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)

In this article we investigate infinitary propositional logics from the perspective of their completeness properties in abstract algebraic logic. It is well-known that every finitary logic is complete with respect to its relatively subdirectly irreducible models. We identify two syntactical notions formulated in terms of intersection-prime theories that follow from finitarity and are sufficient conditions for the aforementioned completeness properties. We construct all the necessary counterexamples to show that all these properties define pairwise different classes of logics. Consequently, we obtain (...) a new hierarchy of logics going beyond the scope of finitarity. (shrink)

IMTL logic was introduced in [12] as a generalization of the infinitely-valued logic of Lukasiewicz, and in [11] it was proved to be the logic of left-continuous t-norms with an involutive negation and their residua. The structure of such t-norms is still not known. Nevertheless, Jenei introduced in [20] a new way to obtain rotation-invariant semigroups and, in particular, IMTL-algebras and left-continuous t-norm with an involutive negation, by means of the disconnected rotation method. In order to give an algebraic interpretation (...) to this construction, we generalize the concepts of perfect, bipartite and local algebra used in the classification of MV-algebras to the wider variety of IMTL-algebras and we prove that perfect algebras are exactly those algebras obtained from a prelinear semihoop by Jenei's disconnected rotation. We also prove that the variety generated by all perfect IMTL-algebras is the variety of the IMTL-algebras that are bipartite by every maximal filter and we give equational axiomatizations for it. (shrink)

The study of perfect, local and bipartite IMTL-algebras presented in [29] is generalized in this paper to the general non-involutive case, i.e. to MTL-algebras. To this end we describe the radical of MTL-algebras and characterize perfect MTL-algebras as those for which the quotient by the radical is isomorphic to the two-element Boolean algebra, and a special class of bipartite MTL-algebras,.

In this paper we carry out an algebraic investigation of the weak nilpotent minimum logic and its t-norm based axiomatic extensions. We consider the algebraic counterpart of WNM, the variety of WNM-algebras and prove that it is locally finite, so all its subvarieties are generated by finite chains. We give criteria to compare varieties generated by finite families of WNM-chains, in particular varieties generated by standard WNM-chains, or equivalently t-norm based axiomatic extensions of WNM, and we study their standard completeness (...) properties. We also characterize the generic WNM-chains, i. e. those that generate the variety [MATHEMATICAL DOUBLE-STRUCK CAPITAL W]ℕ[MATHEMATICAL DOUBLE-STRUCK CAPITAL M], and we give finite axiomatizations for some t-norm based extensions of WNM. (shrink)

This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics. It can also serve as an introduction to algebraic logic, both propositional and first-order, with special attention paid to the role of implication, lattice and residuated connectives, and generalized disjunctions. Based on their recent work, the authors develop a powerful uniform framework for (...) the study of non-classical logics. In a self-contained and didactic style, starting from very elementary notions, they build a general theory with a substantial number of abstract results. The theory is then applied to obtain numerous results for prominent families of logics and their algebraic counterparts, in particular for superintuitionistic, modal, substructural, fuzzy, and relevant logics. The book may be of interest to a wide audience, especially students and scholars in the fields of mathematics, philosophy, computer science, or related areas, looking for an introduction to a general theory of non-classical logics and their algebraic semantics. (shrink)

This paper aims at being a systematic investigation of different completeness properties of first-order predicate logics with truth-constants based on a large class of left-continuous t-norms . We consider standard semantics over the real unit interval but also we explore alternative semantics based on the rational unit interval and on finite chains. We prove that expansions with truth-constants are conservative and we study their real, rational and finite chain completeness properties. Particularly interesting is the case of considering canonical real and (...) rational semantics provided by the algebras where the truth-constants are interpreted as the numbers they actually name. Finally, we study completeness properties restricted to evaluated formulae of the kind , where φ has no additional truth-constants. (shrink)

It is well known that MTL satisfies the finite embeddability property. Thus MTL is complete w. r. t. the class of all finite MTL-chains. In order to reach a deeper understanding of the structure of this class, we consider the extensions of MTL by adding the generalized contraction since each finite MTL-chain satisfies a form of this generalized contraction. Simultaneously, we also consider extensions of MTL by the generalized excluded middle laws introduced in [9] and the axiom of weak cancellation (...) defined in [31]. The algebraic counterpart of these logics is studied characterizing the subdirectly irreducible, the semisimple, and the simple algebras. Finally, some important algebraic and logical properties of the considered logics are discussed: local finiteness, finite embeddability property, finite model property, decidability, and standard completeness. (shrink)

This paper is devoted to the problem of existence of saturated models for first-order many-valued logics. We consider a general notion of type as pairs of sets of formulas in one free variable that express properties that an element of a model should, respectively, satisfy and falsify. By means of an elementary chains construction, we prove that each model can be elementarily extended to a $\kappa $-saturated model, i.e. a model where as many types as possible are realized. In order (...) to prove this theorem we obtain, as by-products, some results on tableaux and their consistency and satisfiability and a generalization of the Tarski–Vaught theorem on unions of elementary chains. Finally, we provide a structural characterization of $\kappa $-saturation in terms of the completion of a diagram representing a certain configuration of models and mappings. (shrink)

This paper is a contribution to the study of the rôle of disjunction inAlgebraic Logic. Several kinds of (generalized) disjunctions, usually defined using a suitable variant of the proof by cases property, were introduced and extensively studied in the literature mainly in the context of finitary logics. The goals of this paper are to extend these results to all logics, to systematize the multitude of notions of disjunction (both those already considered in the literature and those introduced in this paper), (...) and to show several interesting applications allowed by the presence of a suitable disjunction in a given logic. (shrink)

We study classes of graded structures satisfying the properties of amalgamation, joint embedding and hereditariness. Given appropriate conditions, we can build a graded analogue of the Fraïssé limit. Some examples such as the class of all finite weighted graphs or the class of all finite fuzzy orders (evaluated on a particular countable algebra) will be examined.

Stemming from the works of Petr Hájek on mathematical fuzzy logic, graded model theory has been developed by several authors in the last two decades as an extension of classical model theory that studies the semantics of many-valued predicate logics. In this paper we take the first steps towards an abstract formulation of this model theory. We give a general notion of abstract logic based on many-valued models and prove six Lindström-style characterizations of maximality of first-order logics in terms of (...) metalogical properties such as compactness, abstract completeness, the Löwenheim–Skolem property, the Tarski union property, and the Robinson property, among others. As necessary technical restrictions, we assume that the models are valued on finite MTL-chains and the language has a constant for each truth-value. (shrink)

This is the continuation of the paper :417–446, 2010). We continue the abstract study of non-classical logics based on the kind of generalized implication connectives they possess and we focus on semilinear logics, i.e. those that are complete with respect to the class of models where the implication defines a linear order. We obtain general characterizations of semilinearity in terms of the intersection-prime extension property, the syntactical semilinearity metarule and the class of finitely subdirectly irreducible models. Moreover, we consider extensions (...) of the language with lattice connectives and generalized disjunctions, study their interplay with implication and obtain axiomatizations and further descriptions of semilinear logics in terms of disjunctions and the proof by cases property. (shrink)

Substructural logics extending the full Lambek calculus FL have largely benefited from a systematical algebraic approach based on the study of their algebraic counterparts: residuated lattices. Recently, a nonassociative generalization of FL has been studied by Galatos and Ono as the logic of lattice-ordered residuated unital groupoids. This paper is based on an alternative Hilbert-style presentation for SL which is almost MP -based. This presentation is then used to obtain, in a uniform way applicable to most substructural logics, a form (...) of local deduction theorem, description of filter generation, and proper forms of generalized disjunctions. A special stress is put on semilinear substructural logics. Axiomatizations of the weakest semilinear logic over SL and other prominent substructural logics are provided and their completeness with respect to chains defined over the real unit interval is proved. (shrink)

Transfer theorems are central results in abstract algebraic logic that allow to generalize properties of the lattice of theories of a logic to any algebraic model and its lattice of filters. Their proofs sometimes require the existence of a natural extension of the logic to a bigger set of variables. Constructions of such extensions have been proposed in particular settings in the literature. In this paper we show that these constructions need not always work and propose a wider setting in (...) which they can still be used. (shrink)

This paper presents an abstract study of completeness properties of non-classical logics with respect to matricial semantics. Given a class of reduced matrix models we define three completeness properties of increasing strength and characterize them in several useful ways. Some of these characterizations hold in absolute generality and others are for logics with generalized implication or disjunction connectives, as considered in the previous papers. Finally, we consider completeness with respect to matrices with a linear dense order and characterize it in (...) terms of an extension property and a syntactical metarule. This is the final part of the investigation started and developed in the papers :417–446, 2010; Arch Math Logic 53:353–372, 2016). (shrink)

This paper continues the investigation, started in Lávička and Noguera : 521–551, 2017), of infinitary propositional logics from the perspective of their algebraic completeness and filter extension properties in abstract algebraic logic. If follows from the Lindenbaum Lemma used in standard proofs of algebraic completeness that, in every finitary logic, intersection-prime theories form a basis of the closure system of all theories. In this article we consider the open problem of whether these properties can be transferred to lattices of (...) filters over arbitrary algebras of the logic. We show that in general the answer is negative, obtaining a richer hierarchy of pairwise different classes of infinitary logics that we separate with natural examples. As by-products we obtain a characterization of subdirect representation for arbitrary logics, develop a fruitful new notion of natural expansion, and contribute to the understanding of semilinear logics. (shrink)

In this position paper we present a logical framework for modelling reasoning with graded predicates. We distinguish several types of graded predicates and discuss their ubiquity in rational interaction and the logical challenges they pose. We present mathematical fuzzy logic as a set of logical tools that can be used to model reasoning with graded predicates, and discuss a philosophical account of vagueness that makes use of these tools. This approach is then generalized to other kinds of graded predicates. Finally, (...) we propose a general research program towards a logic-based account of reasoning with graded predicates. (shrink)

In the literature on vagueness one finds two very different kinds of degree theory. The dominant kind of account of gradable adjectives in formal semantics and linguistics is built on an underlying framework involving bivalence and classical logic: its degrees are not degrees of truth. On the other hand, fuzzy logic based theories of vagueness—largely absent from the formal semantics literature but playing a significant role in both the philosophical literature on vagueness and in the contemporary logic literature—are logically nonclassical (...) and give a central role to the idea of degrees of truth. Each kind of degree theory has a strength: the classical kind allows for rich and subtle analyses of the comparative form of gradable adjectives and of various types of gradable precise adjectives, while the fuzzy kind yields a compelling solution to the sorites paradox. This paper argues that the fuzzy kind of theory can match the benefits of the classical kind and hence that the burden is on the latter to match the advantages of the former. In particular, we develop a new version of the fuzzy logic approach that—unlike existing fuzzy theories—yields a compelling analysis of the comparative as well as an adequate account of gradable precise predicates, while still retaining the advantage of genuinely solving the sorites paradox. (shrink)

In abstract algebraic logic, the general study of propositional non-classical logics has been traditionally based on the abstraction of the Lindenbaum-Tarski process. In this process one considers the Leibniz relation of indiscernible formulae. Such approach has resulted in a classification of logics partly based on generalizations of equivalence connectives: the Leibniz hierarchy. This paper performs an analogous abstract study of non-classical logics based on the kind of generalized implication connectives they possess. It yields a new classification of logics expanding Leibniz (...) hierarchy: the hierarchy of implicational logics. In this framework the notion of implicational semilinear logic can be naturally introduced as a property of the implication, namely a logic L is an implicational semilinear logic iff it has an implication such that L is complete w.r.t. the matrices where the implication induces a linear order, a property which is typically satisfied by well-known systems of fuzzy logic. The hierarchy of implicational logics is then restricted to the semilinear case obtaining a classification of implicational semilinear logics that encompasses almost all the known examples of fuzzy logics and suggests new directions for research in the field. (shrink)

This paper is a contribution to Mathematical fuzzy logic, in particular to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and Δ-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate on five kinds of distinguished semantics for these logics–namely the class of algebras defined over the real unit (...) interval, the rational unit interval, the hyperreals , the strict hyperreals and finite chains, respectively–and we survey the known completeness methods and results for prominent logics. We also obtain new interesting relations between the real, rational and hyperreal semantics, and good characterizations for the completeness with respect to the semantics of finite chains. Finally, all completeness properties and distinguished semantics are also considered for the first-order versions of the logics where a number of new results are proved. (shrink)

This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on classes given by universal and universal-existential sentences. In particular, we prove two amalgamation results using the technique of diagrams in the setting of structures valued on a finite MTL-algebra, from which analogues of the Łoś–Tarski and the Chang–Łoś–Suszko preservation theorems follow.

Diz o ditado que "quem não gosta de samba, bom sujeito não é: ou é ruim da cabeça ou doente do pé". Os filósofos tradicionalmente são doentes do pé e muitos deles certamente são ruins da cabeça. Isso parece tornar o tema desse livro pouco viável. Entretanto, tentamos mesmo assim. Afinal gente ruim da cabeça também é inconsequente. Na verdade, esse livro é a continuação do desejo compartilhado por seus diversos autores de aproximar a filosofia da cultura brasileira. E nada (...) melhor para tornar esse diálogo palpável do que o motivo fornecido pelo samba. Afinal, ele é uma de nossas manifestações nacionais mais típicas, difundidas e que tem sobrevivido a várias transformações ao longo do tempo. Através desse livro, esperamos ter nos tornado menos doentes do pé e menos ruins da cabeça -- apesar de quase todos gostarem de samba. (shrink)

Por que amamos? O que está por trás desse sentimento que, segundo dizem, move montanhas? É se debruçando sobre a filosofia, a ancestralidade, mitos africanos, indígenas, orientais, ocidentais e até sobre a biologia que Renato Noguera nos leva a refletir sobre os diferentes significados do amor. Amar é querer aprender, ensinam-nos os gregos. A esse aprendizado, soma-se outro fundamental, desta vez proveniente de culturas afro-indígenas: amar não é uma emoção individual, mas coletiva, e pode envolver duas, três, quatro pessoas, (...) ou mesmo uma comunidade inteira – o que é explicado também pela biologia. A alquimia de Noguera está em mostrar como os ensinamentos de filósofos e pensadores das mais diversas eras e sociedades não se contradizem, mas complementam-se. Por que amamos? Não há apenas uma resposta – assim como não há apenas uma forma de amor. (shrink)

La investigación centra su interés en determinar el impacto que ha tenido la implementación de la cátedra de la Paz en las instituciones educativas de Ciudad Bolívar en la construcción de paz y ciudadanía. Desde la investigación cualitativa en una perspectiva hermenéutica y el método narrativo, se realizó una revisión documental. Se concluye que, el abordaje de la cátedra de la paz requiere en la escuela, una perspectiva holística que fomente la reflexión crítica sobre el conflicto armado, construcción de memoria (...) histórica, fortalecimiento del tejido social y cumplimiento de los Objetivos de Desarrollo Sostenible. (shrink)

La sociedad atraviesa una serie de transformaciones en sus relaciones entre instituciones y comunidad; en este marco la universidad, desde su misión académica centrada en la formación e investigación para el desarrollo de conocimientos, está promoviendo una mayor implicación hacia las necesidades de la sociedad, a lo que se denomina responsabilidad social universitaria (RSU). Este artículo presenta cómo, desde una perspectiva humanista, se constituye una comunidad social de investigación entre la Unidad de Investigación Enfoque Centrado en la Persona de la (...) Universidad de Valencia –España-, el grupo Prisma de la Universidad Autónoma de Bucaramanga –Colombia- y la Fundación Albeiro Vargas (FAVAC) –Colombia- cuya finalidad es la atención al adulto mayor. Mediante una metodología de investigación-acción participativa, se genera una base de cooperación institucional para la promoción del bienestar psicológico del adulto mayor. El voluntariado, a través de sus docentes y sus alumnos, se concreta así en una acción de responsabilidad social universitaria cuya primera actividad es la valoración del bienestar psicológico del adulto mayor en la fundación Albeiro Vargas. (shrink)

En este artículo analizo las consecuencias del exilio en varios personajes de Los detectives salvajes de Roberto Bolaño, específicamente Ulises Lima y Arturo Belano, quienes, tras la muerte de Cesárea Tinajero, se marchan de México e inician un recorrido por países de Europa, Medio Oriente, Centroamérica y África. Este desarraigo físico, ideológico y espiritual, causado por la pérdida de sus ideales de juventud, los hace vivir “vidas líquidas”, esto es, vidas regidas por las experiencias de inseguridad, incertidumbre y desprotección. El (...) tema del exilio también afecta la estructura de la novela, sobre todo en lo que tiene que ver con la utilización, en la segunda parte, de múltiples narradores que van contando anécdotas sobre Lima, Belano y otros miembros del realismo visceral. Para abordar estos temas reviso el concepto de “modernidad líquida”, acuñado por Zygmunt Bauman, teniendo en cuenta que, para él, la modernidad líquida ha incentivado la extraterritorialidad en el hombre contemporáneo, así como el culto a lo efímero que afecta todos los aspectos de nuestras vidas, incluyendo la concepción de nosotros mismos y de nuestras relaciones sentimentales. (shrink)

A filosofia é privativa da cultura ocidental ou é uma criação do pensamento humano em geral? As culturas africanas e afrodiaspóricas são relevantes para o entendimento da filosofia? Existe filosofia africana e/ou filosofia afro-brasileira? Em caso afirmativo, como elas podem contribuir para o entendimento das relações étnico-raciais? Como o(a) professor(a) pode incluir a filosofia africana e a afrodiaspórica no currículo de Filosofia do ensino médio? Como formar um(a) professor(a) de Filosofia capaz de fazer essa conexão? Estas são algumas das questões (...) que o professor Renato Noguera discute nesta obra, que contém roteiros de reflexão, referências a autores fundamentais e propostas curriculares práticas. (shrink)

Under what conditions are people responsible for their choices and the outcomes of those choices? How could such conditions be fostered by liberal societies? Should what people are due as a matter of justice depend on what they are responsible for? For example, how far should healthcare provision depend on patients' past choices? What values would be realized and which hampered by making justice sensitive to responsibility? Would it give people what they deserve? Would it advance or hinder equality? The (...) explosion of philosophical interest in such questions has been fuelled by increased focus on individual responsibility in political debates. Political philosophers, especially egalitarians, have responded to such developments by attempting to map out the proper place for responsibility in theories of justice. This book both reflects on these recent developments in normative political theory and moves the debate forwards. (shrink)

This paper discusses the philosophical doctrine of moral luck, as described by Bernard Williams in his book of the same name. It first describes Williams' account and then uses the case of Michael Stone, a convicted murderer with a long history of mental disorder, and mental health practitioners’ interventions in his case, to test and debate Williams’ views. It examines four major areas of these, including the classical notion of moral luck, retroactive judgement, agent regret and justifiable and unjustifiable decision‐making. (...) It concludes that, in view of what has been said, whilst Williams’ views are applicable and appropriate to many areas of the Stone case, ‘traditional’ moral views on rights, obligations and principles cannot be entirely laid aside in evaluating this. (shrink)

This book is an anthology of some of the most influential research on basic income in the period of roughly 1960-2010.

In his historical perspective on the changes in scientific thought over the last 100 years, Carl N. Degler explores the study of social evolution and the ongoing search for human nature. In Search of Human Nature provides a detailed perspective on the reasons behind the shifting emphasis in social thought from biology, to culture, and again to biology. Degler examines why these changes took place, the evidence and people fostering these changes and why students of human nature decided to accept (...) this momentous change in thought. He suggests varying ideologies as the underlying force behind this shift in the study of social science. From Darwin's theory that human social behaviour has drastically evolved from animals, to the belief that human experience serves as the basic differentiating factor in humans, Degler provides a thorough and captivating examination of the roots of human behaviour. (shrink)

Basic Income: An Anthology of Contemporary Research presents a compilation of six decades of Basic Income literature. It includes the most influential empirical research and theoretical arguments on all aspects of the Basic Income proposal. -/- Includes six decades of the most influential literature on Basic Income Includes unpublished and hard-to-find articles The first major compendium on one of the most innovative political reform proposals of our age Explores multidisciplinary views of Basic Income, with philosophical, economic, political, and sociological views (...) Features contributions from key and well-known philosophers and economists, including Atkinson, Simon, Friedman, Fromm, Gorz, Offe, Rawls, Pettit, Van Parijs, and more Presents the best theoretical and empirical arguments for and against Basic Income -/- . (shrink)

Within the book, he discussed the origin and forms of musical activity as well as various theories on the origin of music. This is the first time that this important work is available in English.

Carl Schmitt and the Problem of the Realization of Law 1. The famous pithy aphorisms that Carl Schmitt used to open his major works - 'the sovereign is he who decides on the exception', 'the concept of the state presupposes the concept of the political', etc. - have become a part of the common discourse of contemporary scholarship on politics and the law. The theoretical framework that animates these slogans, however, has remained somewhat opaque. It has often been argued that (...) there is no such framework, that Schmitt was a situational thinker whose works are best understood as interventions in concrete political debates that do not add up to a grand theoretical vision. (shrink)