Evidence has shown that negative distracting stimuli are most difficult to control when we are focused in a relevant task, while positive and neutral distractors might be equally overcome. Still, r...

Forgiveness seeking after a relational transgression is an important aspect of relational repair from an interpersonal perspective, although it has received much less attention than the process of granting forgiveness. This research focuses on the victim's perspective of the transgressor's behaviors and how they are related to forgiveness and offense characteristics. This paper proposes a multidimensional concept of seeking forgiveness that includes four dimensions: apologies, restorative action, relational caring behaviors, and diverting behaviors. A questionnaire for assessing these dimensions was developed (...) and tested with a general population sample of 450 subjects. Participants recalled a specific offense and then answered a questionnaire about the perceived usefulness of different forgiveness-seeking behaviors, a forgiveness inventory, and several questions regarding the characteristics of the offense. Our results support the four-factor structure of the questionnaire. As the perceived intentionality of the offense increases, behaviors that are directly related to the transgression, such as apologies and restorative actions, are experienced as less useful for forgiveness. The more hurtful the offense, the less useful the diverting behaviors are. Behavior such as apologies and restorative action are related to a lower motivation for revenge, while all forgiveness-seeking behaviors are related to an increase in feelings of benevolence toward the offender. (shrink)

For this issue of JBE, Zyphur and Pierides :1–16, 2017) have written a paper on a concept that they have labeled relational validity. The purpose of the paper and of their advocacy for the concept of relational validity is to improve the way that quantitative research is done by expanding our understanding of its ethics-laden aspects. I agree entirely with the authors that every decision regarding QR is an ethics-laden one and that our research as a whole would be improved (...) by recognition of this fact. I disagree with the authors regarding some of the ways that this improvement might be brought about. (shrink)

Each science has its own domain of investigation, but one and the same science can be formalized in different languages with different universes of discourse. The concept of the domain of a science and the concept of the universe of discourse of a formalization of a science are distinct, although they often coincide in extension. In order to analyse the presuppositions and implications of choices of domain and universe, this article discusses the treatment of omega arguments in three very different (...) formalizations of arithmetic. In Peano's formalization the domain is a restricted class of individuals, while the universe of discourse is the unrestricted class of all individuals. In Gödel's formalization the domain is a restricted class of individuals as in Peano's formalization, but the universe of discourse coincides with the domain. In Whitehead-Russell's formalization the domain is a class of logical notions in Tarski's sense, that are necessarily not individuals, whereas the universe of discourse is the unrestricted class of individuals as in Peano's formalization. The present approach emphasizes the viewpoint that the universe of discourse of a given discourse is important in determining which propositions are expressed by which sentences. (shrink)

Tarski's 1936 paper, “On the concept of logical consequence”, is a rather philosophical, non-technical paper that leaves room for conflicting interpretations. My purpose is to review some important issues that explicitly or implicitly constitute its themes. My discussion contains four sections: terminological and conceptual preliminaries, Tarski's definition of the concept of logical consequence, Tarski's discussion of omega-incomplete theories, and concluding remarks concerning the kind of conception that Tarski's definition was intended to explicate. The third section involves subsidiary issues, such as (...) Tarski's discussion concerning the distinction between material and formal consequence and the important question ofthe criterion for distinguishing between logical and non-logical terms.§1. Preliminaries. In this paper an argument is a two-part system composed of a set of propositions P and a single proposition c. The expression ‘c is a [logical] consequence of P’ is used with the same meaning as the expression ‘c is [logically] implied by P’. The expressions ‘is a logical consequence of’ and the converse ‘implies’ are relational. Often, I shall be talking in the same sense of validity of an argument. Validity is a property of arguments; an argument with premise-set P and conclusion c is valid if and only if P implies c; i.e., c is a logical consequence of P. Notice that this notion of argument is strictly ontic; it does not involve any agent that thinks, determines or establishes that a given proposition is or is not a consequence of a given set of propositions. (shrink)

Going from cognitive theory to neural data to ACT‐R models, the authors relate brain activity in a lexical ambiguity priming task to brain processes that resolve ambiguity in word meanings. These detailed data were tested and found compatible to the results of an ACT‐R computational model of reinforcement learning (RL). The model confirms and extends the behavioral findings to provide a RL account of individual differences in lexical ambiguity resolution.

Scholars have long debated whether leader's integrity affects managerial decision making with respect to social responsibility. In this paper, we propose a model in which transformational leadership mediates integrity and corporate social responsibility and examine the relationship between these concepts. A survey of 170 senior managers from 50 organizations was conducted. Results indicate that integrity is a predictor of transformational leadership behavior and that transformational leaders’ behaviors are linked to CSR practices. It was also found that leaders rated with higher (...) integrity are engaged in CSR because they exhibit more transformational leadership behaviors. These findings add to the extant literature by demonstrating that integrity is important as transformational leaders engage more actively on ‘responsible’ behaviors. Practical implications call for an understanding among corporate leaders of the benefits of integrity and how it relates to transformational leadership. Organizations can improve their selection and leadership development processes by focusing on these two dimensions. (shrink)

This article discusses two coextensive concepts of logical consequence that are implicit in the two fundamental logical practices of establishing validity and invalidity for premise-conclusion arguments. The premises and conclusion of an argument have information content (they ?say? something), and they have subject matter (they are ?about? something). The asymmetry between establishing validity and establishing invalidity has long been noted: validity is established through an information-processing procedure exhibiting a step-by-step deduction of the conclusion from the premise-set. Invalidity is established by (...) exhibiting a countermodel satisfying the premises but not the conclusion. The process of establishing validity focuses on information content; the process of establishing invalidity focuses on subject matter. Corcoran's information-theoretic concept of logical consequence corresponds to the former. Tarski's model-theoretic concept of logical consequence formulated in his famous 1936 no-countermodels definition corresponds to the latter. Both are found to be indispensable for understanding the rationale of the deductive method and each complements the other. This study discusses the ontic question of the nature of logical consequence and the epistemic question of the human capabilities presupposed by practical applications of these two concepts as they make validity and invalidity accessible to human knowledge. (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.

En su anuncio del Evangelio dentro del horizonte helenístico, San Pablo encuentra los valores y aberraciones de la cultura pagana. Ante ellos, la fe exige una selección capaz de sacar las consecuencias prácticas de la búsqueda de la verdad y de Dios provocada por Dios. Lejos de caer en el eclecticismo, el apóstol ha encontrado en la “milicia cristocéntrica” el principio unificador y animador de su síntesis. Desde ella, plantea una teología cristocéntrica abierta a la humanitas christiana, en las claves (...) desarrolladas después por los teólogos de la Patrística. Trascendiendo las verdades de los filósofos y sin vararse en ellas, el creyente recibe como un don en Cristo el más alto nivel de la verdad: “Yo soy la VERDAD” (Jn 14,6). Él es la recapitulación de todo lo bueno y verdadero que han dicho los hombres. (shrink)

Ningún luriter debe leerse lejos de su propio Sitz im Leben. El de Parménides se sitúa en el sur de Italia a finales del siglo VI y principios del VII. Se trata de un entorno cultural rico en comunidades órficas y pitagóricas, en el que el antiguo orden mítico-feudal está siendo superado y el politeísmo de Homero es objeto de severas críticas. En consecuencia, el poema de Parménides está impregnado de un profundo ímpetu religioso, que se convierte en la piedra (...) angular de su correcta interpretación. Un análisis riguroso de los fragmentos 6 y 7, en los que se discute ampliamente la tercera vía, muestra, en primer lugar, que esos fragmentos constituyen una unidad autónoma dentro de la obra, que no puede relacionarse con ninguna otra de sus partes; y, en segundo lugar, que una interpretación convincente de esa tercera vía apoya la lectura teológica del poema, como sugiere W. Jaeger, y al mismo tiempo preserva la perfecta coherencia del pensamiento parmedineano frente a otras interpretaciones más recientes, empezando por Burnet y Reinhardt. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Aristotle Rules, OK?José M. Villagrán (bio) and Rogelio Luque (bio)KeywordsAristotle, causes, philosophy, psychiatry, psychopathologyPérez-Alvarez, Sass, and García-Montes (2008) propose a theoretical approach to the nature of mental disorders (MD) that attempts to explain the type of reality they constitute. In line with this approach, they argue that (1) MDs should be considered not from within psychology and psychiatry, but rather from the realm of philosophy, so as to (...) avoid what they call the Charcot effect; (2) the resulting theoretical model is in contrast to naturalist models such as that of internal dysfunction, and involves “strong” constructivist assumptions from which they develop an anthropological perspective based on the clinician–patient situation; 3) this model is applicable, in principle, to all MDs (“at least to some extent”); and (4) it is based on the Aristotelian theory of the four causes.We would argue, however, that (1) it is precisely from within psychology and psychiatry that conceptual models accounting for MDs should be proposed; (2) the naturalist–constructivist dichotomy in these models should be deconstructed, and primacy given not to the ontological approach but to the epistemological one; (3) a theoretical model of this scope should account not only for MDs but also for physical disorders; and (4) only in this way would the Aristotelian theory of causes, understood as types of explanation (and therefore as epistemological approaches) be useful.Approaches from within and from WithoutFor Berrios (2006), the theoretical discourse in relation to the conceptualization of MDs in a particular sociocultural context can be formulated in two ways: on the one hand, in a centripetal fashion, using established philosophical systems (be it phenomenology [Jaspers 1977], logical empiricism [Hempel 1994], or analytic philosophy [Fulford, Thornton, and Graham 2006]). This centripetal approach can be used both by professional philosophers and by psychiatrists/psychologists. When developed by professional philosophers, such proposals, despite their possible brilliance, run the risk of being tangential to the psychiatric issues owing to a lack of first-hand experience of them (Murphy 2006). When developed by psychiatrists and psychologists, the majority of the proposals simply mix fragments of different philosophical systems, in either a kind of syncretism or collage that fails to take into account the contradictions between fragments, or a kind of pluralism that reflects, without entering into analysis, a sort of consensus among the different paradigms (Ghaemi 2003; Kendler 2005).A second way of formulating this theoretical discourse (according to Berrios) would employ a centrifugal approach from the very core of the disciplines, through the reflection of professionals (primarily, although not only, psychiatrists/psychologists with philosophical training) who would conceptualize the problems from within and develop a specific metalanguage for analyzing [End Page 265] them (Lanteri-Laura 1991; Reznek 1991; Sass 1992). Not all problems are of the same type. For those that are extrinsic to psychiatry/psychology (definition of the mental, the mind–body relationship, the distinction between causes and reasons, or interdisciplinary reduction), the methods common to the philosophy of science and of the mind can be used. However, issues intrinsic to the disciplines themselves (the nature of mental symptoms and how they are generated, how to explain their heterogeneity, what a MD is, how to diagnose and classify it, or how to implement a psychopathological project) cannot be dealt with using preestablished formulas, and require new and original proposals that take into account the nature of the disciplines and their object of study (Villagrán 2007).The authors of the target article base their preference for the centripetal approach for responding to one of the intrinsic questions of psychiatry (what MDs are) on the consequences of what they call the Charcot effect, a kind of variant of observer bias applied to psychiatric diagnosis. They offer as an example the classic diagnosis ad iuvantibus in its postmodern version, namely, the efficacy of the pharmaceutical industry in contributing to creating nosological entities for which their drugs are indicated. Consequently, clinicians are not only unable to surmount the substantial epistemological obstacles that hamper attempts to theorize, but also find themselves doomed to assuming an ingenuous essentialism that considers MDs as natural kinds (such as apples, trees, or dogs) determined... (shrink)

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)

In this article, we propose a philosophical exploration on the main problems involved in two neurorights that concern autonomous action, namely free will and cognitive liberty, and sketch a possible solution to these problems by resourcing to a holistic interpretation of human actions. First, we expose the main conceptual and practical issues arising from the neuroright to “free will,” which are far from minor: the term itself is denied by some trends participating in the neurorights debate, the related concept of (...) ultimate control is also disputed, the understanding of free will depends on cultural context, and the exercise of being free to act in several domains may be covered by other regulations. Second, we analyze the historical origin of cognitive liberty, its current status, and its relation with free will. Third, we criticize the concept of decision in mainstream action theory and propose to conceive action as a unified process constituted by three explanatory, non-sequential dimensions: intention, decision, and action realization. Fourth, we discuss two possible cases involving neurotechnologies and suggest ways to interpret them according to a unified framework in which free will and cognitive liberty fall under a single neuroright to personal autonomy. Finally, we outline a recommendation to introduce freedom of thought and personal autonomy as complementary neurorights to protect both the internal and external dimensions of thought and action. (shrink)

Suplemento a / Some Additions to: Jose M. Sevilla, "Bibliografía viquiana en español", Cuadernos sobre Vico, 1, 1991, pp. 179-196 ; ID., "Añadido a la bibliografía viquiana en español", Cuadernos sobre Vico, 3, 1993, pp. 199-205 ; ID., "Nuevo añadido a la Bibliografía Viquiana en español", Cuadernos sobre Vico, 5/6, 1995-1996, pp. 419-422 ; ID., "Tercer añadido a la Bibliografía Viquiana en español", Cuadernos sobre Vico, 7/8, 1997, pp. 451-455 . 307 nuevas entradas / 307 new entries nn. 500 - (...) 807. (shrink)

Suplemento a / Some Additions to: José M. Sevilla, "Bibliografía viquiana en español" entradas / entries 1-266; ID., "Añadido a la Bibliografía viquiana en español" , entradas / entries 267-364. Ahora 62 nuevas entradas / 62 new entries now: 365-426.

The reductionist/anti-reductionist debate about testimonial justification (and knowledge) can be taken to collapse into a controversy about two kinds of underlying monitoring mechanism. The nature and structure of this mechanism remains an enigma in the debate. We suggest that the underlying monitoring mechanism amounts to emotion-based stereotyping. Our main argument in favor of the stereotype hypothesis about testimonial monitoring is that the underlying psychological mechanism responsible for testimonial monitoring has several conditions to satisfy. Each of these conditions is satisfied by (...) our “hot” stereotypical capacities. Intergroup emotions play a key role here. Intergroup emotions inform the agent about which candidate stereotype is better suited to the current situation. Emotions serve as evidence that makes a certain stereotype and its particular profile of features more or less expected. (shrink)

Emotional intelligence (EI) stands at the nexus between intelligence and emotion disciplines, and we outline how EI research might be better integrated within both theoretical frameworks. From the former discipline, empirical research focused upon whether EI is an intelligence and what type of intelligence it constitutes. It is clear that ability-based tests of EI form a group factor of cognitive abilities that may be integrated into the Cattell–Horn–Carroll framework; less clear is the lower order factor structure of EI. From the (...) latter discipline, research linking EI with theoretical frameworks from emotion research remain relatively sparse. Emotion regulation and appraisal theory may be key to explain how EI may reflect different processes. We propose a research agenda to advance the EI study. (shrink)

El concepto de razón que emerge con Vico, y que será análogo al propuesto por Ortega, no es ya el de la razón física y pura, natural y abstracta, sino el de una razón vital e histórica, la cual viene a ejercitarse y expresarse como razón narrativa : aquélla única capaz de comprender "la lingua con cui parla la storia".The concept of reason that emerges with Vico, and that is analogous to the one proposed by Ortega, is not only the (...) one of physical and pure, natural and abstract reason, but rather the one of vital and historic reason, which comes to exercise itself and express itself as narrative reason: that only capacity of comprehension "la lingua con cui parla la storia". (shrink)

Texto de la conferencia pronunciada en Estrasburgo el 19 de Noviembre de 1991, donde replanteándose ciertos aspectos recientes de la fortuna de Vico en España se aboga por la necesidad de establecer una fecunda reflexión a la vez sobre Vico y sobre nuestra propia historia.Text of conference of 19 November 1991 , where reconsidering certain aspects of the chance of Vico in Spain, the need to encourage a fruitful reflection of Vico and our own history is advocated.

En un análisis de las relaciones de Vico con el cartesianismo, se plantea una perspectiva para la comprensión de su proyecto filosófico, enfocado a una dimensión práctica de la filosofía, a través de tres estrategias epistemológicas: dos de ellas en relación al criterio verum-factum y, una tercera, en relación con el principio verum-certum.Within the context defined by Vico’s relations with Cartesianim, a perspective oriented to the understanding of Vico’s philosophical project, casted on to a practical dimension of philosophy, is purported (...) as based on three main epistemological strategies: two of them related with the verum-factum criteron and a third one with the verum-certum principle. (shrink)

In their valuable call-for-action article, Wexler and Specker Sullivan (2023) propose an integration–inclusion–impact axis for “translational neuroethics,” to face the challenges and criticisms tha...

This paper offers a particular intuitionistic negation completion of Urquhart's system C resulting in a super-intuitionistic contractionless propositional logic equivalent to Dummett's LC without contraction.

The notion of memory storage, central to most contemporary theories of remembering, is challenged from a philosophical perspective as being contradictory and untenable. It criticizes this storage hypothesis as relying upon a linear explanation of time, an assumption which results in infinite regression, solipsism, and a failure to contact the real past. A model based on the phenomenological viewpoints of Edmund Husserl and Maurice Merleau-Ponty is offered as an alternative paradigm. Finally, a research method suggested by this descriptive approach to (...) memory is presented and illustrated. (shrink)

A prepositional logic S has the Converse Ackermann Property (CAP) if (AB)C is unprovable in S when C does not contain . In A Routley-Meyer semantics for Converse Ackermann Property (Journal of Philosophical Logic, 16 (1987), pp. 65–76) I showed how to derive positive logical systems with the CAP. There I conjectured that each of these positive systems were compatible with a so-called semiclassical negation. In the present paper I prove that this conjecture was right. Relational Routley-Meyer type semantics are (...) provided for each one of the resulting systems (the positive systems plus the semiclassical negation). (shrink)

RESUMENUna de las líneas de investigación más interesantes de la actual filosofía de la psiquiatría gira en torno a la posibilidad de entender el contenido de los delirios a través de la noción wittgensteiniana de «certeza objetiva». En este artículo se mantiene que el contenido de los delirios se podría entender más fácilmente considerando la existencia de sistemas de creencias individuales y reformulando los conceptos diferenciales de dichos sistemas.PALABRAS CLAVEDELIRIO, CERTEZA OBJETIVA, CERTEZA SUBJETIVA, GRAMÁTICA, JUEGO DE LENGUAJEABSTRACTOne of the most (...) interesting research lines in recent philosophy of psychiatry deals with the possibility of understanding the content of delusions through Wittgenstein’s concept of «objective certainty». In this paper it is held that the content of delusions might be understood more easily by considering the existence of individual belief systems and reformulating the distinguishing concepts of such systems.KEYWORDSDELUSION, OBJECTIVE CERTAINTY, SUBJECTIVE CERTAINTY, GRAMMAR, LANGUAGE-GAME. (shrink)

RESUMENEl hombre moderno puede estar tentado a dar por supuesto que la diferencia entre razón y locura no fue creada en un momento dado; lejos de tal cosa, puede pensar que dicha diferencia constituye un hecho evidente, ya que será suficiente que contemple detenidamente a un loco para convencerse de que no tienen absolutamente nada en común. Sin embargo, este artículo no sólo explica en qué consiste el orden primitivo que el hombre moderno comparte con el loco, sino que además (...) ilustra las resistencias que el hombre moderno muestra al apreciar dicho orden.PALABRAS CLAVERazón, locura, orden, sociedad, voluntadABSTRACTThe modern man may be tempted to presuppose that the difference between reason and madness was not created in a certain moment; far from that, he may think that this difference constitutes an obvious fact as, just by looking carefully at a madman he may realize that they have absolutely nothing in common. However, this paper not only explains the nature of the primitive order the modern man shares with the madman, but also illustrates the resistance the modern man puts up when noticing this order.KEYWORDSReason, madness, order, society, will. (shrink)

Business Ethics, the Environment & Responsibility, EarlyView.

Unlike most American novels on the Iraq wars, which tend to be either celebratory or redemptive, Iraqi-born Sinan Antoon’s The Corspe Washer bears witness to the traumatic effects of destitu...

ResumenLa disputa del positivismo materializó la polémica entre frankfurtianos y popperianos. Pero esta oposición ha sido tan malentendida como exagerada. Entre ambas filosofías existen interesantes vinculaciones y afinidades que remiten a una raíz común: Kant. En concreto, es su optimismo ilustrado el que, según trataré de argumentar, contagia las filosofías de Horkheimer y de Popper, ambas presididas por una decidida confianza en la razón. Filosofías que representan contemporáneamente, aun desde posiciones dispares, la esencial conexión de la razón con la libertad (...) del género humano.Palabras Clave: Razón, Ilustración, dialéctica, historia, libertadAbstractThe positivist dispute exposed the argument between Horkheimer and Popper. But this opposition has been both misunderstood and exaggerated. Between these two philosophies there are interesting affinities which lead to a common root: Kant. Specifically, his illustrated optimism is the one that, as I will try to prove, is present in the philosophies of Horkheimer and Popper, since both are dominated by a determined confidence in reason. These philosophies represent in our time, from different positions, the essential connection between reason and freedom in mankind.Keywords Reason, Enlightenment, dialectics, history, freedom. (shrink)

El presente estudio contiene algunas recientes indagaciones que continúan y se agregan a anteriores trabajos del autor sobre el problema de la recepción de Vico en la cultura hispánica del siglo XIX.The present study contains some recent investigations that continue to previous works of the author on the problem of the reception of Vico during the XIX Century in the Hispanic culture.

The literature addressing bias and fairness in AI models (fair-AI) is growing at a fast pace, making it difficult for novel researchers and practitioners to have a bird’s-eye view picture of the field. In particular, many policy initiatives, standards, and best practices in fair-AI have been proposed for setting principles, procedures, and knowledge bases to guide and operationalize the management of bias and fairness. The first objective of this paper is to concisely survey the state-of-the-art of fair-AI methods and resources, (...) and the main policies on bias in AI, with the aim of providing such a bird’s-eye guidance for both researchers and practitioners. The second objective of the paper is to contribute to the policy advice and best practices state-of-the-art by leveraging from the results of the NoBIAS research project. We present and discuss a few relevant topics organized around the NoBIAS architecture, which is made up of a Legal Layer, focusing on the European Union context, and a Bias Management Layer, focusing on understanding, mitigating, and accounting for bias. (shrink)

This is a survey paper of approaches to the concept of logical implication. Roughly stated the main motivation of these approaches is to provide a necessary and sufficient condition for a set of propositions to logically imply a single proposition. In regard to their affinities these approaches are grouped into two: the transformational conception and the informational conception. Some approaches in each conception are philosophical and some are mathematical in character, their common assumption being that they reflect a previous intuition (...) – in some cases – already at work in classical mathematics. The first part of the paper is devoted to approaches within the transformational conception of logical implication emphasizing the contributions of Bolzano, Russell, Tarski, Quine and current model – theory. The second part of the paper discusses approaches within the informational conception of logical implication. Carnap and Bar Hillel’s extrinsic approach and Corcoran’s intrinsic approach developed in his information-theoretic logic are respectively compared and some of their philosophical underpinnings are brought to light. The paper concludes with some final remarks concerning the ontic question of the nature of logical implication and the epistemic question of the human access to this relation in both conceptions of logical implication. The article also attempts to connect the views of these representative thinkers with the current philosophical debate on the nature of logical consequence and the role of set-theoretic model theory in philosophy of logic. (shrink)

Estudio bibliográfico de: / A Bibliographical Study of: G. Cacciatore, Storicismo problematico e metodo critico, Guida editori, Nápoles, 1993, pp. 426.

In this article, I discuss several of the factors that jeopardize our understanding of the nature of qualitative experiences and the mind. I incorporate the view from neuroscience to clarify the na.

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)