Family firms are ubiquitous and play a crucial role across all world economies, but how they differ in the disclosure of social and environmental actions from non-family firms has been largely overlooked in the literature. Advancing the discourse on corporate social responsibility reporting, we examine how family influence on a business organization affects CSR reporting. The arguments developed here draw on institutional theory, using a rich body of empirical evidence gathered through a content analysis of the CSR reports of 98 (...) large- and medium-sized Italian firms. The grounded theory analysis informs and contextualizes several differences in the type and content of corporate social responsibility reports of family and non-family firms. Our findings show that in comparison to non-family firms, family firms disseminate a greater variety of CSR reports, are less compliant with CSR standards and place emphasis on different CSR topics. We, thus, contribute to the family business and corporate social responsibility reporting literatures in several ways, offering implications for practice and outlining promising avenues for future research. (shrink)
The inclusion of morally binding values such as religious—or in a broader sense, spiritual—values fundamentally alter organizational decision-making and ethical behavior. Family firms, being a particularly value-driven type of organization, provide ample room for religious beliefs to affect family, business, and individual decisions. The influence that the owning family is able to exert on value formation and preservation in the family business makes religious family firms an incubator for value-driven and faith-led decision-making and behavior. They represent a particularly rich and (...) relevant context to re-assess the relationship between ethical beliefs, decision-making processes and behaviors in business organizations at the interface between family and professional logics. This Special Issue is dedicated to deepening our understanding of the role religious values and spirituality play in the formation of organizational ethical practices in faith-led family firms and resulting organizational and family-related outcomes. In this editorial, we introduce the 10 papers included in this Special Issue, which investigate the relationship between religion or spirituality and family firm ethical behavior in various geographical, cultural and religious contexts, using a multitude of qualitative and quantitative methodologies. By focusing on the effects of religious or spiritual orientations on both the business and the family, as well as on the values, norms and goals present in the family business system, further research can gain a more nuanced understanding of the relationship between religious and spiritual believes, and sustainable ethical behavior in family firms. (shrink)
The thesis of the extended mind (ExM) holds that the material underpinnings of an individual’s mental states and processes need not be restricted to those contained within biological boundaries: when conditions are right, material artefacts can be incorporated by the thinking subject in such a way as to become a component of her extended mind. Up to this point, the focus of this approach has been on phenomena of a distinctively cognitive nature, such as states of dispositional belief, and processes (...) of planning and calculation. In this paper, we aim to expand the scope of ExM by considering the case for extended affectivity. We begin by clarifying the central commitments of ExM, before investigating its applicability to a range of affective phenomena, both dispositional and occurrent. We argue that proponents of ExM should also accept that the vehicles of emotions, moods, sentiments, temperaments, and character traits can extend beyond skull and skin. (shrink)
Self-disorders in depression and schizophrenia have been the focus of much recent work in phenomenological psychopathology. But little has been said about the role the material environment plays in shaping the affective character of these disorders. In this paper, we argue that enjoying reliable (i.e., trustworthy) access to the things and spaces around us — the constituents of our material environment — is crucial for our ability to stabilize and regulate our affective life on a day-today basis. These things and (...) spaces often play an ineliminable role in shaping what we feel and how we feel it; when we interact with them, they contribute ongoing feedback that " scaffolds " the character and temporal development of our affective experiences. However, in some psychopathological conditions, the ability to access to these things and spaces becomes disturbed. Individuals not only lose certain forms of access to the practical significance of the built environment but also to its regulative significance, too — and the stability and organization of their affective life is compromised. In developing this view, we discuss core concepts like " affordance spaces " , " scaffolding " , and " incorporation ". We apply these concepts to two case studies, severe depression and schizophrenia, and we show why these cases support our main claim. We conclude by briefly considering implications of this view for developing intervention and treatment strategies. (shrink)
The idea for _Philosophy in a Time of Terror_ was born hours after the attacks on 9/11 and was realized just weeks later when Giovanna Borradori sat down with Jürgen Habermas and Jacques Derrida in New York City, in separate interviews, to evaluate the significance of the most destructive terrorist act ever perpetrated. This book marks an unprecedented encounter between two of the most influential thinkers of our age as here, for the first time, Habermas and Derrida overcome their (...) mutual antagonism and agree to appear side by side. As the two philosophers disassemble and reassemble what we think we know about terrorism, they break from the familiar social and political rhetoric increasingly polarized between good and evil. In this process, we watch two of the greatest intellects of the century at work. (shrink)
In this paper, we start exploring the affective and ethical dimension of what De Jaegher and Di Paolo (Phenomenology and the Cognitive Sciences, 6:485–507, 2007 ) have called ‘participatory sense-making’. In the first part, we distinguish various ways in which we are, and feel, affectively inter-connected in interpersonal encounters. In the second part, we discuss the ethical character of this affective inter-connectedness, as well as the implications that taking an ‘inter-(en)active approach’ has for ethical theory itself.
In this paper we adopt Sterelny's framework of the scaffolded mind, and his related dimensional approach, to highlight the many ways in which human affectivity is environmentally supported. After discussing the relationship between the scaffolded-mind view and related frameworks, such as the extended-mind view, we illustrate the many ways in which our affective states are environmentally supported by items of material culture, other people, and their interplay. To do so, we draw on empirical evidence from various disciplines, and develop phenomenological (...) considerations to distinguish different ways in which we experience the world affectively. (shrink)
In this lively look at current debates in American philosophy, leading philosophers talk candidly about the changing character of their discipline. In the spirit of Emerson's The American Scholar , this book explores the identity of the American philosopher. Through informal conversations, the participants discuss the rise of post-analytic philosophy in America and its relations to European thought and to the American pragmatist tradition. They comment on their own intellectual development as well as each others' work, charting the course of (...) American philosophy over the past few decades. Giovanna Borradori, in her substantial introduction, explains the history of the analytic movement in America and the home-grown reaction against it. In the late nineteenth and early twentieth centuries, American philosophy was a socially engaged interdisciplinary enterprise. In transcendentalism and pragmatism, then the dominant currents in American thought, philosophy was connected to history, psychology, and public issues. But in the 1930s, the imported European movement of logical positivism redefined philosophical discourse in terms of mathematical logic and theory of language. Under the influence of this analytic view, American philosophy became a professionalized discipline, divorced from public debate and intellectual history and antagonistic to the other, more humanistic tradition of continental thought. The American Philosopher explores the opposition between analytic and continental thought and shows how recent American work has begun to bridge the gap between the two traditions. Through a reexamination of pragmatism, and through an attempt to understand philosophy in a more hermeneutical way, the participants narrow the distance between America's distinctly scientific philosophy and Europe's more literary approach. Moving beyond classical analytic philosophy, the participants confront each other on a number of topics. The logico-linguistic orientations of Quine and Davidson come up against the more discursive, interdisciplinary agendas of Rorty, Putnam, and Cavell. Nozick's theory of pluralist anarchism goes face-to-face with the aesthetic neo-foundationalism of Danto. And Kuhn's hypothesis of paradigm shifts is measured against MacIntyre's ethics of "virtues." Borradori's conversations offer an unconventional portrait of the way philosophers think about their work scholars and students will not be its only beneficiaries, so will everyone who wonders about the current state of American philosophy. (shrink)
The experience of agency refers to the feeling that we control our own actions, and through them the outside world. In many contexts, sense of agency has strong implications for moral responsibility. For example, a sense of agency may allow people to choose between right and wrong actions, either immediately, or on subsequent occasions through learning about the moral consequences of their actions. In this study we investigate the relation between the experience of operant action, and responsibility for action outcomes (...) using the intentional binding effect as an implicit, quantitative measure related to sense of agency. We studied the time at which people perceived simple manual actions and their effects, when these actions were embedded in scenarios where their actions had unpredictable consequences that could be either moral or merely economic. We found an enhanced binding of effects back towards the actions that caused them, implying an enhanced sense of agency, in moral compared to non-moral contexts. We also found stronger binding for effects with severely negative, compared to moderately negative, values. A tight temporal association between action and effect may be a low-level phenomenal marker of the sense of responsibility. (shrink)
Predicate extensions of the intermediate logic of the weak excluded middle and of the modal logic S4.2 are introduced and investigated. In particular it is shown that some of them are characterized by subclasses of the class of directed frames with either constant or nested domains.
The paper presents an epistemic logic with quantification over agents of knowledge and with a syntactical distinction between de re and de dicto occurrences of terms. Knowledge de dicto is characterized as ‘knowledge that’, and knowlegde de re as ‘knowledge of’. Transition semantics turns out to be an adequate tool to account for the distinctions introduced.
For many years emotion theory has been characterized by a dichotomy between the head and the body. In the golden years of cognitivism, during the nineteen-sixties and seventies, emotion theory focused on the cognitive antecedents of emotion, the so-called “appraisal processes.” Bodily events were seen largely as byproducts of cognition, and as too unspecific to contribute to the variety of emotion experience. Cognition was conceptualized as an abstract, intellectual, “heady” process separate from bodily events. Although current emotion theory has moved (...) beyond this disembodied stance by conceiving of emotions as involving both cognitive processes (perception, attention, and evaluation) and bodily events (arousal, behavior, and facial expressions), the legacy of cognitivism persists in the tendency to treat cognitive and bodily events as separate constituents of emotion. Thus the cognitive aspects of emotion are supposedly distinct and separate from the bodily ones. This separation indicates that cognitivism’s disembodied conception of cognition continues to shape the way emotion theorists conceptualize emotion. (shrink)
In this paper I advance an enactive view of affectivity that does not imply that affectivity must stop at the boundaries of the organism. I first review the enactive notion of “sense-making”, and argue that it entails that cognition is inherently affective. Then I review the proposal, advanced by Di Paolo, that the enactive approach allows living systems to “extend”. Drawing out the implications of this proposal, I argue that, if enactivism allows living systems to extend, then it must also (...) allow sense-making, and thus cognition as well as affectivity, to extend—in the specific sense of allowing the physical processes underpinning these phenomena to include, as constitutive parts, non-organic environmental processes. Finally I suggest that enactivism might also allow specific human affective states, such as moods, to extend. (shrink)
The theory of autopoiesis is central to the enactive approach. Recent works emphasize that the theory of autopoiesis is a theory of sense-making in living systems, i.e. of how living systems produce and consume meaning. In this chapter I first illustrate (some aspects of) these recent works, and interpret their notion of sense-making as a bodily cognitive- emotional form of understanding. Then I turn to modern emotion science, and I illustrate its tendency to over-intellectualize our capacity to evaluate and understand. (...) I show that this overintellectualization goes hand in hand with the rejection of the idea that the body is a vehicle of meaning. I explain why I think that this over-intellectualization is problematic, and try to reconceptualize the notion of evaluation in emotion theory in a way that is consistent and continuous with the autopoietic notion of sense-making. (shrink)
In this paper I argue that it is misleading to regard the brain as the physical basis or “core machinery” of moods. First, empirical evidence shows that brain activity not only influences, but is in turn influenced by, physical activity taking place in other parts of the organism. It is therefore not clear why the core machinery of moods ought to be restricted to the brain. I propose, instead, that moods should be conceived as embodied, i.e., their physical basis should (...) be enlarged so as to comprise not just brain but also bodily processes. Second, I emphasise that moods are also situated in the world. By this I do not simply mean that moods are influenced by the world, but that they are complexly interrelated with it, in at least three different ways: they are shaped by cultural values and norms; they are materially and intersubjectively “scaffolded”; and they can even “experientially incorporate” parts of the world, i.e., include the experience of parts of the world as part of oneself. (shrink)
The Feeling Body applies several ideas from the enactive approach to the field of affective science, with the aim of both developing enactivism as well as reconceptualizing various affective phenomena. The book is organized into six chapters that examine primordial affectivity (chapter 1), the nature of emotional episodes and moods (chapters 2 and 3), enactive appraisal (chapter 4), the bodily feelings associated with emotional experience (chapter 5), affective neuro-physio-phenomenology (chapter 6), and the affective dimension of intersubjectivity (chapter 7). Giovanna (...) Colombetti’s discussion of these topics effectively integrates scientific research and phenomenological descriptions of lived experience. What results is an insightful and genuinely interdisciplinary discussion of emotion that will be of interest to affective scientists, emotion theorists, phenomenologists, and proponents of enactivism.The version of enactivism that Colombetti draws upon is the theory originally formula .. (shrink)
Emotion theorists tend to separate “arousal” and other bodily events such as “actions” from the evaluative component of emotion known as “appraisal.” This separation, I argue, implies phenomenologically implausible accounts of emotion elicitation and personhood. As an alternative, I attempt a reconceptualization of the notion of appraisal within the so-called “enactive approach.” I argue that appraisal is constituted by arousal and action, and I show how this view relates to an embodied and affective notion of personhood.
‘Valence’ is used in many different ways in emotion theory. It generally refers to the ‘positive’ or ‘negative’ character of an emotion, as well as to the ‘positive’ or ‘negative’ character of some aspect of emotion. After reviewing these different uses, I point to the conceptual problems that come with them. In particular, I dis- tinguish: problems that arise from conflating the valence of an emotion with the valence of its aspects, and problems that arise from the very idea that (...) an emotion (and/or its aspects) can be divided into mutually exclusive opposites. The first group of problems does not question the classic dichotomous notion of valence, but the second does. In order to do justice to the richness of daily emotions, emo- tion science needs more complex conceptual tools. (shrink)
This paper presents the results of an experiment on mutual versus common knowledge of advice in a two-player weak-link game with random matching. Our experimental subjects play in pairs for thirteen rounds. After a brief learning phase common to all treatments, we vary the knowledge levels associated with external advice given in the form of a suggestion to pick the strategy supporting the payoff-dominant equilibrium. Our results are somewhat surprising and can be summarized as follows: in all our treatments both (...) the choice of the efficiency-inducing action and the percentage of efficient equilibrium play are higher with respect to the control treatment, revealing that even a condition as weak as mutual knowledge of level 1 is sufficient to significantly increase the salience of the efficient equilibrium with respect to the absence of advice. Furthermore, and contrary to our hypothesis, mutual knowledge of level 2 induces, under suitable conditions, successful coordination more frequently than common knowledge. (shrink)
In this study, we analyse the notion of “differential heterogenesis” proposed by Deleuze and Guattari on a morphogenetic perspective. We propose a mathematical framework to envisage the emergence of singular forms from the assemblages of heterogeneous operators. In opposition to the kind of differential calculus that is usually adopted in mathematical-physical modelling, which tends to assume a homogeneous differential equation applied to an entire homogeneous region, heterogenesis allows differential constraints of qualitatively different kinds in different points of space and time. (...) These constraints can then change in time, opening the possibility for new kinds of differential dynamics and the emergence of distinct entities and forms. Formally, we show that operators with different phase spaces can be assembled on the basis of a result of Rothschild & Stein. Furthermore, operators with different dynamics can be assembled by means of a partition of the unit. After stating the concept of differential heterogenesis in terms of contemporary mathematics, we show that this construction sheds light on the constitution of the semiotic function. In fact, both the Merleau-Pontian and the Deleuzian approaches share a common conceptualisation of the semiotic function and its emergence in terms of a morphodynamics of heterogeneous assemblages with a divergent actualisation. This divergent actualisation allows the co-constitution of various expression and content planes. Finally, we show that the divergent actualisation can be interpreted as the directions of principal eigenvectors of the actualized flow. (shrink)
How do we feel our body in emotion experience? In this paper I initially distinguish between foreground and background bodily feelings, and characterize them in some detail. Then I compare this distinction with the one between reflective and pre-reflective bodily self-awareness one finds in some recent philosophical phenomenological works, and conclude that both foreground and background bodily feelings can be understood as pre-reflective modes of bodily self-awareness that nevertheless differ in degree of self-presentation or self-intimation. Finally, I use the distinction (...) between foreground and background bodily feelings to characterize the experience of being absorbed in an activity, as opposed to accounts that imply that absorption involves bodily inconspicuousness. (shrink)
Although trust and reciprocity are ubiquitous in social exchange, their neurobiological substrate remains largely unknown. Here, we investigated the effect of damage to the ventromedial prefrontal cortex (vmPFC)—a brain region critical for valuing social information—on individuals’ decisions in a trust game and in a risk game. In the trust game, one player, the investor, is endowed with a sum of money, which she can keep or invest. The amount she decides to invest is tripled and sent to the other player, (...) the trustee, who then decides what fraction to return to the investor. In separate runs, ten patients with focal bilateral damage to the vmPFC and control participants made decision while playing in the role of either investor or trustee with different anonymous counterparts in each run. A risk game was also included in which the investor faced exactly the same decisions as in the trust game, but a random device (i.e., a computer), not another player, determined the final payoffs. Results showed that vmPFC patients’ investments were not modulated by the type of opponent player (e.g., human vs. computer) present in the environment. Thus, vmPFC patients showed comparable risk-taking preferences both in social (trust game) and nonsocial (risk game) contexts. In stark contrast, control participants were less willing to take risk and invest when they believed that they were interacting with people than a computer. Furthermore, when acted as trustee, vmPFC patients made lower back transfers toward investors, thereby showing less reciprocity behavior. Taken together, these results indicate that social valuation and emotion subserved by vmPFC have a critical role in trusting and reciprocity decisions. The present findings support the hypothesis that vmPFC damage may impair affective systems specifically designed for mediating social transaction with other individuals. (shrink)
Recent debates in the field of contemporary art have underlined the political importance of creative reworkings of the past, especially for those subjects that have been traditionally marginalised. A feminist perspective has been nevertheless quite absent from such debates. This article addresses feminist uses of archival documents in the visual arts through the analysis of three works produced in the past two decades: The Fae Richard's Photo Archive by Zoe Leonard and Cheryl Dunye, Some Chance Operations by Renée Green and (...) Queen of the Artists’ Studios by Andrea Geyer. These works share an interest for women's histories and representations by composing a series of documents into complex narratives where history and subjectivity intersect. (shrink)
We call affective brainocentrism the tendency to privilege the brain over other parts of the organism when defining or explaining emotions. We distinguish two versions of this tendency. According to brain-sufficient, emotional states are entirely realized by brain processes. According to brain-master, emotional states are realized by both brain and bodily processes, but the latter are entirely driven by the brain: the brain is the master regulator of bodily processes. We argue that both these claims are problematic, and we draw (...) on physiological accounts of stress to make our main case. These accounts illustrate the existence of complex interactions between the brain and endocrine systems, the immune system, the enteric nervous system, and even gut microbiota. We argue that, because of these complex brain–body interactions, the brain cannot be isolated and identified as the basis of stress. We also mention recent evidence suggesting that complex brain–body interactions characterize the physiology of depression and anxiety. Finally, we call for an alternative dynamical, systemic, and embodied approach to the study of the physiology of emotions that does not privilege the brain, but rather aims at understanding how mutually regulating brain and bodily processes jointly realize a variety of emotional states. (shrink)
According to Discrete Emotion Theory, a number of emotions are distinguishable on the basis of neural, physiological, behavioral and expressive features. Critics of this view emphasize the variability and context-sensitivity of emotions. This paper discusses some of these criticisms, and argues that they do not undermine the claim that emotions are discrete. This paper also presents some works in dynamical affective science, and argues that to conceive of discrete emotions as self-organizing and softly assembled patterns of various processes accounts more (...) naturally than traditional Discrete Emotion Theory for the variability and context-sensitivity of emotions. (shrink)
This paper distinguishes various ways in which language can act on our affect or emotion experience. From the commonsensical consideration that sometimes we use language merely to report or describe our feelings, I move on to discuss how language can constitute, clarify, and enhance them, as well as induce novel and oft surprising experiences. I also consider the social impact of putting feelings into words, including the reciprocal influences between emotion experience and the public dissemination of emotion labels and descriptions, (...) and how these influences depend on the power of labelling to make complex feelings visible and thus easily accessible. Finally, I address and reinterpret some psychological findings on the so-called “verbal overshadowing” effect. (shrink)
This paper addresses the phenomenology of bodily feeling in depersonalization disorder. We argue that not all bodily feelings are intentional states that have the body or part of it as their object. We distinguish three broad categories of bodily feeling: noematic feeling, noetic feeling, and existential feeling. Then we show how an appreciation of the differences between them can contribute to an understanding of the depersonalization experience.
The recent wave of whistleblowers and cyber-dissidents, from Julian Assange to Edward Snowden, has declared war against surveillance. In this context, transparency is presented as an attainable political goal that can be delivered in flesh and bones by spectacular and quasi-messianic moments of disclosure. The thesis of this article is that, despite its progressive promise, the project of releasing classified documents is in line with the Orwellian cold war trope of Big Brother rather than with the complex geography of surveillance (...) today. By indicting the US federal government as the principal agent of surveillance, the ‘logic of the leak’ obfuscates that today’s surveillance is conducted mostly by the private sector in the form of dataveillance. What should we think, then, of this new fetish of transparency? Is it a symptom of the castigation of a desire for surveillance, the wish to be constantly observed and closely inspected? I claim that the meaning of the ‘expository society’, as Bernard Harcourt calls it, depends on how we interpret secrets. For secrets are not only temporary conditions of occultation that can, and should, be indiscriminately exposed, but sites of agency. In this perspective, the emancipatory promise hangs on the right to the secret, assumed as the right not to answer and not to belong. (shrink)
I put forward and defend the thesis (Th) that psychophysical supervenience (PS) in its full generality can be satisfactorily supported if and only if one is willing to make one or another of some substantial assumptions (the Assumptions) about the nature of mental and physical properties. I first deal with the “if” part of the claim by presenting and considering the Assumptions. I then argue for the inadequacy of suggestions of support for PS that do not require any of the (...) Assumptions. Finally, I show that as a result of (Th) a PS claim is made potentially stronger than what it would be if (Th) were false. (shrink)
Damasio's somatic marker hypothesis (SMH) is a prominent neuroscientific hypothesis about the mechanisms implementing decision-making. This paper argues that, since its inception, the SMH has not been clearly formulated. It is possible to identify at least two different hypotheses, which make different predictions: SMH-G, which claims that somatic states generally implement preferences and are needed to make a decision; and SMH-S, which specifically claims that somatic states assist decision-making by anticipating the long-term outcomes of available options. This paper also argues (...) that neither hypothesis is adequately supported empirically; the task originally proposed to test SMH is not a good test for SMH-S, and its results do not support SMH-G either. In addition, it is not clear how SMH-G could be empirically invalidated, given its general formulation. Suggestions are made that could help provide evidence for SMH-S, and make SMH-G more specific. 1 Introduction 2 Two Hypotheses: Somatic Markers as Embodied Preferences, and as a Source of Farsightedness 3 Lack of Evidence for Somatic Farsightedness 4 Does Making Decisions Require Somatic Markers, and can it be Shown in the Laboratory? 5 Conclusion CiteULike Connotea Del.icio.us What's this? (shrink)
This commentary makes three points: (1) There may be no clear-cut distinction between emotion and appraisal “constituents” at neural and psychological levels. (2) The microdevelopment of an emotional interpretation contains a complex microdevelopment of affect. (3) Neurophenomenology is a promising research program for testing Lewis's hypotheses about the neurodynamics of emotion-appraisal amalgams.
I put forward and defend the thesis that psychophysical supervenience in its full generality can be satisfactorily supported if and only if one is willing to make one or another of some substantial assumptions about the nature of mental and physical properties. I first deal with the “if” part of the claim by presenting and considering the Assumptions. I then argue for the inadequacy of suggestions of support for PS that do not require any of the Assumptions. Finally, I show (...) that as a result of a PS claim is made potentially stronger than what it would be if were false. (shrink)
The aim of the paper is to investigate the effects of the corporate governance model on social and environmental disclosure (SED). We analyze the disclosures of the 100 U.S. Best Corporate Citizens in the period 2005–2007, and we posit a series of simultaneous relationships between different attributes of the governance system and a multidimensional construct of corporate social performance (CSP). We consider both the extent and the quality of SED, with the purpose of identifying increasing levels of corporate commitment to (...) stakeholders and shedding some light on whether SED is used as a signal or rather as a legitimacy tool. Our empirical evidence shows that the stakeholders’ orientation of corporate governance is positively associated with CSP and SED. On the other hand, we do not find support for the monitoring intensity of corporate governance being negatively associated with social performance. We also find that CSP in the “product” dimension is positively associated with the extent and quality of SED whilst CSP in the “people” dimension is negatively associated with the extent and quality of SED. At a time when shareholders and stakeholders share more common aspects in their relationships with firms, this is a significant area to explore and this research fills an important lacuna in this respect. (shrink)
In this paper we first recall geometrical models of neurogeometical in Lie groups and we show that geometrical properties of horizontal cortical connectivity can be considered as a neural correlate of a geometry of the visual plane. Then we introduce a new model of non isotropic cortical connectivity modeled on statistics of images. In this way we are able to justify oblique phenomena comparable with experimental findings.
Dummett's logic LC quantified, Q-LC, is shown to be characterized by the extended frame Q+, ,D, where Q+ is the set of non-negative rational numbers, is the numerical relation less or equal then and D is the domain function such that for all v, w Q+, Dv and if v w, then D v . D v D w . Moreover, simple completeness proofs of extensions of Q-LC are given.
We discuss the interpolation property on some important families of non classical logics, such as intuitionistic, modal, fuzzy, and linear logics. A special paragraph is devoted to a generalization of the interpolation property, uniform interpolation.
A general strategy for proving completeness theorems for quantified modal logics is provided. Starting from free quantified modal logic K, with or without identity, extensions obtained either by adding the principle of universal instantiation or the converse of the Barcan formula or the Barcan formula are considered and proved complete in a uniform way. Completeness theorems are also shown for systems with the extended Barcan rule as well as for some quantified extensions of the modal logic B. The incompleteness of (...) Q°.B + BF is also proved. (shrink)