José M. Méndez

The "depth relevance condition" (drc) is a strengthening of the "variable-sharing property" (vsp). Deep relevant logics are logics fulfilling the drc, and Brady's DR is a key item in this class. The "qualified factorization principles" (qfp) are strong distribution principles. The qfp can be added to Relevance logic R without the result collapsing in a logic lacking the vsp. The aim of this paper is to show that DR (and any logic included in it) can be extended with the qfp, the drc being preserved. © 2016 Elsevier B.V., All rights reserved.

Let us refer by MK3 to Kleene’s strong 3-valued matrix. An implicative expansion of MK3 is natural if the conditional function defining it verifies modus ponens, assigns a designated value to a conditional whenever it assigns the same value to its antecedent and its consequent, and, finally, it coincides with the classical conditional function when restricted to the “classical” values ????\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {t}$$\end{document} and ????\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak {f}$$\end{document}. Two are the main results of this paper. (1) It is proven that, from the viewpoint of functional strength, there is only one 3-valued natural implication expansion of MK3 with the variable-sharing property, the logic we dub L3VSP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ }^{\text{VSP}}$$\end{document}. (2) It is shown that L3VSP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${ }^{\text{VSP}}$$\end{document} is a significant and strong logic that can be seen from different perspectives, one of them being to consider it an expansion of classical positive propositional logic.

En el escenario actual de Cuba y el mundo la migración al software libre constituye una necesidad para el desarrollo para garantizar la independencia tecnológica. Los procedimientos para realizar dicho proceso son fundamentales en la estrategia definida por el país que incluye la "Guía cubana de migración al software libre", sin embargo, su aplicación práctica enfrenta dificultades que han motivado a los autores a la elaboración de una estrategia específica para la migración al software libre en el sector de la Salud Pública de la provincia de Camagüey, Cuba. En esta estrategia se proponen las acciones concretas, los programas docentes que permitirán la recalificación del capital humano y las acciones que posibiliten garantizar la sostenibilidad de la migración al concluir el proceso. In the present Cuban and world scenarios the migration to free software constitutes a need for the development to guarantee technological independence. The procedures to carry out that process are vital in the strategy defined by the country that includes “Cuban guidelines for the migration to free software” however its practical implementation is facing difficulties that have motivated the authors to elaborate a specific strategy form the migration to free software in the Public health sector in the province of Camagüey, Cuba. In this strategy actions are suggested, like teaching programs that will allow the recertification of the capital human resources and steps that will make possible to guarantee the sustainability of the migration at the end of the process

We present new results on the Hubble diagram of distant type Ia supernovae segregated according to the type of host galaxy. This makes it possible to check earlier evidence for a cosmological constant by explicitly comparing SNe residing in galaxies likely to contain negligible dust with the larger sample. The cosmological parameters derived from these SNe Ia hosted by presumed dust-free early-type galaxies support earlier claims for a cosmological constant, which we demonstrate at ≃5σ significance, and the internal extinction implied is small even for late-type systems. Thus, our data demonstrate that host galaxy extinction is unlikely to systematically dim distant SNe Ia in a manner that would produce a spurious cosmological constant. Our analysis is based on new Hubble Space Telescope STIS 'snapshot' images and Keck-II echellette spectroscopy at the locations of the SNe, spanning the redshift range 0 < z < 0.8. Selecting from the sample discovered by the Supernova Cosmology Project, we classify the host galaxies of 39 distant SNe using the combination of STIS imaging, Keck spectroscopy and ground-based broad-band photometry. The distant data are analysed in comparison with a low-redshift sample of 25 SNe Ia re-calibrated according to the precepts of the SCP. The scatter observed in the SNe Ia Hubble diagrams correlates closely with host galaxy morphology. We find this scatter is smallest for SNe Ia occurring in early-type hosts and largest for those occurring in late-type galaxies. Moreover, SNe residing in late-type hosts appear ≃0.14 ± 0.09 mag fainter in their light-curve-width-corrected luminosity than those in early-type hosts, as expected if a modest amount of dust extinction is a contributing factor. As in previous studies, these results are broadly independent of whether corrections based upon SN light-curve shapes are performed. We also use our high-redshift data set to search for morphological dependences in the SNe light curves, as are sometimes seen in lowredshift samples. No significant trends are found, possibly because the range of light-curve widths is too limited.

The present paper is inspired by Sylvan and Plumwood’s logicBM defined in “Non-normal relevant logics” and by their treatmentof negation with the ∗-operator in “The semantics of first-degree en-tailment”. Given a positive logic L including Routley and Meyer’sbasic positive logic and included in either the positive fragment of Eor in that of RW, we investigate the essential De Morgan negation ex-pansions of L and determine all the deductive relations they maintainto each other. A Routley-Meyer semantics is provided for each logicdefined in the paper.

En este artículo, su autor hace un recorrido histórico, excelentemente documentado, por toda la historia de la Aviación Militar Española, desde sus inicios, allá por 1910, hasta nuestros días. Como puntos más importantes podemos destacar: La Campaña de Marruecos, donde se realizó el primer bombardeo específicamente aéreo y se constato la necesidad de contar con apoyo aéreo para el desarrollo de las operaciones militares. Los grandes vuelos de la Aviación Militar Española: Palos de la Frontera-Buenos Aires, Madrid-Manila, Melilla-Santa Isabel. La época de la guerra civil española, escenario de las nuevas doctrinas aéreas y de ensayo de nuevas tácticas que marcarían la futura actuación de la Aviación en la II Guerra Mundial. La creación del Ejército del Aire, la "Escuadrilla Azul" y el difícil quinquenio 1945-50, hasta que se inició su modernización. En el área operativa se trata la actuación del Poder Aéreo en Ifni, Sahara y los Balcanes. En el área de organización se habla sobre el programa ORGEA (Organización del Ejército del Aire), la creación del Ministerio de Defensa y la estructura orgánica actual. En lo referente a material, destacan la creación de la red de alerta y control, la llegada de los primeros cazas, para terminar con los más recientes planes de modernización. Por último, debemos hacer mención especial de nuestra integración en Europa e ingreso en la OTAN, por la gran influencia que estos dos hechos han tenido y tendrán en el futuro del Ejército del Aire.

The well-known logic first degree entailment logic (FDE), introduced by Belnap and Dunn, is defined with |$\wedge $|⁠, |$\vee $| and |$\sim $| as the sole primitive connectives. The aim of this paper is to establish the lattice formed by the class of all 4-valued C-extending implicative expansions of FDE verifying the axioms and rules of Routley and Meyer’s basic logic B and its useful disjunctive extension B|$^{\textrm {d}}$|⁠. It is to be noted that Boolean negation (so, classical propositional logic) is definable in the strongest element in the said class.

Los instrumentos curriculares suelen ser objeto de luchas políticas; están atravesados por opciones, renuncias y escogencias. No son nunca neutros. Estas páginas quieren ser una contribución a la urgente tarea de revisión curricular desde una perspectiva intercultural. En este artículo se presenta el currículo como “un camino” en el que las personas ‘aprendientes’ pueden encontrarse, dialogar y aprender gracias a su diversidad, y en el que es posible promover el diálogo de saberes y culturas. No se trata solamente de prestar atención a la diversidad cultural (lo cual sería ya un paso importante), sino de convertir los procesos educativos en un espacio para la convivencia en la diversidad y para la justicia cultural.

Belnap and Dunn’s well-known 4-valued logic FDE is an interesting and useful non-classical logic. FDE is defined by using conjunction, disjunction and negation as the sole propositional connectives. Then the question of expanding FDE with an implication connective is of course of great interest. In this sense, some implicative expansions of FDE have been proposed in the literature, among which Brady’s logic BN4 seems to be the preferred option of relevant logicians. The aim of this paper is to define a class of implicative expansions of FDE in whose elements Boolean negation is definable, whence strong logics such as the paraconsistent and paracomplete logic PŁ4 and BN4 itself are definable, in addition to classical propositional logic.

The logic E4 is related to Brady’s BN4 in a similar way to which Anderson and Belnap’s logic of entailment E is related to their logic of the relevant implication R. In ‘A companion to Brady’s 4-valued relevant logic: the 4-valued logic of entailment E4’, quoted in this paper, three alternatives to BN4 and another three to E4 are summarily introduced in a couple of pages as the only alternatives containing Routley and Meyer’s basic logic B, provided some conditions are fulfilled. The aim of this note is to prove BN4 and its three alternatives are the same logic up to some point, since they are functionally equivalent to each other, as it is the case with E4 and its three alternatives, which are also functionally equivalent to each other; to some extent, E4 is superior to BN4, since the latter is functionally included in the former, but not conversely.

The basic quasi-Boolean negation expansions of relevance logics included in Anderson and Belnap’s relevance logic R are defined. We consider two types of QB-negation: H-negation and D-negation. The former one is of paraintuitionistic or superintuitionistic character, the latter one, of dual intuitionistic nature in some sense. Logics endowed with H-negation are paracomplete; logics with D-negation are paraconsistent. All logics defined in the paper are given a Routley-Meyer ternary relational semantics.

The logic DHb is the result of extending Sylvan and Plumwood’s minimal De Morgan logic BM with a dual intuitionistic negation of the type Sylvan defined for the extension CCω of da Costa’s paraconsistent logic Cω. We provide Routley–Meyer ternary relational semantics with a set of designated points for DHb and a wealth of its extensions included in G3DH, the expansion of G3+ with a dual intuitionistic negation of the kind considered by Sylvan (G3+ is the positive fragment of Gödelian 3-valued logic G3). All logics in the paper are paraconsistent.

As it is well known, in the forties of the past century, Curry proved that in any logic S closed under Modus Ponens, uniform substitution of propositional variables and the Contraction Law, the naïve Comprehension axiom trivializes S in the sense that all propositions are derivable in S plus CA. Not less known is the fact that, ever since Curry published his proof, theses and rules weaker than W have been shown to cause the same effect as W causes. Among these, the Contraction rule or the Modus Ponens axiom, for example, are to be noted. But, moreover, as Brady has proved, even the Generalized Modus Ponens axiom or the Generalized Contraction rule give rise to “Curry’s Paradox” under the same circumstances as W does. In some previous work by us, “weak relevant model structures” are defined on “weak relevant matrices” by generalizing Brady’s model structure MCL built upon Meyer’s Crystal matrix CL. We have proved that wr-ms only verify logics with the “depth relevance condition”. The aim of this paper is to show how to falsify gMPa and gRW in certain wr-ms. In particular, it will be shown that gMPa is falisfied in any wr-ms and gRW in any wr-ms verifying Routley and Meyer’s basic positive logic B+.

Minimal Negation is defined within the basic positive relevance logic in the relational ternary semantics: B+. Thus, by defining a number of subminimal negations in the B+ context, principles of weak negation are shown to be isolable. Complete ternary semantics are offered for minimal negation in B+. Certain forms of reductio are conjectured to be undefinable (in ternary frames) without extending the positive logic. Complete semantics for such kinds of reductio in a properly extended positive logic are offered.