Classical logic has proved inadequate in various areas of computer science, artificial intelligence, mathematics, philosopy and linguistics. This is an introduction to extensions of first-order logic, based on the principle that many-sorted logic (MSL) provides a unifying framework in which to place, for example, second-order logic, type theory, modal and dynamic logics and MSL itself. The aim is two fold: only one theorem-prover is needed; proofs of the metaproperties of the different existing calculi can be avoided by borrowing them from (...) MSL. To make the book accessible to readers from different disciplines, whilst maintaining precision, the author has supplied detailed step-by-step proofs, avoiding difficult arguments, and continually motivating the material with examples. Consequently this can be used as a reference, for self-teaching or for first-year graduate courses. (shrink)

This paper focuses on the evolution of the notion of completeness in contemporary logic. We discuss the differences between the notions of completeness of a theory, the completeness of a calculus, and the completeness of a logic in the light of Gödel's and Tarski's crucial contributions.We place special emphasis on understanding the differences in how these concepts were used then and now, as well as on the role they play in logic. Nevertheless, we can still observe a certain ambiguity in (...) the use of the close notions of completeness of a calculus and completeness of a logic. We analyze the state of the art under which Gödel's proof of completeness was developed, particularly when dealing with the decision problem for first-order logic. We believe that Gödel had to face the following dilemma: either semantics is decidable, in which case the completeness of the logic is trivial or, completeness is a critical property but in this case it cannot be obtained as a corollary of a previous decidability result. As far as first-order logic is concerned, our thesis is that the contemporary understanding of completeness of a calculus was born as a generalization of the concept of completeness of a theory. The last part of this study is devoted to Henkin's work concerning the generalization of his completeness proof to any logic from his initial work in type theory. (shrink)

Term Functor Logic is a term logic that recovers some important features of the traditional, Aristotelian logic; however, it turns out that it does not preserve all of the Aristotelian properties a valid inference should have insofar as the class of theorems of Term Functor Logic includes some inferences that may be considered irrelevant (e.g. ex falso, verum ad, and petitio principii). By following an Aristotelian or syllogistic notion of relevance, in this contribution we adapt a tableaux method for Term (...) Functor Logic in order to avoid irrelevance and we offer some sort of intuitive semantics in terms of traditional inferential situations (e.g. propter quid, quia, non causa ut causa, and non sequitur). (shrink)

This paper is dedicated to Alonzo Church, who died in August 1995 after a long life devoted to logic. To Church we owe lambda calculus, the thesis bearing his name and the solution to the Entscheidungsproblem.His well-known book Introduction to Mathematical LogicI, defined the subject matter of mathematical logic, the approach to be taken and the basic topics addressed. Church was the creator of the Journal of Symbolic Logicthe best-known journal of the area, which he edited for several decades This (...) paper is in three sections. The first is written in journalistic style:the story of the life of AlonzoChurch is told, including some of the many anecdotes I have collected from different sources. The secondpart is devoted to his work, but is far from being exhaustive. The last part is more original; in it I attempto show that Church’s great discovery was lambda calculus and that his remaining contributions weremainly inspired afterthoughts in the sense that most of his contributions as well as some of his pupils derivefrom that initial achievement. Included are Kleene’s Recursion Theory and the completeness proof ofHenkin. I have added an appendix in which is presented the typed lambda calculus and a proof of theundecidability of first-order logic. (shrink)

¿Cuántas imágenes hacen un poema? ¿Cuántas palabras se necesitan para construir un pensamiento? Vemos palabras de la misma manera que vemos árboles y casas, pero no vemos el bosque ni la ciudad como no vemos el poema y el pensamiento; lo verdaderamente esencial de ambos permanece oculto a nuestra simple y cotidiana mirada. El ojo y el oído se han acostumbrado a ver y a oír, es natural, es lo que se espera de dos órganos que están hechos para cumplir (...) esta misión. Pero ni vemos ni oímos más allá de los límites creados por la rutina de nuestra cotidianidad, hemos fijado a la superficie el paisaje y todo cuanto lo contiene: colores, olores, sonidos y texturas; vemos sin ver, oímos sin oír, olemos sin oler, tocamos sin sentir; esto es, sin diferenciar. Sin duda, establecer la diferencia, en cada acontecimiento particular, nos permitiría ir más allá de lo que simplemente se pone frente a nosotros; estamos tentados a nombrar esta diferencia como profundidad, pero mucho me temo que la profundidad también es una trampa, se trataría más bien de saber moverse entre ambas; sería algo así como dejarse sorprender por lo nuevo que hay en lo mismo, por lo imperceptible e invisible que existe en lo real y visible de la cotidianidad. (shrink)

El presente número de la Revista Escritos recoge algunos artículos cuyos resultados fueron presentados en el II Congreso Iberoamericano de Bioética e Investigación, llevado a cabo por la Universidad Pontificia Bolivariana en convenio con la Corporación Universitaria Lasallista, entre el 17 y 19 de agosto de 2016. Así mismo, se incluyen algunas de las ponencias leídas por los invitados centrales del evento.

In this paper we propose a tableaux method for the intermediate syllogistic of Peterson and Thompson by using the algebra of Sommers and Englebretsen. The result is an analytic tableaux method capable of modeling inference in basic, relational, and intermediate syllogistic.

The following dialogue is a product of the accessibility and attention of the master Raul Fornet-Betancourt (virtues that are rarely found at this level and height of thought which the philosophy of Fornet-Betancourt enjoys internationally) for students who like my self, are initiating the ac..

This article is a continuation of our promenade along the winding roads of identity, equality, nameability and completeness. We continue looking for a place where all these concepts converge. We assume that identity is a binary relation between objects while equality is a symbolic relation between terms. Identity plays a central role in logic and we have looked at it from two different points of view. In one case, identity is a notion which has to be defined and, in the (...) other case, identity is a notion used to define other logical concepts. In our previous paper, [16], we investigated whether identity can be introduced by definition arriving to the conclusion that only in full higher-order logic with standard semantics a reliable definition of identity is possible. In the present study we have moved to modal logic and realized that here we can distinguish in the formal language between two different equality symbols, the first one shall be interpreted as extensional genuine identity and only applies for objects, the second one applies for non rigid terms and has the characteristic of synonymy. We have also analyzed the hybrid modal logic where we can introduce rigid terms by definition and can express that two worlds are identical by using the nominals and the @ operator. We finish our paper in the kingdom of identity where the only primitives are lambda and equality. Here we show how other logical concepts can be defined in terms of the identity relation. We have found at the end of our walk a possible point of convergence in the logic Equational Hybrid Propositional Type Theory, [14] and [15]. (shrink)

In this paper I will examine Vandana Shiva’s ecofeminist thought with two goals: on the one hand, I will argue that her ecofeminism defines a vitalist materialist approach of feminine roots, since Shiva concedes an epistemological value to the practices and knowledge historically originated from the sustainability tasks that women have carried out. On the other hand and as a consequence, I will defend that she presents a political proposal, which entails a suggestive and radical redefinition of the traditional concept (...) of politics. Finally, I will try to show that the ability of attributing political meaning to experiences and actions of specific women allows for a change in perspective that Shiva accomplishes in an extremely fruitful double movement: the recognition of the existing and the affirmation of politics as present. (shrink)

¿En qué momento la palabra “crisis” se convirtió en un lugar común para interpretar el presente? ¿De qué vocabularios filosóficos disponemos y/o necesitamos crear para pensar el presente? En este artículo, mi objetivo consiste en plantear un diálogo entre el feminismo posthumano de Rosi Braidotti y la práctica teórica de la descolonización de Silvia Rivera Cusicanqui para elaborar una lectura afirmativa del presente a partir de la visión que estas pensadoras proponen sobre el tiempo, problemática común en la obra de (...) ambas autoras. Se trata de dos prespectivas contemporáneas de pensamiento y práctica política densas e imaginativas que, hasta el momento, no han sido puestas en relación. Establecer y desarrollar los términos conceptuales en que esta conversación puede ser relevante para el análisis crítico de nuestra contemporaneidad y para configurar una comprensión creativa de la temporalidad constituirá el principal aporte de este trabajo. Para abordar esta temática, en primer lugar, atenderé al análisis de la experiencia contemporánea del tiempo como la vivencia de una “crisis sin fin” y me preguntaré, con Myriam Revault, acerca de la capacidad explicativa del término “crisis” para dar cuenta del presente. En segundo lugar, expondré el estudio llevado a cabo por Braidotti sobre la experiencia temporal en el capitalismo actual y discutiré su noción de “sincronización”. Por último, explicaré las fuentes y repercusiones de la multiplicidad y heterogeneidad de los tiempos según la epistemología ch’ixi de Rivera Cusicanqui. (shrink)

Ficción y mito son algo más que lenguajes o formas narrativas, son estructuras arquitectónicas a través de las que se fija el pensamiento y su forma manifiesta de aparecer en la cotidianidad; este texto pretende rastrear la fundación de América Latina a través de la literatura en su forma de ficción y mito.

¿Estamos los seres humanos predeterminado o somos creadores de nuestro propio destino? La respuesta puede ser inmediata, algo parecido al texto de Erich Fromm que nos sirvió de epigrafe, o demorarse un poco en algunas consideraciones históricas que nos permitan hacer el recorrido de aquello que hemos pensado a lo largo de una historia en la cual no nos conformamos con simplemente ser o existir, sino que buscamos razones que expliquen esos modos de ser y de existir, intentando claridad sobre (...) nuestro ethos. (shrink)

In this paper we ask ourselves whether Szabolcsi’s numerical term logic is a fuzzy logic. Our answer is in the affirmative. In order to justify such a claim, we first expound some preliminaries that help us understand why the inclusion of fuzzy quantifiers is a sufficient condition for fuzziness. Then we present Szabolcsi’s logic, which includes said quantifiers.

Tras la llegada de los conquistadores españoles y durante los dos siglos del reinado de su monopolio, no se permitió el ingreso de extranjeros y la población permaneció distribuida en las regiones, en proporciones casi inversas a las actuales. Con la caída del régimen español y los avances del monopolio inglés, comenzó a desplazarse el centro territorial argentino desde el Noroeste hacia el Litoral y a producirse variaciones en la dinámica demográfica. El establecimiento del modelo agroexportador produjo una afluencia excepcional (...) de inmigrantes de ultramar, que generaron cambios vertiginosos en la estructura de la población. Asimismo, el fin del modelo agroexportador que provocó la abrupta interrupción del flujo inmigratorio de ultramar, generó nuevamente otro intenso cambio demográfico que incidió en la estructura poblacional hasta la actualidad. Este artículo se centra en el movimiento migratorio que produjo el modelo agroexportador, con el objetivo de analizar sus efectos en el ritmo de crecimiento de la población, en la distribución de las variables demográficas básicas —sexo y edad—, y en los cambios en la distribución espacial, siendo su fuente principal los censos nacionales de población realizados hasta la actualidad. (shrink)

Nietzsche’s experiences seem to be like mysticism. Several texts are examined:..

Given some links between Lyndon’s Interpolation Theorem, term distribution, and Sommers and Englebretsen’s logic, in this contribution we attempt to capture a sense of interpolation for Sommers and Englebretsen’s Term Functor Logic. In order to reach this goal we first expound the basics of Term Functor Logic, together with a sense of term distribution, and then we offer a proof of our main contribution.

En esta contribución proponemos una representación de un fragmento de la silogística estadística de Thompson usando la lógica de términos de Sommers. El resultado es una interpretación terminista de la silogística estadística.

Resumen En esta contribución ofrecemos una interpretación del pons asinorum que se basa en una lógica de términos contemporánea. Esto nos permite revitalizar la idea del pons asinorum para generar el -políticamente correcto- pons scholasticorum, una versión terminística del pons asinorum que conecta la inventio medii con el dictum de omni et nullo.In this contribution we offer an interpretation of the pons asinorum by using a contemporary term logic. This interpretation allows us to revitalize the concept of the pons asinorum (...) in order to produce the -politically correct- pons scholasticorum, a terministic version of the pons asinorum that relates the inventio medii with the dictum de omni et nullo. (shrink)

Partimos de que en sociedades políticas complejas, aun siendo el Estado un artificio necesario para evitar situaciones de dominación, su entramado institucional no está exento de reproducir análogas situaciones a aquellas cuya eliminación justificaba su existencia. Analizaremos desde esta óptica las críticas de Rawls y Nozick al utilitarismo, al que acusan de amparar actuaciones injustas por parte del colectivo hacia los individuos. En concreto, abordaremos el problema de los derechos inviolables desde estas tres líneas de pensamiento para concluir que, a (...) pesar de que existen marcadas diferencias en sus respectivos planteamientos metodológicos, hay en las tres líneas de convergencia en lo sustantivo. Concluiremos con una réplica a las objeciones antiutilitaristas y una defensa, siguiendo a John Stuart Mill de la mayor adecuación de esta escuela a la hora de defender la inviolabilidad de ciertos derechos fundamentales. (shrink)

Un análisis de la situación actual del estado de salud mental de un alto número de la población global basta para dar cuenta de la gravedad del asunto y plantear diversas posibles soluciones. El transhumanismopropone mejorar al ser humano mediante innovación tecnológica. En este trabajo se explica cómo esa innovación pude mejorar el bienestar del ser humano, analizando las consecuencias éticas y sociales de la propuesta del superbienestar y discutiendo también las críticas al transhumanismo por parte de los bioconservadores.

El artículo explora algunos de los principales rasgos políticos de la época globalizada y defiende la necesidad de entidades políticas representativas que superen el marco del Estado nación. A continuación se pregunta bajo qué presupuestos ético-políticos podría defenderse un modelo político-jurídico global para un mundo axiológicamente diverso y qué concepciones políticas y valores podrían proponerse como referente normativo para una gobernanza global cuya meta habría de ser el ejercicio legítimo del poder. Teniendo en cuenta las dificultades de tal empresa, se (...) presentan posibles estrategias y razones que invitan a considerar que la posibilidad de un acuerdo global no es del todo implausible. (shrink)

Equational hybrid propositional type theory ) is a combination of propositional type theory, equational logic and hybrid modal logic. The structures used to interpret the language contain a hierarchy of propositional types, an algebra and a Kripke frame. The main result in this paper is the proof of completeness of a calculus specifically defined for this logic. The completeness proof is based on the three proofs Henkin published last century: Completeness in type theory, The completeness of the first-order functional calculus (...) and Completeness in propositional type theory. More precisely, from and we take the idea of building the model described by the maximal consistent set; in our case the maximal consistent set has to be named, \-saturated and extensionally algebraic-saturated due to the hybrid and equational nature of \. From, we use the result that any element in the hierarchy has a name. The challenge was to deal with all the heterogeneous components in an integrated system. (shrink)

La conocida obra Muʿǧam al-buldān (Diccionario de los países), terminada por el geógrafo y erudito Yāqūt al-Rūmī al-Ḥamawī (m. 626/1229) un año antes de su muerte, ofrece una valiosa información sobre los múltiples topónimos recogidos por este autor. Dicha información no se limita solo a los aspectos geográficos, sino también a los literarios y biográficos, y ha sido abordada en trabajos relacionados con al-Andalus. Mi propósito en el presente artículo es realizar una primera aproximación a la imagen que Yāqūt proyecta (...) del Mágreb a través de algunos ejemplos concretos, realizando un breve recorrido de las fuentes que empleó, entre las cuales destacó especialmente el geógrafo andalusí Abū ʿUbayd al-Bakrī (m. 487/1094), muy citado en toda la obra. (shrink)

Es paradójico cómo la vida suele entenderse de manera menos equivocada desde la ficción, la realidad en sí y por sí se convierte en una trampa donde la razón que la justifica termina por dibujarle sus propios barrotes. Tal vez lo que sucede es que la razón no tiene tan completamente asegurada una razón, de la misma manera que la locura no está ausente de razón y de sentido; es evidente que siempre hallaremos una razón en la locura y una (...) locura en cada razón. Exacerbar la razón o la locura nos pondrá siempre en el ojo del huracán, nos hará visibles ante los demás, nos personalizará, es decir, descubrirá en cada uno de nosotros a un personaje. (shrink)

In Scotus the person is treated in an intelectual atmosphere in which has already been enhanced a considerable effort intelectual in views to an understanding and clarification of what is the person. The author of this work on Scotus, professor emeritus of Antonianum of Rome, intends to make understand the originality of the grief escotista on the person. For it, it is about creating the place in which makes sense speak of person, as Escoto. This place is not other but (...) that in the one that the ontological language is overcome. The person, indeed, indicates and she says something that surpasses and she is added the intellectual constituted individual or the individual of rational nature. In consequence, Prof. Manzano pursues and it indicates the roads from Scotus to this original reality that is the one of being person. These roads are, in short, the road toward the person’s understanding like «an absolute event that happens», the road of the person’s understanding like «absolute independence» and the road of the person’s understanding like «incommunicable existence». At the end, the author treats the scotish dialectic on the question of if the person is carácter of being something positive real, although not ontological, or she is merely somethig relational. In this lasta case, it will be abolut a «relationship» extremely original and diverse of the nature of the relationship as predicament. (shrink)

This article sets out a global analysis of the weaknesses, threats, strengths and opportunities that define the current situation of nursing in Europe. The nursing profession in Europe is suffering from a crisis of self‐efficacy with the syndrome of burnout being one of its consequences. Other weaknesses include shortage of staff, job insecurity, devalued nursing image in society and the lack of recognition of emotional and psychological dimensions of care. The threats to this profession are linked to the lack of (...) prestige and social recognition and to the current economic crisis in Europe. The European economic crisis favours staff shortages and increased European migration flow. The strength of the group lies in the art of caring, which is its defining feature. Primary Care Nursing and Hospital Liaison Nursing demonstrate the great professional adaptability in meeting the needs of the ever‐changing society. The European Higher Education Area and the strengthening of the specialties provide opportunities for the nursing profession. Both represent an important progress towards solid professionalism that will give nursing greater visibility. Moreover, nursing must implement strategies to disseminate its activity and emerge from anonymity. Nursing must show society the image it wants to project. (shrink)

This article is an extended promenade strolling along the winding roads of identity, equality, nameability and completeness, looking for places where they converge. We have distinguished between identity and equality; the first is a binary relation between objects while the second is a symbolic relation between terms. Owing to the central role the notion of identity plays in logic, you can be interested either in how to define it using other logical concepts or in the opposite scheme. In the first (...) case, one investigates what kind of logic is required. In the second case, one is interested in the definition of the other logical concepts in terms of the identity relation, using also abstraction. The present paper investigates whether identity can be introduced by definition arriving to the conclusion that only in full higher-order logic a reliable definition of identity is possible. However, the definition needs the standard semantics and we know that with this semantics completeness is lost. We have also studied the relationship of equality with comprehension and extensionality and pointed out the relevant role played by these two axioms in Henkin’s completeness method. We finish our paper with a section devoted to general semantics, where the role played by the nameable hierarchy of types is the key in Henkin’s completeness method. (shrink)

Model theory is the branch of mathematical logic looking at the relationship between mathematical structures and logic languages. These formal languages are free from the ambiguities of natural languages, and are becoming increasingly important in areas such as computing, philosophy and linguistics. This book provides a clear introduction to the subject for both mathematicians and the non-specialists now needing to learn some model theory.