In this paper, we present a prenex form theorem for a version of Independence Friendly logic, a logic with imperfect information. Lifting classical results to such logics turns out not to be straightforward, because independence conditions make the formulas sensitive to signalling phenomena. In particular, nested quantification over the same variable is shown to cause problems. For instance, renaming of bound variables may change the interpretations of a formula, there are only restricted quantifier extraction theorems, and slashed connectives cannot be (...) so easily removed. Thus we correct some claims from Hintikka [8], Caicedo & Krynicki [3] and Hodges [11]. We refine definitions, in particular the notion of equivalence, and sharpen preconditions, allowing us to restore those claims, including the prenex form theorem of Caicedo & Krynicki [3], and, as a side result, we obtain an application to Skolem forms of classical formulas. It is a known fact that a complete calculus for IF-logic is impossible, but with our results we establish several quantifier rules that form a partial calculus of equivalence for a general version of IF-logic reflecting general properties of information flow in games. (shrink)

We prove strong completeness of the □-version and the ◊-version of a Gödel modal logic based on Kripke models where propositions at each world and the accessibility relation are both infinitely valued in the standard Gödel algebra [0,1]. Some asymmetries are revealed: validity in the first logic is reducible to the class of frames having two-valued accessibility relation and this logic does not enjoy the finite model property, while validity in the second logic requires truly fuzzy accessibility relations and this (...) logic has the finite model property. Analogues of the classical modal systems D, T, S4 and S5 are considered also, and the completeness results are extended to languages enriched with a discrete well ordered set of truth constants. (shrink)

It is shown that axiomatic extensions of intuitionistic propositional calculus defining univocally new connectives, including those proposed by Gabbay, are strongly complete with respect to valuations in Heyting algebras with additional operations. In all cases, the double negation of such a connective is equivalent to a formula of intuitionistic calculus. Thus, under the excluded third law it collapses to a classical formula, showing that this condition in Gabbay's definition is redundant. Moreover, such connectives can not be interpreted in all Heyting (...) algebras, unless they are already equivalent to a formula of intuitionistic calculus. These facts relativize to connectives over intermediate logics. In particular, the intermediate logic with values in the chain of length n may be "completed" conservatively by adding a single unary connective, so that the expanded system does not allow further axiomatic extensions by new connectives. (shrink)

We study a class of [0,1][0,1]-valued logics. The main result of the paper is a maximality theorem that characterizes these logics in terms of a model-theoretic property, namely, an extension of the omitting types theorem to uncountable languages.

It is shown that axiomatic extensions of intuitionistic propositional calculus defining univocally new connectives, including those proposed by Gabbay, are strongly complete with respect to valuations in Heyting algebras with additional operations. In all cases, the double negation of such a connective is equivalent to a formula of intuitionistic calculus. Thus, under the excluded third law it collapses to a classical formula, showing that this condition in Gabbay's definition is redundant. Moreover, such connectives can not be interpreted in all Heyting (...) algebras, unless they are already equivalent to a formula of intuitionistic calculus. These facts relativize to connectives over intermediate logics. In particular, the intermediate logic with values in the chain of length n may be "completed" conservatively by adding a single unary connective, so that the expanded system does not allow further axiomatic extensions by new connectives. (shrink)

An extensions by new axioms and rules of an algebraizable logic in the sense of Blok and Pigozzi is not necessarily algebraizable if it involves new connective symbols, or it may be algebraizable in an essentially different way than the original logic. However, extension whose axioms and rules define implicitly the new connectives are algebraizable, via the same equivalence formulas and defining equations of the original logic, by enriched algebras of its equivalente quasivariety semantics. For certain strongly algebraizable logics, all (...) connectives defined implicitly by axiomatic extensions of the logic are explicitly definable. (shrink)

An extensions by new axioms and rules of an algebraizable logic in the sense of Blok and Pigozzi is not necessarily algebraizable if it involves new connective symbols, or it may be algebraizable in an essentially different way than the original logic. However, extension whose axioms and rules define implicitly the new connectives are algebraizable, via the same equivalence formulas and defining equations of the original logic, by enriched algebras of its equivalente quasivariety semantics. For certain strongly algebraizable logics, all (...) connectives defined implicitly by axiomatic extensions of the logic are explicitly definable. (shrink)

Lindström’s theorem obviously fails as a characterization of first-order logic without identity ( $\mathcal {L}_{\omega \omega }^{-} $ ). In this note, we provide a fix: we show that $\mathcal {L}_{\omega \omega }^{-} $ is a maximal abstract logic satisfying a weak form of the isomorphism property (suitable for identity-free languages and studied in [11]), the Löwenheim–Skolem property, and compactness. Furthermore, we show that compactness can be replaced by being recursively enumerable for validity under certain conditions. In the proofs, we (...) use a form of strong upwards Löwenheim–Skolem theorem not available in the framework with identity. (shrink)

We generalize a theorem of Mundici relating compactness of a regular logic L to a strong form of normality of the associated spaces of models. Moreover, it is shown that compactness is in fact equivalent to ordinary normality of the model spaces when L has uniform reduction for infinite disjoint sums of structures. Some applications follow. For example, a countably generated logic is countably compact if and only if every clopen class in the model spaces is elementary. The model spaces (...) of L are not normal for vocabularies of uncountable power ωα. It also follows that first-order logic is the only finite-dependence logic having normal model spaces and satisfying at the same time the downward Löwenheim-Skolem theorem and uniform reduction for pairs. (shrink)

It is shown that Friedman's problem, whether there exists a proper extension of first order logic satisfying the compactness and interpolation theorems, has extremely simple positive solutions if one considers extensions by generalized (finitary) propositional connectives. This does not solve, however, the problem of whether such extensions exist which are also closed under relativization of formulas.

Este trabajo se encuadra dentro de una nueva visión de la lógica de Leibniz, la cual pretende mostrar que sus escritos fueron ricos no solamente en proyectos ambiciosos sino también en desarrollos lógico-matematicos concretos. Se demuestra que su “Caracteristica Numerica” que asigna pares de números a las proposiciones categóricas es una semántiea para la cual la silogística aristotélica es correcta y completa, y que el sistema algebraico presentado en Fundamentos de un Cálculo Lógico es una lógica algebraica similar a la (...) de Boole.This work is a contribution to a new view of Leibniz’s logic, pretending to show that his writings were not only rich in projects, but also in concrete logico-mathematical developments. We prove that his “Numerical Characteristic” assigning pairs of numbers to terms of categorical propositions, is a complete and correct semantics for aristotelian syllogistic, and the algebraic system presented in Fundamentals of Logical Calculus is essentially a complete version of boolean algebraic logic. (shrink)

In any model theoretic logic, Beth’s definability property together with Feferman-Vaught’s uniform reduction property for pairs imply recursive compactness, and the existence of models with infinitely many automorphisms for sentences having infinite models. The stronger Craig’s interpolation property plus the uniform reduction property for pairs yield a recursive version of Ehrenfeucht-Mostowski’s theorem. Adding compactness, we obtain the full version of this theorem. Various combinations of definability and uniform reduction relative to other logics yield corresponding results on the existence of non-rigid (...) models. (shrink)

We introduce a natural class of quantifiersTh containing all monadic type quantifiers, all quantifiers for linear orders, quantifiers for isomorphism, Ramsey type quantifiers, and plenty more, showing that no sublogic ofL ωω (Th) or countably compact regular sublogic ofL ∞ω (Th), properly extendingL ωω , satisfies the uniform reduction property for quotients. As a consequence, none of these logics satisfies eitherΔ-interpolation or Beth's definability theorem when closed under relativizations. We also show the failure of both properties for any sublogic ofL (...) ∞ω (Th) in which Chang's quantifier or some cardinality quantifierQ α, with α≧1, is definable. (shrink)

"Contains a balanced account of recent advances in set theory, model theory, algebraic logic, and proof theory, originally presented at the Tenth Latin American Symposium on Mathematical Logic held in Bogata, Columbia. Traces new interactions among logic, mathematics, and computer science. Features original research from over 30 well-known experts worldwide.".

En enero de 1974 Zubiri dio un breve curso en la Sociedad de Estudios y Publicaciones de Madrid sobre el tema Tres dimensiones del ser humano: individual, social e histórica. Meses después publicó la última de esas lecciones bajo el título de La dimensión histórica del ser humano. El presente volumen recoge el texto de las tres conferencias, más la versión escrita de la última de ellas. La tesis que Zubiri desarrolla en estas lecciones es que el ser humano es (...) a la vez y necesariamente individual, social e histórico, y que estas dimensiones vienen exigidas por su propia realidad específica, que es pluralizante, continuante y prospectiva. (shrink)

The past decade has seen a burgeoning of scholarly interest in conscientious objection in healthcare. While the literature to date has focused primarily on individual healthcare practitioners who object to participation in morally controversial procedures, in this article we consider a different albeit related issue, namely, whether publicly funded healthcare institutions should be required to provide morally controversial services such as abortions, emergency contraception, voluntary sterilizations, and voluntary euthanasia. Substantive debates about institutional responsibility have remained largely at the level of (...) first-order ethical debate over medical practices which institutions have refused to offer; in this article, we argue that more fundamental questions about the metaphysics of institutions provide a neglected avenue for understanding the basis of institutional conscientious objection. To do so, we articulate a metaphysical model of institutional conscience, and consider three well-known arguments for undermining institutional conscientious objection in light of this model. We show how our metaphysical analysis of institutions creates difficulties for justifying sanctions on institutions that conscientiously object. Thus, we argue, questions about the metaphysics of institutions are deserving of serious attention from both critics and defenders of institutional conscientious objection. (shrink)

Many if not most sperm donors in the early years of IVF donated under conditions of anonymity. There is, however, a growing awareness of the ethical cost of withholding identifying parental information from donor children. Today, anonymous donation is illegal in many jurisdictions, and some jurisdictions have gone as far as retrospectively invalidating contracts whereby donors were guaranteed anonymity. This article provides a critical evaluation of the ethics and legality of anonymous donation. We defend Australian and British legislation that has (...) outlawed donor anonymity, and we argue for the establishment of a central registry that provides donor children with the ability to easily and reliably access identifying information about their donor parents. (shrink)

LA ÉTICA DE EDMUND HUSSERL trata de recoger la doctrina ética de Edmund Husserl (1859–1938), con la idea de dar a conocer el contenido moral que encierra la rica obra husserliana. Además, constituye una buena introducción a quienes se aproximan a la filosofía del fundador de la fenomenología, y un buen servicio incluso para quienes ya conocen su pensamiento solamente en relación con la teoría del conocimiento o con la lógica. Concretamente, la ética de Husserl —en un cuidado y ajustado (...) equilibrio entre el papel de la razón, el de la voluntad y el del sentimiento— ofrece la posibilidad de rescatar la afectividad del sentimentalismo ciego e instintivo sin caer en el extremo contrario del racionalismo inhumano; enseña cómo tomar libre y realmente nuestra vida en nuestras propias manos y dirigirnos a un ideal personal; muestra cómo comportarnos con nuestros semejantes reconociéndolos en su verdadera dignidad, y cómo podemos ayudarnos los unos a los otros. Y para todo ello, en fin, nos proporciona el suelo seguro de la experiencia interna evidente, resistente a toda crítica procedente de la ciencia empírica o del cinismo posmoderno. La exposición del discurso ético pasa necesariamente por meandros psicológicos y antropológicos, como no podía ser de otra manera. De modo que la doctrina moral de Husserl desvela asimismo e inseparablemente un sustancioso contenido psicológico y antropológico. Por otra parte, se ha preferido mantener en general el estilo fenomenológico del autor, esto es, procediendo analíticamente en sucesivos niveles de profundidad. (shrink)

Giubiliniet aloffer some helpful reflections on the conscientious provision of medical care and whether and in what circumstances professional associations ought to support the conscientious provision of abortion in circumstances where abortion is banned or heavily restricted. I have several reservations, however, about the argument developed in the article. First, the essay makes questionable use of the case of Savita Halappanavar to justify its central argument about conscientious provision. Second, there is an apparent inconsistency between this article and the authors’ (...) statements elsewhere about the conscientious refusal of care. Third, there are risks that attend to professional associations supporting practitioners who break the law, and yet Giubiliniet aldo not give sufficient attention to this. This response will briefly discuss these three concerns. (shrink)

Cet ouvrage confronte les pensées de Frege à Husserl à propos du psychologisme et pose la question de savoir comment ces deux penseurs ont pu à la fois lutter contre l'influence grandissante de ce courant et parvenir à une telle incompréhension mutuelle. L'auteur cherche à montrer comment la différence de perspective sur les sciences mathématiques les a conduit à s'opposer sur le statut de la logique et de son rapport à la pensée. S'ils s'accordent pour reconnaître que l'arithmétique implique le (...) recours à la pensée, l'un parvient à une logique symbolique, et l'autre à une logique transcendantale, deux perspectives qui supposent des idées très différentes de ce que signifie " penser ". Quels rapports la pensée entretient-elle avec la représentation et avec les symboles? L'esprit qui pense, aussi bien dans les mathématiques que dans la logique, n'est - il qu'un simple " automate " qui développe les conséquences de la vérité ou est-il responsable des lois qu'il découvre? Par-delà l'étude des divergences sur le statut de la logique, de la psychologie et de leur rapport aux mathématiques, il s'agit d'explorer une divergence plus profonde sur le rapport de la pensée à la nécessité et à la liberté. (shrink)

Este libro es parte de la colección e-Libro en BiblioBoard.

Through skepticism and dialectics, German idealism transformed our understanding of the world and ourselves. This book shows how Kant, Fichte, Schelling, and Hegel revolutionized reason and made possible the critical reversal of values present in 20th-century philosophy.

El adiós a las escuelas -- El capitalismo, motor de la modernidad tardía.

**" CHAPTER * HUMAN NATURE In May, at the time when the French Civil Code was being drafted, one of the orators of the Tribunat, in seeking to justify the ...

Sistemas jurídicos -- Enunciados jurídicos preinterpretivos -- Enunciados jurídicos interpretivos.

En un diálogo continuo con la tradición filosófica, Zubiri va página a página describiendo el acto de la intelección humana y desmontando el cúmulo de hipótesis y teorías que subyacen al llamado «problema del conocimiento». Zubiri consigue descubrir, mediante el recurso a un procedimiento puramente descriptivo, en qué consiste el acto humano por excelencia, la intelección. La intelección humana, dice Zubiri, no es una síntesis trascendental, sino algo más simple a la vez que más radical, la mera actualización de lo (...) real en la inteligencia sentiente. (shrink)

Desde hace ya bastante tiempo existe una tendencia a afirmar que el derecho o las normas de diferente tipo no son adecuadas o aplicables para las diferentes nuevas tecnologías que van apareciendo de forma continua. Este trabajo intentará dar la vuelta a ese razonamiento y, centrándose en la inteligencia artificial, tratará de plantear criterios adecuados para que esa tecnología y muchas otras sean desarrolladas y aplicadas de forma adecuada a los derechos fundamentales en general y a la privacidad en particular. (...) Dentro de esos criterios se analizará lo que debe aportar la explicabilidad de la tecnología mencionada y se profundizará en algunos conceptos adicionales como la posibilidad y la necesidad de controlar y de auditar sistemas de inteligencia artificial. Para realizar la mencionada profundización se recurrirá a lo que se conoce como objetivos de protección y a los principios de la ciberética, incluyendo una referencia especial a la sostenibilidad y a la resiliencia de este tipo de sistemas. (shrink)

In the absence of Woodin cardinals, fine structural inner models for mild large cardinal hypotheses admit forcing extensions where bounded forcing axioms hold and yet the reals are projectively well-ordered.