This article presents a parametrized functional interpretation. Depending on the choice of two parameters one obtains well-known functional interpretations such as Gödel's Dialectica interpretation, Diller-Nahm's variant of the Dialectica interpretation, Kohlenbach's monotone interpretations, Kreisel's modified realizability, and Stein's family of functional interpretations. A functional interpretation consists of a formula interpretation and a soundness proof. I show that all these interpretations differ only on two design choices: first, on the number of counterexamples for A which became witnesses for ¬A when defining (...) the formula interpretation and, second, the inductive information about the witnesses of A which is considered in the proof of soundness. Sufficient conditions on the parameters are also given which ensure the soundness of the resulting functional interpretation. The relation between the parametrized interpretation and the recent bounded functional interpretation is also discussed. (shrink)

La presente investigación tuvo por objetivo analizar los usos del discurso institucional de universidades chilenas autodefinidas como complejas en relación a la organización del conocimiento e iniciativas inter-transdisciplinarias relevantes informadas a nivel de estructuras estáticas y noticias en sitios web oficiales de cada una de ellas. En este contexto y a través de un Análisis Crítico del Discurso, se indaga en el despliegue de estrategias comunicativas, la producción y difusión del discurso institucional, como asimismo, su exposición y disposición en las (...) páginas web. Desde esta base, se contribuye con información cualitativa a la discusión en torno a los formatos y dispositivos de comunicación social referidos a las nociones de inter y transdisciplina en el contexto de la educación superior en el país. Los resultados dan cuenta de la emergencia, centralidad y valor comunicacional de la prospectiva inter y transdisciplinaria en el contexto universitario chileno, no obstante, también evidencian las condicionantes epistemológicas y metodológicas para su despliegue organizacional crítico y sostenible. (shrink)

Resumen: La presente investigación tuvo por objetivo analizar los usos del discurso institucional de universidades chilenas autodefinidas como complejas en relación con la organización del conocimiento e iniciativas intertransdisciplinarias relevantes informadas a nivel de estructuras estáticas y noticias en sitios web oficiales de cada una de ellas. En este contexto y mediante un Análisis Crítico del Discurso, se indaga en el despliegue de estrategias comunicativas, la producción y difusión del discurso institucional, como asimismo, su exposición y disposición en las páginas (...) web. Desde esta base se contribuye con información cualitativa a la discusión en torno a los formatos y dispositivos de comunicación social referidos a las nociones de inter y transdisciplina en el contexto de la educación superior en el país. Los resultados dan cuenta de la emergencia, centralidad y valor comunicacional de la prospectiva inter y transdisciplinaria en el contexto universitario chileno, no obstante, también evidencian las condicionantes epistemológicas y metodológicas para su despliegue organizacional crítico y sostenible.: The following investigation had as an objective to analyse the usages of the Institutional Discourse from Chilean universities self-described as complex, in relation to the Knowledge Organization and relevant inter-disciplinaries initiatives that are informed at the level of static structures and pieces of news published on each official website. In this context, and, through a Critical Discourse Analysis, the communicative strategies deployment is explored, as well as the production and broadcasting of their institutional discourse. Likewise, their exposure and disposal on web pages. On this basis, the qualitative information is contributed to the discussion around the formats and social communication devices, referred to the concepts of inter and trans-disciplines in the context of higher education in the nation. The results, reflect the emergency, centrality and communicational value of the inter and trans-disciplinary prospective in the Chilean university context. However, the epistemological and methodological conditions are evidenced for its organizational, critical, and sustainable deployment. (shrink)

In this paper, we present another case study in the general project of proof mining which means the logical analysis of prima facie non-effective proofs with the aim of extracting new computationally relevant data. We use techniques based on monotone functional interpretation developed in Kohlenbach , Oxford University Press, Oxford, 1996, pp. 225–260) to analyze Cheney's simplification 189) of Jackson's original proof 320) of the uniqueness of the best L1-approximation of continuous functions fC[0,1] by polynomials pPn of degree n. Cheney's (...) proof is non-effective in the sense that it is based on classical logic and on the non-computational principle WKL . The result of our analysis provides the first effective uniform modulus of uniqueness . Moreover, the extracted modulus has the optimal ε-dependency as follows from Kroó 331). The paper also describes how the uniform modulus of uniqueness can be used to compute the best L1-approximations of a fixed fC[0,1] with arbitrary precision. The second author uses this result to give a complexity upper bound on the computation of the best L1-approximation in Oliva 66–77). (shrink)

Schwichtenberg showed that the System T definable functionals are closed under a rule-like version Spector’s bar recursion of lowest type levels 0 and 1. More precisely, if the functional Y which controls the stopping condition of Spector’s bar recursor is T-definable, then the corresponding bar recursion of type levels 0 and 1 is already T-definable. Schwichtenberg’s original proof, however, relies on a detour through Tait’s infinitary terms and the correspondence between ordinal recursion for α < ε₀ and primitive recursion over (...) finite types. This detour makes it hard to calculate on given concrete system T input, what the corresponding system T output would look like. In this paper we present an alternative (more direct) proof based on an explicit construction which we prove correct via a suitably defined logical relation. We show through an example how this gives a straightforward mechanism for converting bar recursive definitions into T-definitions under the conditions of Schwichtenberg’s theorem. Finally, with the explicit construction we can also easily state a sharper result: if Y is in the fragment Tᵢ then terms built from BR^ℕ,σ for this particular Y are definable in the fragment T_i+max{1,level(σ)}+2. (shrink)

This article presents an analysis of Gödel's dialectica interpretation via a refinement of intuitionistic logic known as linear logic. Linear logic comes naturally into the picture once one observes that the structural rule of contraction is the main cause of the lack of symmetry in Gödel's interpretation. We use the fact that the dialectica interpretation of intuitionistic logic can be viewed as a composition of Girard's embedding of intuitionistic logic into linear logic followed by de Paiva's dialectica interpretation of linear (...) logic. We then investigate the various properties of the dialectica interpretation, such as the characterisation theorem, and variants of Gödel's interpretation within the linear logic context. The role of contraction in extensions to classical logic, arithmetic and analysis is also discussed. (shrink)

We present a new functional interpretation, based on a novel assignment of formulas. In contrast with Gödel’s functional “Dialectica” interpretation, the new interpretation does not care for precise witnesses of existential statements, but only for bounds for them. New principles are supported by our interpretation, including the FAN theorem, weak König’s lemma and the lesser limited principle of omniscience. Conspicuous among these principles are also refutations of some laws of classical logic. Notwithstanding, we end up discussing some applications of the (...) new interpretation to theories of classical arithmetic and analysis. (shrink)

We show that Spector's “restricted” form of bar recursion is sufficient (over system T) to define Spector's search functional. This new result is then used to show that Spector's restricted form of bar recursion is in fact as general as the supposedly more general form of bar recursion. Given that these two forms of bar recursion correspond to the (explicitly controlled) iterated products of selection function and quantifiers, it follows that this iterated product of selection functions is T‐equivalent to the (...) corresponding iterated product of quantifiers. (shrink)

This article presents an analysis of Gödel's dialectica interpretation via a refinement of intuitionistic logic known as linear logic. Linear logic comes naturally into the picture once one observes that the structural rule of contraction is the main cause of the lack of symmetry in Gödel's interpretation. We use the fact that the dialectica interpretation of intuitionistic logic can be viewed as a composition of Girard's embedding of intuitionistic logic into linear logic followed by de Paiva's dialectica interpretation of linear (...) logic. We then investigate the various properties of the dialectica interpretation, such as the characterisation theorem, and variants of Gödel's interpretation within the linear logic context. The role of contraction in extensions to classical logic, arithmetic and analysis is also discussed. (shrink)

It is well known that for a given continuous function f : [0, 1] → ℝ and a number n there exists a unique polynomial pn ∈ Pn which best L1-approximates f. We establish the first upper bound on the complexity of the sequence n∈ ℕ, assuming f is polynomial-time computable. Our complexity analysis makes essential use of the modulus of uniqueness for L1-approximation presented in [13].

We show that the types of the witnesses in the Herbrand functional interpretation can be simplified, avoiding the use of “sets of functionals” in the interpretation of implication and universal quantification. This is done by presenting an alternative formulation of the Herbrand functional interpretation, which we show to be equivalent to the original presentation. As a result of this investigation we also strengthen the monotonicity property of the original presentation, and prove a monotonicity property for our alternative definition.

In this article we study applications of the bounded functional interpretation to theories of feasible arithmetic and analysis. The main results show that the novel interpretation is sound for considerable generalizations of weak König’s Lemma, even in the presence of very weak induction. Moreover, when this is combined with Cook and Urquhart’s variant of the functional interpretation, one obtains effective versions of conservation results regarding weak König’s Lemma which have been so far only obtained non-constructively.

This paper presents an algebraic framework for investigating proposed translations of classical logic into intuitionistic logic, such as the four negative translations introduced by Kolmogorov, Gödel, Gentzen and Glivenko. We view these asvariant semanticsand present a semantic formulation of Troelstra’s syntactic criteria for a satisfactory negative translation. We consider how each of the above-mentioned translation schemes behaves on two generalisations of Heyting algebras: bounded pocrims and bounded hoops. When a translation fails for a particular class of algebras, we demonstrate that (...) failure via specific finite examples. Using these, we prove that the syntactic version of these translations will fail to satisfy Troelstra’s criteria in the corresponding substructural logical setting. (shrink)

We show how two iterated products of selection functions can both be used in conjunction with systemTto interpret, via the dialectica interpretation and modified realizability, full classical analysis. We also show that one iterated product is equivalent over systemTto Spector’s bar recursion, whereas the other isT-equivalent to modified bar recursion. Modified bar recursion itself is shown to arise directly from the iteration of a different binary product of ‘skewed’ selection functions. Iterations of the dependent binary products are also considered but (...) in all cases are shown to beT-equivalent to the iteration of the simple products. (shrink)

This article systematically investigates so-called “truth variants” of several functional interpretations. We start by showing a close relation between two variants of modified realizability, namely modified realizability with truth and q-modified realizability. Both variants are shown tobe derived from a single “functional interpretation with truth” of intuitionistic linear logic. This analysis suggests that several functional interpretations have truth and q-variants. These variants, however, require a more involved modification than the ones previously considered. Following this lead we present truth and q-variants (...) of the Diller-Nahm interpretation, the bounded modified realizability and the bounded functional interpretation. (shrink)

We present a refinement ofthe bounded modified realizability which provides both upper and lower bounds for witnesses. Our interpretation is based on a generalisation of Howard/Bezem's notion of strong majorizability. We show how the bounded modified realizability coincides with our interpretation in the case when least elements exist . The new interpretation, however, permits the extraction of more accurate bounds, and provides an ideal setting for dealing directly with data types whose natural ordering is not well-founded.

The Perfection of the Universe gives an account of the idea of the universe and its perfection in Aquinas's philosophy, but at the same time it provides an example of how a cosmology can be developed in a teleological framework. Although this is the cosmology of one who was first and foremost a theologian, the book tries to show how it was articulated philosophically and in relation to a particular model of the universe. As a contribution to the history of (...) philosophy, and Thomistic studies in particular, it seeks to draw more attention to Aquinas's view of the world, which has been relatively neglected in favor of emphasis on his theory of knowledge and theory of being, and at the same time to show how it is integral to his very understanding of being. The book thereby brings out a dimension of rationality in Aquinas's philosophy that is often ignored, especially as it concerns creation as a whole and what Aquinas refers to as convenientia in this whole. The systematic nature of Aquinas's conception of the universe is highlighted by the author's attempt to reconstruct the movement of his thought. Thus Oliva Blanchette focuses not just on the universe or on perfection but on the perfection of the universe as a unified idea that recurs frequently in both the philosophy and the theology of Aquinas and that has its own philosophical dynamic both as a logic and as an actuality. In doing so, he endeavors to correct misconceptions about Aquinas's idea of the universe, such as that found in Lovejoy's Great Chain of Being, and to show how the idea stands up philosophically even while being connected with a scientific model of the universe now viewed as obsolete. (shrink)

Resumen En este trabajo se analizan las pautas de elección entre los cuatro paradigmas gramaticales de segunda persona del español peninsular (los prototípicos, representados por los pronombres tú y vosotros, y los desplazados, por usted y ustedes), cuando se usan para indexar a interlocutores específicos, en un corpus de discurso radiofónico de la ciudad española de Salamanca. Se plantea la hipótesis de que los fundamentos cognitivos de las personas gramaticales se proyectan en su potencial sociopragmático como recursos para la configuración (...) de identidades contextuales. Tras clasificar a los participantes del corpus en cuatro tipos de identidad socioprofesional recurrentes en la comunicación radiofónica (locutores, personajes públicos, políticos y hablantes particulares), se calculan las frecuencias con que cada tipo dirige y recibe cada tratamiento de segunda persona. El análisis cuantitativo constituye un punto de partida para la observación cualitativa de los contextos de uso. Tras este se concluye que la elección entre las cuatro formas de segunda persona combina los parámetros sociopragmáticos de cercanía-distancia (que afecta a la elección entre formas prototípicas y desplazadas) e individualidad-grupalidad (que afecta a la elección entre formas singulares y plurales). Tales parámetros remiten, a su vez, al continuum discursivo-cognitivo entre la subjetividad y la objetividad. (shrink)

The purpose of this article is to analyze Spanish first-person plural subjects as a cognitively grounded grammatical choice serving various discursive functions. Both the expressed and omitted variants of the subject will be considered, even if omission is by far the more frequent choice in Spanish and the more communicatively versatile one. The particularly vague reference of omitted nosotros ‘we’ – always involving an extension of the self towards a wider notional scope – results in a remarkable variety of possible (...) contextual projections. It can be used to signal speaker identities as well as manage interpersonal relationships through the iconic suggestion of viewpoint coincidence. First-person plural clauses are quantitatively and qualitatively investigated across two corpora of contemporary Spanish comprising a variety of spoken and written genres. It is found that, aside from the basic distinction between hearer-exclusive and hearer-inclusive first persons, a third, intermediate variant can be considered, that of empathic hearer-exclusive uses. These are typical of interactions where involvement of the audience is sought even if they are not referentially included in the subject, as is usual in some varieties of spoken mass-media discourse. Each one of the referential variants is used with different frequencies and contextual repercussions, depending on the socio-functional demands and goals of particular textual genres. (shrink)

Este artículo se adentra en los temas y tópicos vitales de la obra literaria de Eliacer Cansino, escritor dedicado a la literatura juvenil, e invita a reflexionar sobre cómo su lectura puede desarrollar el pensamiento crítico de los jóvenes lectores del siglo XXI. Para abordar esta investigación, se ha recurrido a una metodología de corte cualitativo, con especial atención a la narrativa biográfica. De esta manera, dado que literatura y realidad constituyen dos caras de una moneda al forjar lectores, se (...) analizó el perimundo literario de Eliacer Cansino. Los resultados justifican que la lectura de la obra de este autor es un referente literario para el desarrollo del pensamiento crítico desde la experiencia lectora de los adolescentes. (shrink)

This work aims to reopen the fundamental question of being. It raises the question of being after the natural sciences and phenomenology have run their course and pursues it according to a method that is properly metaphysical as well as critical.

This Article defines four distinct conceptions of cruelty found in underdeveloped form in domestic and international criminal law sources. The definition is analytical, focusing on the types of agency, victimization, causality, and values in each conception of cruelty. But no definition of cruelty will do justice to its object until complemented by the kind of understanding practical reason provides of the implications of the phenomenon of cruelty. -/- No one should be neutral in relation to cruelty. Eminently, cruelty in criminal (...) law, a human-created phenomenon, vigorously calls for responses in the form of preventive and corrective action on the part of private and public actors. It is in this sense that cruelty is a problem of practical reason, one of action preoccupied with its legal or moral obligations, rational grounds, value commitments, and actual consequences. -/- However, the connection between conceptions of cruelty and the implications practical reason can draw from the correct application of a conception of cruelty to phenomena in the world remains too detached to be able to capture and explain people's actual experiences both of seeing cruelty in the world and of confronting the question of what to do about cruelty and how to address its cultural and institutional aspects. Something is missing. -/- What is missing is the integration of conceptions of cruelty and the practical reason implications of detecting cruelty in the world into normative models which operate as meaning matrixes for cognition, meaning, and action. This Article undertakes this explanatory task through an exercise of reconstructing seminal philosophical ideas about cruelty. The result is that the four conceptions of cruelty are placed within three distinct normative models, which ultimately render intelligible legal conceptions of cruelty and legal reactions to it. (shrink)