A simple complete axiomatic system is presented for the many-valued propositional logic based on the conjunction interpreted as product, the coresponding implication (Goguen's implication) and the corresponding negation (Gödel's negation). Algebraic proof methods are used. The meaning for fuzzy logic (in the narrow sense) is shortly discussed.

Companies are faced with a choice of which type of power to use in their efforts to persuade their first-tier suppliers to adopt socially responsible procurement practices with key second-tier suppliers. However, we know little about how first-tier suppliers will react to different types of power and which are most effective in encouraging the adoption of socially responsible procurement practices. We are also ignorant of the impact of these practices on first-tier suppliers’ performance. This paper uses bases of power theory (...) to examine the impact of buyer companies’ power usage on first-tier suppliers’ adoption of socially responsible procurement practices with their own suppliers. We surveyed managers responsible for sustainable supply chain management in 156 firms and analyzed the results using structural equation modeling. Our findings show that non-mediated power use influences the adoption of process-based and market-based practices, while mediated power use has no significant impact on the adoption of either type of practice. Additionally, we find that the adoption of market-based socially responsible procurement practices leads to enhanced performance for first-tier suppliers who adopt these practices with their second-tier suppliers. (shrink)

Residuated fuzzy logic calculi are related to continuous t-norms, which are used as truth functions for conjunction, and their residua as truth functions for implication. In these logics, a negation is also definable from the implication and the truth constant $\overline{0}$ , namely $\neg \varphi$ is $\varphi \to \overline{0}$. However, this negation behaves quite differently depending on the t-norm. For a nilpotent t-norm (a t-norm which is isomorphic to Łukasiewicz t-norm), it turns out that $\neg$ is an involutive negation. However, (...) for t-norms without non-trivial zero divisors, $\neg$ is Gödel negation. In this paper we investigate the residuated fuzzy logics arising from continuous t-norms without non-trivial zero divisors and extended with an involutive negation. (shrink)

Cette lecture illustrée de l'Odyssée d'Homère nous introduit aux thèses de la Dialectique de la Raison de Theodor W. Adorno et Max Horkheimer, une des oeuvres maîtresses de l'école dite de " Francfort ", écrite entre 1941 et 1944 au moment où la civilisation basculait dans le gouffre. Les deux auteurs y démontraient comme la raison occidentale fondatrice de la société européenne est viciée en son essence : une terreur originelle la motive. Sa relation à la Nature est pensée dans (...) les termes antagonistes du tuer ou mourir. La fameuse raison des Lumières perpétue finalement la violence et les réflexes irrationnels qu'elle prétendait vouloir éliminer, elle contient son contraire, elle est d'essence dialectique. Pour illustrer leur propos, Adorno et Horkheimer sont remontés jusqu'à l'Ulysse d'Homère qu'ils présentent comme le passeur de la pensée mythique - qui pactise encore avec les forces naturelles - à la pensée rationnelle, qui est une stratégie, une ruse en vue de dominer celles-ci. Il incarne à la fois une victime ballottée par les éléments et un bourreau, le porteur d'un espoir - en grande partie déçu - d'émancipation et l'ancêtre du bourgeois qui défend à tout prix ses intérêts contre ceux des autres. Ce livre, illustré en eaux-fortes avec un anachronisme assumé, commente l'Odyssée depuis les jalons posés par les penseurs allemands. Il nous dévoile ainsi la geste sanglante de la naissance de la rationalité européenne. (shrink)

The aim of the paper is to analyze the expressive power of the square operator of Łukasiewicz logic: ∗x=x⊙x⁠, where ⊙ is the strong Łukasiewicz conjunction. In particular, we aim at understanding and characterizing those cases in which the square operator is enough to construct a finite MV-chain from a finite totally ordered set endowed with an involutive negation. The first of our main results shows that, indeed, the whole structure of MV-chain can be reconstructed from the involution and the (...) Łukasiewicz square operator if and only if the obtained structure has only trivial subalgebras and, equivalently, if and only if the cardinality of the starting chain is of the form n+1 where n belongs to a class of prime numbers that we fully characterize. Secondly, we axiomatize the algebraizable matrix logic whose semantics is given by the variety generated by a finite totally ordered set endowed with an involutive negation and Łukasiewicz square operator. Finally, we propose an alternative way to account for Łukasiewicz square operator on involutive Gödel chains. In this setting, we show that such an operator can be captured by a rather intuitive set of equations. (shrink)

In Spain before the 1990s there was no clear and explicit comprehensive training for future engineers with regard to social responsibility and social commitment. Following the Spanish university curricular reform, which began in the early 1990s, a number of optional subjects became available to students, concerning science, technology and society (STS), international cooperation, the environment and sustainability. The latest redefinition of the Spanish curriculum in line with the Bologna agreements has reduced the number of non-obligatory subjects, but could lead to (...) improving preparation for social responsibility due to the requirement that the design of curricula and the assessment of students should be based on competencies, some of which include human values and attitudes. (shrink)

Both a method of therapy and an exploration of psychic reality, free association is a fundamental element of psychoanalytical practices that refers to the way a patient is asked to describe what comes spontaneously to mind in the therapeutic setting. This paper examines the role of free association from the point of view of psychoanalysis and neuroscience in order to improve our understanding of therapeutic effects induced by psychoanalytic therapies and psychoanalysis. In this regard, we first propose a global overview (...) of the historical origins of the concept of free association in psychoanalysis and examine how Freud established its principles. Then, from Freud’s distinction between primary and secondary processes, we proceed to compare the psychoanalytic model with research originating from cognitive psychology and neuroscience. The notions of entropy and free energy appear particularly relevant at the intersection of these different domains. Finally, we propose the notion of symbolizing transmodality to describe certain specificities of symbolization processes within free association and we summarize the main functions of free association in psychoanalytic practices. (shrink)

The monoidal t-norm based logic MTL is obtained from Hájek''s Basic Fuzzy logic BL by dropping the divisibility condition for the strong (or monoidal) conjunction. Recently, Jenei and Montgana have shown MTL to be standard complete, i.e. complete with respect to the class of residuated lattices in the real unit interval [0,1] defined by left-continuous t-norms and their residua. Its corresponding algebraic semantics is given by pre-linear residuated lattices. In this paper we address the issue of standard and rational completeness (...) (rational completeness meaning completeness with respect to a class of algebras in the rational unit interval [0,1]) of some important axiomatic extensions of MTL corresponding to well-known parallel extensions of BL. Moreover, we investigate varieties of MTL algebras whose linearly ordered countable algebras embed into algebras whose lattice reduct is the real and/or the rational interval [0,1]. These embedding properties are used to investigate finite strong standard and/or rational completeness of the corresponding logics. (shrink)

The monoidal t-norm based logic MTL is obtained from Hájek's Basic Fuzzy logic BL by dropping the divisibility condition for the strong (or monoidal) conjunction. Recently, Jenei and Montgana have shown MTL to be standard complete, i.e. complete with respect to the class of residuated lattices in the real unit interval [0,1] defined by left-continuous t-norms and their residua. Its corresponding algebraic semantics is given by pre-linear residuated lattices. In this paper we address the issue of standard and rational completeness (...) (rational completeness meaning completeness with respect to a class of algebras in the rational unit interval [0,1]) of some important axiomatic extensions of MTL corresponding to well-known parallel extensions of BL. Moreover, we investigate varieties of MTL algebras whose linearly ordered countable algebras embed into algebras whose lattice reduct is the real and/or the rational interval [0,1]. These embedding properties are used to investigate finite strong standard and/or rational completeness of the corresponding logics. (shrink)

Our work is a contribution to the model theory of fuzzy predicate logics. In this paper we characterize elementary equivalence between models of fuzzy predicate logic using elementary mappings. Refining the method of diagrams we give a solution to an open problem of Hájek and Cintula (J Symb Log 71(3):863–880, 2006, Conjectures 1 and 2). We investigate also the properties of elementary extensions in witnessed and quasi-witnessed theories, generalizing some results of Section 7 of Hájek and Cintula (J Symb Log (...) 71(3):863–880, 2006) and of Section 4 of Cerami and Esteva (Arch Math Log 50(5/6):625–641, 2011) to non-exhaustive models. (shrink)

This article proposes the meeting of fuzzy logic with paraconsistency in a very precise and foundational way. Specifically, in this article we introduce expansions of the fuzzy logic MTL by means of primitive operators for consistency and inconsistency in the style of the so-called Logics of Formal Inconsistency (LFIs). The main novelty of the present approach is the definition of postulates for this type of operators over MTL-algebras, leading to the definition and axiomatization of a family of logics, expansions of (...) MTL, whose degree-preserving counterpart are paraconsistent and moreover LFIs. (shrink)

In this paper we show that the subvarieties of BL, the variety of BL-algebras, generated by single BL-chains on [0, 1], determined by continous t-norms, are finitely axiomatizable. An algorithm to check the subsethood relation between these subvarieties is provided, as well as another procedure to effectively find the equations of each subvariety. From a logical point of view, the latter corresponds to find the axiomatization of every residuated many-valued calculus defined by a continuous t-norm and its residuum. Actually, the (...) paper proves the results for a more general class than t-norm BL-chains, the so-called regular BL-chains. (shrink)

María de Echarri y Dolors Monserdà fueron dos de las figuras más significativas del feminismo católico de principios del siglo XX. La prensa fue uno de los altavoces más importantes para la difusión de las ideas de ambas propagandistas sobre la situación laboral de las obreras, así como la defensa del catolicismo, que les valieron una relevancia social y política muy importante. En este trabajo se repasarán algunos de sus escritos publicados en la prensa que mostrarán su pensamiento social, con (...) el objetivo de plasmar cuáles fueron sus ideas, adscritas a dos movimientos ideológicos: el feminismo conservador y el catolicismo social. (shrink)

Ante la diversidad y complejidad que vivimos en las aulas se proponen tareas interesantes que involucren a los discentes en la importancia del trabajo diario y el compromiso personal para aprender los contenidos de la asignatura. El presente texto nace en el marco de un proyecto más amplio que indaga sobre el análisis de situaciones de aula en Formación Profesional (FP) desde un enfoque de investigación cualitativa. Esta experiencia se vincula con la teoría sociocultural de la enseñanza y siguiendo los (...) planteamientos de Freire toma como referente la reflexión y acción de las personas sobre el mundo para transformarlo. (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)

Research on Augmented Reality in education has demonstrated that AR applications designed with diverse components boost student motivation in educational settings. However, most of the research conducted to date, does not define exactly what those components are and how these components positively affect student motivation. This study, therefore, attempts to identify some of the components that positively affect student motivation in mobile AR learning experiences to contribute to the design and development of motivational AR learning experiences for the Vocational Education (...) and Training level of education. To identify these components, a research model constructed from the literature was empirically validated with data obtained from two sources: 35 students from four VET institutes interacting with an AR application for learning for a period of 20 days, and a self-report measure obtained from the Instructional Materials Motivation Survey. We found that the following variables: use of scaffolding, real-time feedback, degree of success, time on-task and learning outcomes are positively correlated with the four dimensions of the ARCS model of motivation: Attention, Relevance, Confidence, and Satisfaction. Implications of these results are also described. (shrink)

In this paper we show that the subvarieties of BL, the variety of BL-algebras, generated by single BL-chains on [0, 1], determined by continous t-norms, are finitely axiomatizable. An algorithm to check the subsethood relation between these subvarieties is provided, as well as another procedure to effectively find the equations of each subvariety. From a logical point of view, the latter corresponds to find the axiomatization of every residuated many-valued calculus defined by a continuous t-norm and its residuum. Actually, the (...) paper proves the results for a more general class than t-norm BL-chains, the so-called regular BL-chains. (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)

Distributive bounded lattices with a dual homomorphism as unary operation, called Ockham algebras, were firstly studied by Berman (1977). The varieties of Boolean algebras, De Morgan algebras, Kleene algebras and Stone algebras are some of the well known subvarieties of Ockham algebra. In this paper, new results about the congruence lattice of Ockham algebras are given. From these results and Urquhart's representation theorem for Ockham algebras a complete characterization of the subdirectly irreducible Ockham algebras is obtained. These results are particularized (...) for a large number of subvarieties of Ockham algebras. For these subvarieties a full description of their subdirectly irreducible algebras is given as well. (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)

Se presenta la hipótesis de que la mirada más allá de la modernidad puede descubrir la nueva sociedad que ha estado surgiendo en el vientre de la vieja. La insurrección de saberes subyugados e imaginaciones reprimidas, que caracteriza la transición, estaría definiendo una nueva perspectiva e interpretación del mundo, que serían expresión de la resistencia a la destrucción aún vinculada al viejo orden social y de los empeños de construcción del nuevo.

Los movimientos sociales contemporáneos se hacen antisistémicos en su propia dinámica, cuando profundizan sus empeños y descubren la naturaleza e interconexiones de los obstáculos que enfrentan. Empieza a generalizarse la intuición, anticipada por pensadores radicales del último medio siglo, de que estamos al fin de una era. A partir de las experiencias de la Asamblea Popular de los Pueblos de Oaxaca, reflexiono en este trabajo sobre la necesidad de limpiar nuestras miradas –contaminadas aún por la era que termina- al concebir (...) las luchas actuales y emprender esfuerzos de transformación. Serían desgaste estéril si están atrapados en elementos de la víspera. La nueva sociedad no puede ser mera extrapolación de la antigua. Al plantear la necesidad de preparar el funeral de la sociedad económica (capitalismo y socialismo), del imperio estadounidense y del régimen político mexicano, sugiero también caminos para acotar con mayor precisión los rumbos y maneras de la lucha anticapitalista actual. (shrink)

In nine essays, each related to a different time frame, author analyzes diverse aspects of Venezuelans' cultural behavior in regard to what the author considers 'taste.' Witty and amusing, often sarcastic and colloquial, book does not lose perspective of the historical context. A curious x-ray of Venezuelan idiosyncrasies"--Handbook of Latin American Studies, v. 58.

In this paper we study and equationally characterize the subvarieties of BL, the variety of BL-algebras, which are generated by families of single-component BL-chains, i.e. MV-chains, Product-chain or Gödel-chains. Moreover, it is proved that they form a segment of the lattice of subvarieties of BL which is bounded by the Boolean variety and the variety generated by all single-component chains, called ŁΠG.

In this paper we prove strong completeness of axiomatic extensions of first-order strict core fuzzy logics with the so-called quasi-witnessed axioms with respect to quasi-witnessed models. As a consequence we obtain strong completeness of Product Predicate Logic with respect to quasi-witnessed models, already proven by M.C. Laskowski and S. Malekpour in [19]. Finally we study similar problems for expansions with Δ, define Δ-quasi-witnessed axioms and prove that any axiomatic extension of a first-order strict core fuzzy logic, expanded with Δ, and (...) Δ-quasi-witnessed axioms are complete with respect to Δ-quasi-witnessed models. (shrink)

A symmetric residuated lattice is an algebra such that is a commutative integral bounded residuated lattice and the equations x=x and =xy are satisfied. The aim of the paper is to investigate the properties of the unary operation ε defined by the prescription εx=x→0. We give necessary and sufficient conditions for ε being an interior operator. Since these conditions are rather restrictive →0)=1 is satisfied) we consider when an iteration of ε is an interior operator. In particular we consider the (...) chain of varieties of symmetric residuated lattices such that the n iteration of ε is a boolean interior operator. For instance, we show that these varieties are semisimple. When n=1, we obtain the variety of symmetric stonean residuated lattices. We also characterize the subvarieties admitting representations as subdirect products of chains. These results generalize and in many cases also simplify, results existing in the literature. (shrink)

In this paper we provide a finite axiomatization (using two finitary rules only) for the propositional logic (called $L\Pi$ ) resulting from the combination of Lukasiewicz and Product Logics, together with the logic obtained by from $L \Pi$ by the adding of a constant symbol and of a defining axiom for $\frac{1}{2}$ , called $L \Pi\frac{1}{2}$ . We show that $L \Pi \frac{1}{2}$ contains all the most important propositional fuzzy logics: Lukasiewicz Logic, Product Logic, Gödel's Fuzzy Logic, Takeuti and Titani's (...) Propositional Logic, Pavelka's Rational Logic, Pavelka's Rational Product Logic, the Lukasiewicz Logic with $\Delta$ , and the Product and Gödel's Logics with $\Delta$ and involution. Standard completeness results are proved by means of investigating the algebras corresponding to $L \Pi$ and $L \Pi \frac{1}{2}$ . For these algebras, we prove a theorem of subdirect representation and we show that linearly ordered algebras can be represented as algebras on the unit interval of either a linearly ordered field, or of the ordered ring of integers, Z. (shrink)

In this paper we study intermediate logics between the logic G≤∼, the degree preserving companion of Gödel fuzzy logic with involution G∼ and classical propositional logic CPL, as well as the intermediate logics of their finite-valued counterparts G≤n∼. Although G≤∼ and G≤ are explosive w.r.t. Gödel negation ¬, they are paraconsistent w.r.t. the involutive negation ∼. We introduce the notion of saturated paraconsistency, a weaker notion than ideal paraconsistency, and we fully characterize the ideal and the saturated paraconsistent logics between (...) G≤n∼ and CPL. We also identify a large family of saturated paraconsistent logics in the family of intermediate logics for degree-preserving finite-valued Łukasiewicz logics. (shrink)

Every region of the world is confronted with ongoing ecosystem degradation, species extinctions, and the loss of cultural diversity and knowledge associated with indigenous peoples. We face a global biocultural extinction crisis. The proposition that traditional knowledge along with scientific understanding can inform approaches to solving practical conservation problems has been widely accepted in principle. Attempts to promote a more bilateral approach, however, are hampered by the lack of a common framework for integrating the two knowledge systems in a way (...) that is coherent and useful. This problem can be addressed by drawing upon, as a case study, the principle elements of traditional knowledge and their practical application to governance as articulated by the Kuuku I’yu Northern Kaanju people of Cape York Peninsula, Australia. Four points of contact can help bridge traditional and scientific knowledge in addressing the biocultural crisis: post-normal science; conservation values and goals; land management; and sustainable development. Key insights that emerge from these considerations include the propositions that holders of traditional knowledge can be validly seen as members of the extended peer community needed to address post-normal science problems; that traditional knowledge provide guideposts to the positive values being lost from view by an increasingly urban-based society; that there are practical conservation benefits to be derived from adopting a “two-tool box” approach; and that traditional knowledge provides the basis for criteria to help discern for a given community and landscape the kinds of economic activities which are ecologically and culturally compatible. There are multiple benefits for society that arise from appropriate recognition of biocultural resources in legislation and decision making. (shrink)