.After a careful, erudite analysis of various philosophical viewpoints of logic, Chateaubriand comes to the conclusion that:Pure propositional logic, as just characterized, belongs to ontological logic, (...) and it does not include a theory of deduction as a human activity. This is a part of epistemological logic, and is more closely connected to the applications of pure propositional logic.An implicit assumption in Chateaubriand’s reasoning appears to be that propositions have a timeless status. I will present arguments for the opposite viewpoint which leads to an analysis of Propositional Logic not covered under Chateaubriand’s monograph and perhaps resolves some conflicts therein; much as the conflict between the Intuitionist and Classical Mathematician on whether every function on the Reals is continuous is resolved by the realization that they are talking about different “entities”.Em Logical Forms II, Chateaubriand inicia o capítulo “Lógica Proposi-cional” considerando a leitura do ‘condicional’ como ‘implica’. De fato, ele diz o seguinte:Na verdade, existe uma confusão, e ela é profunda, mas é uma confusão na lógica proposicional ela mesma, e a leitura de um matemático é bastante sensível.Depois de uma análise cuidadosa e erudita dos vários pontos de vista filosóficos da lógica , Chateaubriand chega à conclusão que:A lógica proposicional pura, tal como aqui caracterizada, pertence à lógica ontológica, e não inclui uma teoria da dedução como atividade humana. Isto é parte da lógica epistemológica, e é mais intimamente conectada às aplicações da lógica proposicional.Uma premissa implícita no raciocínio de Chateaubriand parece ser a de que proposições têm um estatuto atemporal. Eu argumentarei em favor da visão oposta, que leva a uma análise da Lógica Proposicional não abordada no texto de Chateaubriand e que talvez resolva alguns conflitos. Muito do conflito entre Intuicionistas e Matemáticos Clássicos sobre se toda função sobre os números reais é contínua é resolvido pela compreensão de que eles estão falando de “entidades” diferentes. (shrink)

A conservative extension of first order logic, suitable for circumscriptive inference, is introduced.

A reduction algebra is defined as a set with a collection of partial unary functions (called reduction operators). Motivated by the lambda calculus, the Church-Rosser property is defined for a reduction algebra and a characterization is given for those reduction algebras satisfying CRP and having a measure respecting the reductions. The characterization is used to give (with 20/20 hindsight) a more direct proof of the strong normalization theorem for the impredicative second order intuitionistic propositional calculus.

En reseña de: Clavero, Bartolomé, España, 1978. Amnesia constituyente. Marcial Pons, Madrid, 2013.

Nowadays, the quality standards of higher education institutions pay special attention to the performance and evaluation of the students. Then, having a complete academic record of each student, such as number of attempts, average grade and so on, plays a key role. In this context, the existence of missing data, which can happen for different reasons, leads to affect adversely interesting future analysis. Therefore, the use of imputation techniques is presented as a helpful tool to estimate the value of missing (...) data. This work deals with the academic records of engineering students, in which imputation techniques are applied. More specifically, it is assessed and compared to the performance of the multivariate imputation by chained equations methodology, the adaptive assignation algorithm based on multivariate adaptive regression splines and a hybridization based on self-organisation maps with Mahalanobis distances and AAA algorithm. The results show that proposed methods obtain successfully results regardless the number of missing values, in general terms. (shrink)

The study of these fundamental questions, which were in part already addressed in a first monographic section dedicated to Ḥasdai Crescas in the last issue of this journal, is expanded in its perspective and scope by the articles contained in this second dossier.

El propósito de este artículo es explorar y analizar los principales objetivos y la evolución de la política de inmigración en Canadá desde mediados del siglo XIX hasta la actualidad. Como un país de inmigración, la cuestión de la regulación migratoria y de los procesos selectivos en la admisión de inmigrantes se han convertido en elementos centrales del disputado debate académico y político en torno a la identidad y la gestión de la diferencia en Canadá. Sin embargo, como veremos, la (...) política migratoria ha evolucionado a lo largo del tiempo por una combinación de intereses de naturaleza económica, cultural, social y política. (shrink)

Some doctors and nurses played a key role in Nazism. They were responsible for the sterilization and murder of people with disabilities. Nazi doctors used concentration camp inmates as guinea pigs in medical experiments that had military or racial objectives. What we have learnt about the behaviour of doctors and nurses during the Nazi period enables us to reflect on several issues in present-day medicine. In some authors' opinions, the teaching of the medical aspects of the Holocaust could be a (...) new model for education relating to professionalism, Human Rights, Bioethics and the respect of diversity. Teaching Medicine and the Holocaust could be a way of informing doctors and nurses of violations of Ethics in the past. Moreover, a Study Trip to Holocaust and Medicine related sites has a strong pedagogical value. Visiting Holocaust related sites, T4 centres and the places where medical experiments were carried out, has a special meaning for medical students. Additionally, tolerance, anti-discrimination, and the value of human life can be both taught and learned through this curriculum. The following article recounts our experiences of organizing and supervising a study trip with a group of medical students to some Holocaust and medicine-related sites in Berlin and Hadamar. The study tour included lectures at universities in Düsseldorf and Berlin. (shrink)

El objetivo de este estudio era ampliar el conocimiento sobre la experiencia de mujeres en videojuegos multijugador online (VMO), indagar sobre si existen situaciones de violencia y acoso por razón de género 2.0.La muestra estuvo compuesta por 454 mujeres de entre 16 y 29 años, de Castilla – La Mancha (España).Los resultados muestran que una alta proporción de las mujeres utilizan los VMO como espacio de ocio e interacción y que prácticamente una de cada dos mujeres ha vivido en primera (...) persona o ha presenciado episodios de violencia durante las partidas de VMO. (shrink)