ABSTRACTA conditional is natural if it fulfils the three following conditions. It coincides with the classical conditional when restricted to the classical values T and F; it satisfies the Modus Ponens; and it is assigned a designated value whenever the value assigned to its antecedent is less than or equal to the value assigned to its consequent. The aim of this paper is to provide a ‘bivalent’ Belnap-Dunn semantics for all natural implicative expansions of Kleene's strong 3-valued matrix with two (...) designated elements. (shrink)

As is well known, the variable-sharing property (vsp) is, according to Anderson and Belnap, a necessary property of any relevant logic. In this paper, we shall consider two versions of the vsp, what we label the "weak vsp" (wvsp) and the "strong vsp" (svsp). In addition, the "no loose pieces property," a property related to the wvsp and the svsp, will be defined. Each one of these properties shall generally be characterized by means of a class of logical matrices. In (...) this way, any logic verified by an actual matrix in one of these classes has the property the class generally represents. Particular matrices (and so, logics) in each class are provided. (shrink)

The importance of fairness in machine learning models is widely acknowledged, and ongoing academic debate revolves around how to determine the appropriate fairness definition, and how to tackle the trade-off between fairness and model performance. In this paper we argue that besides these concerns, there can be ethical implications behind seemingly purely technical choices in fairness interventions in a typical model development pipeline. As an example we show that the technical choice between in-processing and post-processing is not necessarily value-free and (...) may have serious implications in terms of who will be affected by the specific fairness intervention. The paper reveals how assessing the technical choices in terms of their ethical consequences can contribute to the design of fair models and to the related societal discussions. (shrink)

Routley-Meyer Ternary Relational Semantics for Intuitionistic-type Negations examines how to introduce intuitionistic-type negations into RM-semantics. RM-semantics is highly malleable and capable of modeling families of logics which are very different from each other. This semantics was introduced in the early 1970s, and was devised for interpreting relevance logics. In RM-semantics, negation is interpreted by means of the Routley operator, which has been almost exclusively used for modeling De Morgan negations. This book provides research on particular features of intuitionistic-type of negations (...) in RM-semantics, while also defining the basic systems and many of their extensions by using models with or without a set of designated points. (shrink)

We consider the logics determined by the set of all natural implicative expansions of Kleene’s strong 3-valued matrix and select the class of all logics functionally equivalent to Łukasiewicz’s 3-valued logic Ł3. The concept of a “natural implicative matrix” is based upon the notion of a “natural conditional” defined in Tomova.

A classical result by Słupecki states that a logic L is functionally complete for the 3-element set of truth-values THREE if, in addition to functionally including Łukasiewicz’s 3-valued logic Ł3, what he names the ‘$T$-function’ is definable in L. By leaning upon this classical result, we prove a general theorem for defining binary expansions of Kleene’s strong logic that are functionally complete for THREE.

The logic E4 is related to Brady’s BN4 in a similar way to which Anderson and Belnap’s logic of entailment E is related to their logic of the relevant implication R. In ‘A companion to Brady’s 4-valued relevant logic: the 4-valued logic of entailment E4’, quoted in this paper, three alternatives to BN4 and another three to E4 are summarily introduced in a couple of pages as the only alternatives containing Routley and Meyer’s basic logic B, provided some conditions are (...) fulfilled. The aim of this note is to prove BN4 and its three alternatives are the same logic up to some point, since they are functionally equivalent to each other, as it is the case with E4 and its three alternatives, which are also functionally equivalent to each other; to some extent, E4 is superior to BN4, since the latter is functionally included in the former, but not conversely. (shrink)

The COVID-19 global health emergency has greatly impacted the educational field. Faced with unprecedented stress situations, professors, students, and families have employed various coping and resilience strategies throughout the confinement period. High and persistent stress levels are associated with other pathologies; hence, their detection and prevention are needed. Consequently, this study aimed to design a predictive model of stress in the educational field based on artificial intelligence that included certain sociodemographic variables, coping strategies, and resilience capacity, and to study the (...) relationship between them. The non-probabilistic snowball sampling method was used, involving 337 people from the university education community in south-eastern Spain. The Perceived Stress Scale, Stress Management Questionnaire, and Brief Resilience Scale were administered. The Statistical Package for the Social Sciences was used to design the architecture of artificial neural networks. The results found that stress levels could be predicted by the synaptic weights of coping strategies and timing of the epidemic, with a predictive capacity of over 80% found in the neural network model. Additionally, direct and significant associations were identified between the use of certain coping strategies, stress levels, and resilience. The conclusions of this research are essential for effective stress detection, and therefore, early intervention in the field of educational psychology, by discussing the influence of resilience or lack thereof on the prediction of stress levels. Identifying the variables that maintain a greater predictive power in stress levels is an effective strategy to design more adjusted prevention programs and to anticipate the needs of the community. (shrink)

This paper is a sequel to ‘Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated values’, where a ‘bivalent’ Belnap-Dunn semantics is provided for all the expansions referred to in its title. The aim of the present paper is to carry out a parallel investigation for all natural implicative expansions of Kleene's strong 3-valued matrix now with only one designated value.

8 March, now known as International Women’s Day, is a day for feminist claims where demonstrations are organized in over 150 countries, with the participation of millions of women all around the world. These demonstrations can be viewed as collective rituals and thus focus attention on the processes that facilitate different psychosocial effects. This work aims to explore the mechanisms involved in participation in the demonstrations of 8 March 2020, collective and ritualized feminist actions, and their correlates associated with personal (...) well-being and collective well-being, collective efficacy and collective growth, and behavioral intention to support the fight for women’s rights. To this end, a cross-cultural study was conducted with the participation of 2,854 people from countries in Latin America and Europe, with a retrospective correlational cross-sectional design and a convenience sample. Participants were divided between demonstration participants and non-demonstrators or followers who monitored participants through the media and social networks. Compared with non-demonstrators and with males, female and non-binary gender respondents had greater scores in mechanisms and criterion variables. Further random-effects model meta-analyses revealed that the perceived emotional synchrony was consistently associated with more proximal mechanisms, as well as with criterion variables. Finally, sequential moderation analyses showed that proposed mechanisms successfully mediated the effects of participation on every criterion variable. These results indicate that participation in 8M marches and demonstrations can be analyzed through the literature on collective rituals. As such, collective participation implies positive outcomes both individually and collectively, which are further reinforced through key psychological mechanisms, in line with a Durkheimian approach to collective rituals. (shrink)

In this paper, consistency is understood as the absence of the negation of a theorem, and not, in general, as the absence of any contradiction. We define the basic constructive logic BKc1 adequate to this sense of consistency in the ternary relational semantics without a set of designated points. Then we show how to define a series of logics extending BKc1 within the spectrum delimited by contractionless minimal intuitionistic logic. All logics defined in the paper are paraconsistent logics.

The aim of this paper is to introduce an alternative to Łukasiewicz’s 4-valued modal logic Ł. As it is known, Ł is afflicted by “Łukasiewicz type paradoxes”. The logic we define, PŁ4, is a strong paraconsistent and paracomplete 4-valued modal logic free from this type of paradoxes. PŁ4 is determined by the degree of truth-preserving consequence relation defined on the ordered set of values of a modification of the matrix MŁ characteristic for the logic Ł. On the other hand, PŁ4 (...) is a rich logic in which a number of connectives can be defined. It also has a simple bivalent semantics of the Belnap–Dunn type. (shrink)

Este trabajo aborda el nuevo paradigma de la Open Science o ciencia en abierto desde la perspectiva europea, pero destacando su necesario alcance global. Se analiza el concepto, origen y evolución de la Open Science y se discuten sus retos y la demora de su completa implementación. Se parte de la hipótesis de que la Open Science debería de ser el paradigma de comunicación científico por defecto en el siglo XXI. En primer lugar, se revisa el concepto y alcance de (...) Open Science frente a Open Access y en su interacción con Open Knowledge, así como la necesidad de mantener la denominación como «marca». En segundo lugar, se recogen los requisitos, reflexiones y parámetros para hacer de la ciencia un bien común y se describen los retos de la Open Science en Europa, que se han convertido en los principales pilares y/o elementos constitutivos de la ciencia en abierto. Se reflexiona sobre su puesta en práctica, detallando dos aproximaciones: 1) la creación de políticas y estrategias formales a nivel Estados miembros, y 2) la implementación bottom-up a través de Compromisos Prácticos de Implementación. Asimismo, se destacan los problemas reales que alejan a los agentes implicados de protagonizar el cambio sistémico hacia la Open Science. Finalmente se reflexiona sobre el efecto de la COVID-19 que ha corroborado la necesidad urgente de la ciencia en abierto. Este artículo recoge, a modo de ensayo, la experiencia y el trabajo realizado en los últimos cuatro años en la European Open Science Policy Platform, donde la autora ha presidido el segundo mandato desde 2018 a 2020. La autora expone algunas de sus principales teorías en torno a la Open Science y defiende su tesis de los compromisos prácticos de implementación y la confluencia de aproximaciones de prácticas de los agentes implicados y políticas de ciencia abierta, así como su categórica aproximación a la Open Science como marca, actitud y derecho. (shrink)

The logic TM is the result of adding the mingle axiom, M to Ticket Entailment logic, T. In the present study, it is proved that TM has the variable-sharing property . Ternary relational semantics for TM is provided. Finally, an interesting extension of TM with the vsp is briefly discussed.

Stem cells are likely to be used as an alternate source of biological material for neural transplantation to treat Parkinson’s disease in the not too distant future. Among the several ethical criteria that must be fulfilled before proceeding with clinical research, a favourable benefit to risk ratio must be obtained. The potential benefits to the participant and to society are evaluated relative to the risks in an attempt to offer the participants a reasonable choice. Through examination of preclinical studies transplanting (...) stem cells in animals and the transplantation of fetal tissue in patients with Parkinson’s disease, a current set of potential benefits and risks for neural transplantation of stem cells in clinical research of Parkinson’s disease are derived. The potential benefits to research participants undergoing stem cell transplantation are relief of parkinsonian symptoms and decreasing doses of parkinsonian drugs. Transplantation of stem cells as a treatment for Parkinson’s disease may benefit society by providing knowledge that can be used to help determine better treatments in the future. The risks to research participants undergoing stem cell transplantation include tumour formation, inappropriate stem cell migration, immune rejection of transplanted stem cells, haemorrhage during neurosurgery and postoperative infection. Although some of these risks are general to neurosurgical transplantation and may not be reduced for participants, the potential risk of tumour formation and inappropriate stem cell migration must be minimised before obtaining a favourable potential benefit to risk calculus and to provide participants with a reasonable choice before they enrol in clinical studies. (shrink)

A simple, bivalent semantics is defined for Łukasiewicz’s 4-valued modal logic Łm4. It is shown that according to this semantics, the essential presupposition underlying Łm4 is the following: A is a theorem iff A is true conforming to both the reductionist and possibilist theses defined as follows: rt: the value of modal formulas is equivalent to the value of their respective argument iff A is true, etc.); pt: everything is possible. This presupposition highlights and explains all oddities arising in Łm4.

In our paper “A general characterization of the variable-sharing property by means of logical matrices”, a general class of so-called “Relevant logical matrices”, RMLs, is defined. The aim of this paper is to define a class of simpler Relevant logical matrices RMLs′serving the same purpose that RMLs, to wit: any logic verified by an RML′has the variable-sharing property and related properties predicable of the logic of entailment E and of the logic of relevance R.

Routley-Meyer type ternary relational semantics are defined for relevant logics including Routley and Meyer’s basic logic B plus the reductio rule and the disjunctive syllogism. Standard relevant logics such as E and R (plus γ ) and Ackermann’s logics of ‘strenge Implikation’ Π and Π ′ are among the logics considered.

“Weak relevant model structures” (wr-ms) are defined on “weak relevant matrices” by generalizing Brady’s model structure ${\mathcal{M}_{\rm CL}}$ built upon Meyer’s Crystal matrix CL. It is shown how to falsify in any wr-ms the Generalized Modus Ponens axiom and similar schemes used to derive Curry’s Paradox. In the last section of the paper we discuss how to extend this method of falsification to more general schemes that could also be used in deriving Curry’s Paradox.

Sylvan and Plumwood’s is the relevant De Morgan minimal logic in the Routley-Meyer semantics with a set of designated points. The aim of this paper is to define the logic and some of its extensions. The logic is the non-relevant De Morgan minimal logic in the Routley-Meyer semantics without a set of designated points.

Comparing the relative sensitivity of direct and indirect measures of learning is proposed as the best way to provide evidence for unconscious learning when both conceptual and operative definitions of awareness are lacking. This approach was first proposed by Reingold & Merikle (1988) in the context of subliminal perception. In this paper, we apply it to a choice reaction time task in which the material is generated based on a probabilistic finite-state grammar (Cleeremans, 1993). We show (1) that participants progressively (...) learn about the statistical structure of the stimulus material over training with the choice reaction time task, and (2) that they can use some of this knowledge to predict the location of the next stimulus in a subsequent “generation” task. However, detailed partial correlational analyses of the correspondence between performance during the reaction time task and the statistical structure of the training material showed that large effects remained even when controlling for explicit knowledge as assessed by the generation task. Hence we conclude (1) that at least some of the knowledge expressed through reaction time performance can not be characterized as conscious, and (2) that even when associations are found at a global level of analysis, dissociations can still be obtained when more detailed analyses are conducted. Finally, we also show that participants are limited in the depth of the contingencies they can learn about, and that these limitations are shared by the Simple Recurrent Network model of Cleeremans & McClelland (1991). (shrink)

Łukasiewicz three-valued logic Ł3 is often understood as the set of all 3-valued valid formulas according to Łukasiewicz’s 3-valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: “well-determined” Ł3a and “truth-preserving” Ł3b defined by two different consequence relations on the 3-valued matrices. The aim of this paper is to provide (by using Dunn semantics) dual equivalent two-valued under-determined and over-determined interpretations for Ł3, Ł3a and Ł3b. The logic Ł3 is axiomatized as an extension of Routley (...) and Meyer’s basic positive logic following Brady’s strategy for axiomatizing many-valued logics by employing two-valued under-determined or over-determined interpretations. Finally, it is proved that “well determined” Łukasiewicz logics are paraconsistent. (shrink)

Łukasiewicz 3-valued logic Ł3 is often understood as the set of all valid formulas according to Łukasiewicz 3-valued matrices MŁ3. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: ‘truth-preserving’ Ł3a and ‘well-determined’ Ł3b defined by two different consequence relations on the 3-valued matrices MŁ3. The aim of this article is to provide a Routley–Meyer ternary semantics for each one of these three versions of Łukasiewicz 3-valued logic: Ł3, Ł3a and Ł3b.

In Rogerson and Restall’s, the “class of implication formulas known to trivialize ” is recorded. The aim of this paper is to show how to invalidate any member in this class by using “weak relevant model structures”. Weak relevant model structures verify deep relevant logics only.

Łukasiewicz three-valued logic Ł3 is often understood as the set of all 3-valued valid formulas according to Łukasiewicz’s 3-valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: “well-determined” Ł3a and “truth-preserving” Ł3b defined by two different consequence relations on the 3-valued matrices. The aim of this paper is to provide dual equivalent two-valued under-determined and over-determined interpretations for Ł3, Ł3a and Ł3b. The logic Ł3 is axiomatized as an extension of Routley and Meyer’s basic positive (...) logic following Brady’s strategy for axiomatizing many-valued logics by employing two-valued under-determined or over-determined interpretations. Finally, it is proved that “well determined” Łukasiewicz logics are paraconsistent. (shrink)

Equivalent overdetermined and underdetermined bivalent Belnap–Dunn type semantics for the logics determined by all natural implicative expansions of Kleene’s strong 3-valued matrix with only one designated value are provided.

Łukasiewicz presented two different analyses of modal notions by means of many-valued logics: the linearly ordered systems Ł3,..., Open image in new window,..., \; the 4-valued logic Ł he defined in the last years of his career. Unfortunately, all these systems contain “Łukasiewicz type paradoxes”. On the other hand, Brady’s 4-valued logic BN4 is the basic 4-valued bilattice logic. The aim of this paper is to show that BN4 can be strengthened with modal operators following Łukasiewicz’s strategy for defining truth-functional (...) modal logics. The systems we define lack “Łukasiewicz type paradoxes”. Following Brady, we endow them with Belnap–Dunn type bivalent semantics. (shrink)

The aim of this paper is to define the logical system Sm4 characterised by the degree of truth-preserving consequence relation defined on the ordered set of values of Smiley’s four-element matrix MSm4. The matrix MSm4 has been of considerable importance in the development of relevant logics and it is at the origin of bilattice logics. It will be shown that Sm4 is a most interesting paraconsistent logic which encloses a sound theory of logical necessity similar to that of Anderson and (...) Belnap’s logic of entailment E. Intuitively, Sm4 can be described as a four-valued expansion of the positive fragment of Lewis’ S5 or, alternatively, as a four-valued version of S5. (shrink)

IntroductionCardiology is characterized by its state-of-the-art biomedical technology and the predominance of Evidence-Based Medicine. This predominance makes it difficult for healthcare professionals to deal with the ethical dilemmas that emerge in this subspecialty. This paper is a first endeavor to empirically investigate the axiological foundations of the healthcare professionals in a cardiology hospital. Our pilot study selected, as the target population, cardiology personnel not only because of their difficult ethical deliberations but also because of the stringent conditions in which they (...) have to make them. Therefore, there is an urgent need to reconsider clinical ethics and Value-Based Medicine. This study proposes a qualitative analysis of the values and the virtues of healthcare professionals in a cardiology hospital in order to establish how the former impact upon the medical and ethical decisions made by the latter.ResultsWe point out the need for strengthening the roles of healthcare personnel as educators and guidance counselors in order to meet the ends of medicine, as well as the need for an ethical discernment that is compatible with our results, namely, that the ethical values developed by healthcare professionals stem from their life history as well as their professional education.ConclusionWe establish the kind of actions, communication skills and empathy that are required to build a stronger patient-healthcare professional relationship, which at the same time improves prognosis, treatment efficiency and therapeutic adhesion. (shrink)

As it is well known, in the forties of the past century, Curry proved that in any logic S closed under Modus Ponens, uniform substitution of propositional variables and the Contraction Law, the naïve Comprehension axiom trivializes S in the sense that all propositions are derivable in S plus CA. Not less known is the fact that, ever since Curry published his proof, theses and rules weaker than W have been shown to cause the same effect as W causes. Among (...) these, the Contraction rule or the Modus Ponens axiom, for example, are to be noted. But, moreover, as Brady has proved, even the Generalized Modus Ponens axiom or the Generalized Contraction rule give rise to “Curry’s Paradox” under the same circumstances as W does. In some previous work by us, “weak relevant model structures” are defined on “weak relevant matrices” by generalizing Brady’s model structure MCL built upon Meyer’s Crystal matrix CL. We have proved that wr-ms only verify logics with the “depth relevance condition”. The aim of this paper is to show how to falsify gMPa and gRW in certain wr-ms. In particular, it will be shown that gMPa is falisfied in any wr-ms and gRW in any wr-ms verifying Routley and Meyer’s basic positive logic B+. (shrink)

We provide Routley-Meyer type semantics for relevant logics including Contractionless Ticket Entailment TW (without the truth constant t and o) plus reductio R and Ackermann’s rule γ (i.e., disjunctive syllogism). These logics have the following properties. (i) All have the variable sharing property; some of them have, in addition, the Ackermann Property. (ii) They are stable. (iii) Inconsistent theories built upon these logics are not necessarily trivial.

Our question is: can we embed minimal negation in implicative logics weaker than I→? Previous results show how to define minimal negation in the positive fragment of the logic of relevance R and in contractionless intuitionistic logic. Is it possible to endow weaker positive logics with minimal negation? This paper prooves that minimal negation can be embedded in even such a weak system as Anderson and Belnap’s minimal positive logic.

Cardiology is characterized by its state-of-the-art biomedical technology and the predominance of Evidence-Based Medicine. This predominance makes it difficult for healthcare professionals to deal with the ethical dilemmas that emerge in this subspecialty. This paper is a first endeavor to empirically investigate the axiological foundations of the healthcare professionals in a cardiology hospital. Our pilot study selected, as the target population, cardiology personnel not only because of their difficult ethical deliberations but also because of the stringent conditions in which they (...) have to make them. Therefore, there is an urgent need to reconsider clinical ethics and Value-Based Medicine. This study proposes a qualitative analysis of the values and the virtues of healthcare professionals in a cardiology hospital in order to establish how the former impact upon the medical and ethical decisions made by the latter. (shrink)

The logic DHb is the result of extending Sylvan and Plumwood’s minimal De Morgan logic BM with a dual intuitionistic negation of the type Sylvan defined for the extension CCω of da Costa’s paraconsistent logic Cω. We provide Routley–Meyer ternary relational semantics with a set of designated points for DHb and a wealth of its extensions included in G3DH, the expansion of G3+ with a dual intuitionistic negation of the kind considered by Sylvan (G3+ is the positive fragment of Gödelian (...) 3-valued logic G3). All logics in the paper are paraconsistent. (shrink)

The logic B+ is Routley and Meyer’s basic positive logic. We define the logics BK+ and BK'+ by adding to B+ the K rule and to BK+ the characteristic S4 axiom, respectively. These logics are endowed with a relatively strong non-constructive negation. We prove that all the logics defined lack the K axiom and the standard paradoxes of consistency.

A restriction of R-Mingle with the variable-sharing property and the Ackermann properties is defined. From an intuitive semantical point of view, this restriction is an alternative to Anderson and Belnap’s logic of entailment E.

The aim of this paper is to provide a Routley-Meyer semantics for Ackermann’s logics of “strenge Implikation” Π ′ and Π ′′ . Besides the Disjunctive Syllogism, this semantics validates the rules Necessitation and Assertion. Strong completeness theorems for Π ′ and Π ′′ are proved. A brief discussion on Π ′ , Π ′′ and paraconsistency is included.

IntroductionCardiology is characterized by its state-of-the-art biomedical technology and the predominance of Evidence-Based Medicine. This predominance makes it difficult for healthcare professionals to deal with the ethical dilemmas that emerge in this subspecialty. This paper is a first endeavor to empirically investigate the axiological foundations of the healthcare professionals in a cardiology hospital. Our pilot study selected, as the target population, cardiology personnel not only because of their difficult ethical deliberations but also because of the stringent conditions in which they (...) have to make them. Therefore, there is an urgent need to reconsider clinical ethics and Value-Based Medicine. This study proposes a qualitative analysis of the values and the virtues of healthcare professionals in a cardiology hospital in order to establish how the former impact upon the medical and ethical decisions made by the latter.ResultsWe point out the need for strengthening the roles of healthcare personnel as educators and guidance counselors in order to meet the ends of medicine, as well as the need for an ethical discernment that is compatible with our results, namely, that the ethical values developed by healthcare professionals stem from their life history as well as their professional education.ConclusionWe establish the kind of actions, communication skills and empathy that are required to build a stronger patient-healthcare professional relationship, which at the same time improves prognosis, treatment efficiency and therapeutic adhesion. (shrink)

Fairness is central to the ethical and responsible development and use of AI systems, with a large number of frameworks and formal notions of algorithmic fairness being available. However, many of the fairness solutions proposed revolve around technical considerations and not the needs of and consequences for the most impacted communities. We therefore want to take the focus away from definitions and allow for the inclusion of societal and relational aspects to represent how the effects of AI systems impact and (...) are experienced by individuals and social groups. In this paper, we do this by means of proposing the ACROCPoLis framework to represent allocation processes with a modeling emphasis on fairness aspects. The framework provides a shared vocabulary in which the factors relevant to fairness assessments for different situations and procedures are made explicit, as well as their interrelations. This enables us to compare analogous situations, to highlight the differences in dissimilar situations, and to capture differing interpretations of the same situation by different stakeholders. (shrink)