In this paper we show that, in Gentzen systems, there is a close relation between two of the main characters in algebraic logic and proof theory respectively: protoalgebraicity and the cut rule. We give certain conditions under which a Gentzen system is protoalgebraic if and only if it possesses the cut rule. To obtain this equivalence, we limit our discussion to what we call regular sequent calculi, which are those comprising some of the structural rules and some logical rules, in (...) a sense we make precise. We note that this restricted set of rules includes all the usual rules in the literature. We also stress the difference between the case of two-sided sequents and the case of many-sided sequents, in which more conditions are needed. (shrink)

ABSTRACT In this paper we study consequence relations on the set of many sided sequents over a propositional language. We deal with the consequence relations axiomatized by the sequent calculi defined in [2] and associated with arbitrary finite algebras. These consequence relations are examples of what we call Gentzen systems. We define a semantics for these systems and prove a Strong Completeness Theorem, which is an extension of the Completeness Theorem for provable sequents stated in [2]. For the special case (...) of the finite linear MV-algebras, the Strong Completeness Theorem was proved in [10], as a consequence of McNaughton's Theorem. The main tool to prove this result for arbitrary algebras is the deduction-detachment theorem for Gentzen systems. (shrink)

Łukasiewicz’s infinite-valued logic is commonly defined as the set of formulas that take the value 1 under all evaluations in the Łukasiewicz algebra on the unit real interval. In the literature a deductive system axiomatized in a Hilbert style was associated to it, and was later shown to be semantically defined from Łukasiewicz algebra by using a “truth-preserving” scheme. This deductive system is algebraizable, non-selfextensional and does not satisfy the deduction theorem. In addition, there exists no Gentzen calculus fully adequate (...) for it. Another presentation of the same deductive system can be obtained from a substructural Gentzen calculus. In this paper we use the framework of abstract algebraic logic to study a different deductive system which uses the aforementioned algebra under a scheme of “preservation of degrees of truth”. We characterize the resulting deductive system in a natural way by using the lattice filters of Wajsberg algebras, and also by using a structural Gentzen calculus, which is shown to be fully adequate for it. This logic is an interesting example for the general theory: it is selfextensional, non-protoalgebraic, and satisfies a “graded” deduction theorem. Moreover, the Gentzen system is algebraizable. The first deductive system mentioned turns out to be the extension of the second by the rule of Modus Ponens. (shrink)

When considering m-sequents, it is always possible to obtain an m-sequent calculus VL for every m-valued logic (defined from an arbitrary finite algebra L of cardinality m) following for instance the works of the Vienna Group for Multiple-valued Logics. The Gentzen relations associated with the calculi VL are always finitely equivalential but might not be algebraizable. In this paper we associate an algebraizable 2-Gentzen relation with every sequent calculus VL in a uniform way, provided the original algebra L has a (...) reduct that is a distributive lattice or a pseudocomplemented distributive lattice. We also show that the sentential logic naturally associated with the provable sequents of this algebraizable Gentzen relation is the logic that preserves degrees of truth with respect to the original algebra (in contrast with the more common logic that merely preserves truth). Finally, for some particular logics we obtain 2-sequent calculi that axiomatize the algebraizable Gentzen relations obtained so far. (shrink)

The Gait Deviation Index is a multivariate measure of overall gait pathology based on 15 gait features derived from three-dimensional kinematic data. GDI aims at providing a comprehensive, easy to interpret, and clinically meaningful metric of overall gait function. It has been used as an outcome measure to study gait in several conditions: cerebral palsy, post-stroke hemiparetic gait, Duchenne muscular dystrophy, and Parkinson’s disease, among others. Nevertheless, its use in population with Spinal Cord Injury has not been studied yet. The (...) aim of the present study was to investigate the applicability of the GDI to SCI through the assessment of the relationship of the GDI with the Walking Index for Spinal Cord Injury II. 3D gait kinematics of 34 patients with incomplete SCI was obtained. Besides, 3D gait kinematics of a sample of 50 healthy volunteers was also gathered with Codamotion motion capture system. A total of 302 and 446 strides were collected. GDI was calculated for each stride and grouped for each WISCI II level. HV data were analyzed as an additional set. Normal distribution for each group was assessed with Kolmogorov-Smirnov tests. Afterward, ANOVA tests were performed between each pair of WISCI II levels to identify differences among groups. The results showed that the GDI was normally distributed across all WISCI II levels in both iSCI and HV groups. Furthermore, our results showed an increasing relationship between the GDI values and WISCI II levels in subjects with iSCI, but only discriminative in WISCI II levels 13, 19, and 20. The index successfully distinguished HV group from all the individuals with iSCI. Findings of this study indicated that the GDI is not an appropriate multivariate walking metric to represent the deviation of gait pattern in adult population with iSCI from a normal gait profile when it is compared with the levels of walking impairment described by the WISCI II. Future work should aim at defining and validating an overall gait index derived from 3D kinematic gait variables appropriate for SCI, additionally taking into account other walking ability outcome measures. (shrink)

Libro sumamente valioso. Tras sendas visiones de conjunto, muy logradas, del positivismo en América Latina en general y en Venezuela en particular, siguen capítulos sobre: Adolfo Ernst; Rafael Villavicencio; Vicente Marcano; Lasandro Alvarado; Luis Razetti; Guillermo Delgado Palacios; Luis López Méndez; José Gil Fortoul; Laureano Vallenilla Lanz; César Zumeta y Manuel Arcaya. Tiende a hacer comparaciones con otras manifestaciones del positivismo latinoamericano"--Handbook of Latin American Studies, v. 58.

The history of Spain in the 20th and 21st century provides us with many examples of mimetic rivalry: the permanent conflict between peoples who inhabit a common territory, seeking their identity through the affirmation of differences. In the never-ending reciprocities that occur throughout the decades, with ferocious feuding between the left and right wings, and disputes between nationalities, we appreciate how the Girardian theses shine some light on conflictive and at times bloody relationships that would be difficult to understand without (...) the illuminating mimetic theory and the scapegoat mechanism.Mimetic theory and the scapegoat mechanism, together with some of Girard's most innovative intuitions (passion for... (shrink)

In this text, the relationship between fallibilism and cognitive vulnerability is examined using Richard Rorty’s thinking as an example. First, some of Rorty’s central ideas are collected and commented on, especially the substitution of objectivity for solidarity, since it affects relevant issues of epistemology and of reflection on rationality. Next, the notions of fallibilism and cognitive vulnerability are examined, which will be connected to an existential dimension of vulnerability. Examples of all those things are also given from Rorty’s thinking and (...) it is highlighted that the author operates with both a negative and a positive sense of existential vulnerability. It is then stated that Rorty’s proposal implies pessimistic fallibilism and an excess of cognitive vulnerability. First, it is argued that the cause of this lies in the fact that his approach is imprisoned in what Richard Bernstein called Cartesian anxiety and secondly, this generates unwanted consequences for the Rortyan goals themselves to raise his ethnocentric proposal as a non-relativistic alternative to realism and authoritarianism. In this respect, it is maintained that the priority that Rorty attributes to solidarity is accompanied by the rejection of any notion of evidence. This produces a conceptual lacuna in the structure of his thought that makes it impossible to reflect philosophically on an epistemic activity (the activity of adducing or requesting evidence) that is a normal part of day-to-day conversational exchanges as important as controversies to determine the best option in each case. In response, we will argue that one can better work towards the achievement of Rortyan goals if we bear in mind that reasons based on solidarity do not replace and do not deactivate the value of epistemic reasons, although they do combine and reinforce each other. (shrink)

La noción butleriana de política como resistencia destaca por su originalidad, pues se dobla de performatividad y, al mismo tiempo, está abierta a las alianzas. En este texto se argumenta que su singularidad proviene del marco teórico materialista elaborado por Butler, pues ofrece una caracterización de los seres humanos que los vincula socialmente por su mutua dependencia y vulnerabilidad. Finalmente, comentaré tres aspectos confusos o problemáticos de la propuesta butleriana: el primero relacionado con la reconciliación, el segundo con la emancipación (...) y el tercero con la universalidad. (shrink)

Leucipo y los orígenes del atomismo griego.--La ética de Demócrito.--Escepticismo y atomismo en Metrodoro de Quíos.--Anaxarco de Abdera, la búsqueda de la felicidad.--Epicuro y la muerte.