Feminism controversially, but fundamentally, influences why and how women's groups become implicated in politics. The debates around the meaning of feminism and the practice of feminist activism have established a discourse and created common melodies as well as some dissonance among women's groups in Hungary. This article discusses different interpretations of women's status that affect how Hungarian feminism has developed in what the author sees, contrary to a more common view, as an East—West continuum. The article analyzes how women's groups (...) in Hungary create affiliations and relate to the West, both ideologically and materially. The article unfolds the many different forms of Hungarian women's groups according to different `layers' of feminist consciousness. A vital element in forming these layers has been anti-feminism and how it has sometimes hindered consciousness or perhaps made some `differently sensitive'. Subsequently, the article uses a feminist reinterpretation of politics — women's interpretations of what belongs to the private and public spheres — without which, the author claims, contemporary women's activism in Hungary cannot be understood or even seen. The author argues that the interlocking forms of political actions among women's groups shape the postCommunist arena, although this shaping may be less immediately visible to the casual observer. (shrink)

Jelena Ćeriman, Rebellious Parents: Parental Movements in Central-Eastern Europe and Russia, Indiana University Press, Bloomington, 2017).

On the dust jacket of The Subject's Point of View there is a detail from Vilhelm Hammershoi's Interior with Sitting Woman. It is hard to think of a painter who better captures the inner in his work. From the monochrome colour, to the back that faces us, to the door swung open to reveal yet another doorway, we are led to interiority – to the inner. This is a perfect image for a book whose author wants to persuade us to (...) return to the interior – a Cartesian interior.The Cartesian interior has come in for quite a drubbing in philosophy for some considerable time. In the mid-to-late 1970s, a style of argument emerged, designed to challenge this conception of mind and establish in its place an externalist conception of language and of mind. One version of the argument was due to Hilary Putnam and emerged in the context of considerations concerning linguistic meaning; another was due to Tyler Burge and emerged first in the context of considerations concerning the individual in relation to his/her social environment. In his earliest paper, on this topic, Burge wrote of ‘the elderly Cartesian tradition’ where ‘the spotlight is on what exists or transpires “in” the individual – his secret cognition, his innate cognitive structures, his private perceptions and introspections, his grasping of ideas, concepts or forms’. Farkas wants to defend this ‘elderly tradition’, but she does add to it some interesting twists. First and foremost, she places to one side ideas of privacy, of incorrigibility and infallibility. She also wishes to place the issue of dualism to one side. What Farkas concentrates on is privileged access and argues that this is …. (shrink)

According to the Extended Mind thesis, the mind extends beyond the skull or the skin: mental processes can constitutively include external devices, like a computer or a notebook. The Extended Mind thesis has drawn both support and criticism. However, most discussions—including those by its original defenders, Andy Clark and David Chalmers—fail to distinguish between two very different interpretations of this thesis. The first version claims that the physical basis of mental features can be located spatially outside the body. Once we (...) accept that the mind depends on physical events to some extent, this thesis, though not obvious, is compatible with a large variety of views on the mind. The second version applies to standing states only, and has to do with how we conceive the nature of such states. This second version is much more interesting, because it points to a potential tension in our conception of minds or selves. However, without properly distinguishing between the two theses, the significance of the second is obscured by the comparative triviality of the first. (shrink)

Reader-friendly without compromising the precision of exposition, the book includes many new research results not found in the available literature.

Nonclassical logics have played an increasing role in recent years in disciplines ranging from mathematics and computer science to linguistics and philosophy. _Generalized Galois Logics_ develops a uniform framework of relational semantics to mediate between logical calculi and their semantics through algebra. This volume addresses normal modal logics such as K and S5, and substructural logics, including relevance logics, linear logic, and Lambek calculi. The authors also treat less-familiar and new logical systems with equal deftness.

Theodor W. Adorno inspired much of Germany’s 1960s student movement, but he came increasingly into conflict with this movement about the practical implications of his critical theory. Others – including his friend and colleague Herbert Marcuse – also accused Adorno of a quietism that is politically objectionable and in contradiction with his own theory. In this article, I reconstruct, and partially defend, Adorno’s views on theory and (political) praxis in Germany’s 1960s in 11 theses. His often attacked and maligned stance (...) during the 1960s is based on his analysis of these historical circumstances. Put provocatively, his stance consists in the view that people in the 1960s have tried to change the world, in various ways; the point – at that time – was to interpret it. (shrink)

The study explores the future of AI-driven media and info-communication as envisioned by experts from all world regions, defining relevant terminology and expectations for 2050. Participants engaged in a 4-week series of surveys, questioning their definitions and projections about AI for the field of media and communication. Their expectations predict universal access to democratically available, automated, personalized and unbiased information determined by trusted narratives, recolonization of information technology and the demystification of the media process. These experts, as technology ambassadors, advocate (...) AI-to-AI solutions to mitigate technology-driven misuse and misinformation. The optimistic scenarios shift responsibility to future generations, relying on AI-driven solutions and finding inspiration in nature. Their present-based forecasts could be construed as being indicative of professional near-sightedness and cognitive dissonance. Visualizing our findings into a Glasses Model of AI Trust, the study contributes to key debates regarding AI policy, developmental trajectories, and academic research in media and info-communication fields. (shrink)

Two consecution calculi are introduced: one for the implicational fragment of the logic of entailment with truth and another one for the disjunction free logic of nondistributive relevant implication. The proof technique—attributable to Gentzen—that uses a double induction on the degree and on the rank of the cut formula is shown to be insufficient to prove admissible various forms of cut and mix in these calculi. The elimination theorem is proven, however, by augmenting the earlier double inductive proof with additional (...) inductions. We also give a new purely inductive proof of the cut theorem for the original single cut rule in Gentzen’s sequent calculus $ LK $ without any use of mix. (shrink)

The implicational fragment of the logic of relevant implication, $R_\to$ is known to be decidable. We show that the implicational fragment of the logic of ticket entailment, $T_\to$ is decidable. Our proof is based on the consecution calculus that we introduced specifically to solve this 50-year old open problem. We reduce the decidability problem of $T_\to$ to the decidability problem of $R_\to$. The decidability of $T_\to$ is equivalent to the decidability of the inhabitation problem of implicational types by combinators over (...) the base $\{\textsf{B},\textsf{B}',\textsf{I},\textsf{W}\}$. (shrink)

Descartes's philosophy has had a considerable influence on the modern conception of the mind, but many think that this influence has been largely negative. The main project of The Subject's Point of View is to argue that discarding certain elements of the Cartesian conception would be much more difficult than critics seem to allow, since it is tied to our understanding of basic notions, including the criteria for what makes someone a person, or one of us. The crucial feature of (...) the Cartesian view defended here is not dualism--which is not adopted--but internalism. Internalism is opposed to the widely accepted externalist thesis, which states that some mental features constitutively depend on certain features of our physical and social environment. In contrast, this book defends the minority internalist view, which holds that the mind is autonomous, and though it is obviously affected by the environment, this influence is merely contingent and does not delimit what is thinkable in principle. Defenders of the externalist view often present their theory as the most thoroughgoing criticism of the Cartesian conception of the mind; Katalin Farkas offers a defence of an uncompromising internalist Cartesian conception. (shrink)

We define dual and symmetric combinatory calculi (inequational and equational ones), and prove their consistency. Then, we introduce algebraic and set theoretical relational and operational - semantics, and prove soundness and completeness. We analyze the relationship between these logics, and argue that inequational dual logics are the best suited to model computation.

In this paper I begin to develop an account of the acquaintance that each of us has with our own conscious states and processes. The account is a speculative proposal about human mental architecture and specifically about the nature of the concepts via which we think in first personish ways about our qualia. In a certain sense my account is neutral between physicalist and dualist accounts of consciousness. As will be clear, a dualist could adopt the account I will offer (...) while maintaining that qualia themselves are non-physical properties. In this case the non-physical nature of qualia may play no role in accounting for the features of acquaintance. But although the account could be used by a dualist, its existence provides support for physicalism. (shrink)

Economists, in stressing the prescriptive implications of their analysis, typically have ignored the potential contributions of their theorems and methodological principles to the understanding of human behavior as an end in itself. The purpose of the paper is to establish the principle, by detailed reference to the literature of economics, that the 'deductive pattern of explanation' constitutes a valid approach to the general study of human behavior. As such, it is a potentially useful method of analysis in the other social (...) sciences. Literature from the philosophy of social science bearing on the applicability of deductive theory to the study of human behavior is subjected to detailed critical analysis. (shrink)

The paper begins with the account of a focus group discussion of Hungarian female managers who demonstrated high level of trust. Drawing on the discussion the author explores the nature of trust and looks at works and research findings in different disciplines. In psychology Erikson’s findings on human growth and development are discussed. Representatives of Eastern and Western philosophy are quoted to highlight the underlying differences of thinking in relation to trust. The impact of cultural heritage and the influence of (...) the environment on trust add further dimensions to the argument. In conclusion it is suggested that management education could be a platform for further research and exploration of trust in individuals and organisations. (shrink)

Graphical AbstractDevelopment, life cycle evolution and immunity were among the topics discussed at a recent meeting in Tutzing dedicated to the biology of the ‘basal’ metazoan taxa Porifera, Ctenophora, Placozoa and Cnidaria.

Urquhart works in several areas of logic where he has proved important results. Our paper outlines his topological lattice representation and attempts to relate it to other lattice representations. We show that there are different ways to generalize Priestley’s representation of distributive lattices—Urquhart’s being one of them, which tries to keep prime filters in the representation. Along the way, we also mention how semi-lattices and lattices figured into Urquhart’s work.

After the parliamentary elections in Germany in September 2017, the Christian Democratic Union (CDU), the Christian Social Union (CSU), The Greens (Bündnis90/Die Grünen) and the Free Democratic Party (FDP) started to negotiate about forming a coalition government. But, surprising to many, the FDP decided to let these coalition talks collapse, and many commentators in Germany found it highly problematic for a political party to refuse to take responsibility in government. Interestingly, the question whether (or: when) democratic parties may legitimately refuse (...) to govern has so far been neglected in political theory and political philosophy. The article develops a general answer by discussing several possible reasons for thinking that it is sometimes wrong to refuse to govern and thereby engages both democratic theory and the recent literature on compromise. The resulting view is that parties have an ‘integrity prerogative’ that allows them to refuse to govern, except when there is no reasonable and stable alternative government coalition available. (shrink)

This article considers Theodor W. Adorno’s thesis of the ‘liquidation of the individual’ as a contribution to the critique of political economy insofar as it links structural economic imperatives o...

The purpose of our study was to measure the relationship between performance on various attentional tasks and hypnotic susceptibility. Healthy volunteers participated in a study, where they had to perform several tasks measuring various attention components in a waking state: sustained attention, selective or focused attention, divided attention and executive attention in task switching. Hypnotic susceptibility was measured in a separate setting by the Waterloo-Stanford Groups Scale of Hypnotic Susceptibility, Form C .We found no significant correlation between any of the (...) attentional measures and hypnotic susceptibility. Highly hypnotizables did not prove to be superior to or worse than the other individuals in any of the tests.These results do not support the neuropsychophysiological model of hypnosis, as they show no consistent relationship between hypnotic susceptibility and waking attentional performance. (shrink)

Sequent calculi constitute an interesting and important category of proof systems. They are much less known than axiomatic systems or natural deduction systems are, and they are much less known than they should be. Sequent calculi were designed as a theoretical framework for investigations of logical consequence, and they live up to the expectations completely as an abundant source of meta-logical results. The goal of this book is to provide a fairly comprehensive view of sequent calculi -- including a wide (...) range of variations. The focus is on sequent calculi for various non-classical logics, from intuitionistic logic to relevance logic, through linear and modal logics. A particular version of sequent calculi, the so-called consecution calculi, have seen important new developments in the last decade or so. The invention of new consecution calculi for various relevance logics allowed the last major open problem in the area of relevance logic to be solved positively: pure ticket entailment is decidable. An exposition of this result is included in chapter 9 together with further new decidability results (for less famous systems). A series of other results that were obtained by J. M. Dunn and me, or by me in the last decade or so, are also presented in various places in the book. Some of these results are slightly improved in their current presentation. Obviously, many calculi and several important theorems are not new. They are included here to ensure the completeness of the picture; their original formulations may be found in the referenced publications. This book contains very little about semantics, in general, and about the semantics of non-classical logic in particular. (shrink)

This paper was chosen by The Philosopher’s Annual as one of the ten best articles appearing in print in 2000. Reprinted in Volume XXIII of The Philosopher’s Annual. In his very influential book David Chalmers argues that if physicalism is true then every positive truth is a priori entailed by the full physical description – this is called “the a priori entailment thesis – but ascriptions of phenomenal consciousness are not so entailed and he concludes that Physicalism is false. As (...) he puts it, “zombies” are metaphysically possible. I attempt to show that this argument is refuted by considering an analogous argument in the mouth of a zombie. The conclusion of this argument is false so one of the premises is false. I argue at length that this shows that the original conceivability argument also has a false premise and so is invalid. (shrink)

In recent years, several philosophers have defended the idea of phenomenal intentionality : the intrinsic directedness of certain conscious mental events which is inseparable from these events’ phenomenal character. On this conception, phenomenology is usually conceived as narrow, that is, as supervening on the internal states of subjects, and hence phenomenal intentionality is a form of narrow intentionality. However, defenders of this idea usually maintain that there is another kind of, externalistic intentionality, which depends on factors external to the subject. (...) We may ask whether this concession to content externalism is obligatory. In this paper, I shall argue that it isn’t. I shall suggest that if one is convinced that narrow phenomenal intentionality is legitimate, there is nothing stopping one from claiming that all intentionality is narrow. (shrink)

This thesis aims to clarify a number of conceptual aspects of the debate surrounding algorithmic fairness. The particular focus here is the role of causal modeling in defining criteria of algorithmic fairness. In Chapter 1, I argue that in the discussion of algorithmic fairness, two fundamentally distinct notions of fairness have been conflated. Subsequently, I propose that what is usually taken to be the problem of algorithmic fairness should be divided into two subproblems, the problem of predictive fairness, and the (...) problem of allocative fairness. At the core of Chapter 2 is the proof of a theorem that establishes that three of the most popular (predictive) fairness criteria are pairwise incompatible. In particular, I show that under certain conditions, a predictive algorithm that satisfies a criterion called counterfactual fairness will with logical necessity violate two other popular predictive fairness criteria called equalized odds and predictive parity. In Chapter 3, a new predictive fairness criterion is developed using a mathematical framework for causal modeling. This fairness criterion, which I call causal relevance fairness, is a relaxation of another popular fairness criterion, counterfactual fairness, but turns out to be more closely in line with philosophical theories of discrimination. In Chapter 4, another infamous impossibility result in algorithmic fairness is analyzed through the lens of causality. I argue that by using a causal inference method called matching, we can modify the two fairness criteria equalized odds and predictive parity in a way that resolves the impossibility. Lastly, Chapter 5 contains an empirical case study. In it, the fairness of a popular recidivism risk prediction tool is analyzed using the criteria of (predictive) fairness developed earlier. (shrink)

In this chapter, I revisit the issue of the explanatory gap that is supposed to open when considering identity statements between physical and mental phenomena. I show that the question asked in the original formulation of the explanatory gap was this: ʻwhy this phenomenal character, rather than any other, is attached to this physiological process?ʼ I argue that this question can be answered, because there is a natural fit between the phenomenal character of experiences and their functional roles. For example, (...) pains feel inherently unpleasant, and that explains why they cause avoidance behaviour, and the felt location and intensity of pain indicates the location and extent of damage to the body. I discuss some other possible gaps in our understanding the relationship between the mental and the physical, and conclude that the fit between functional role and phenomenal character goes a long way, though probably not the whole way, to closing the explanatory gap. (shrink)

On a Cartesian conception of the mind, I could be a solitary being and still have the same mental states as I currently have. This paper asks how the lives of other people fit into this conception. I investigate the second-person perspective—thinking of others as ‘you’ while engaging in reciprocal communicative interactions with them—and argue that it is neither epistemically nor metaphysically distinctive. I also argue that the Cartesian picture explains why other people are special: because they matter not just (...) for the effect that they have on us. (shrink)

In many critical investigations of machine vision, the focus lies almost exclusively on dataset bias and on fixing datasets by introducing more and more diverse sets of images. We propose that machine vision systems are inherently biased not only because they rely on biased datasets but also because theirperceptual topology, their specific way of representing the visual world, gives rise to a new class of bias that we callperceptual bias. Concretely, we define perceptual topology as the set of those inductive (...) biases in machine vision systems that determine its capability to represent the visual world. Perceptual bias, then, describes the difference between the assumed “ways of seeing” of a machine vision system, our reasonable expectations regarding its way of representing the visual world, and its actual perceptual topology. We show how perceptual bias affects the interpretability of machine vision systems in particular, by means of a close reading of a visualization technique called “feature visualization”. We conclude that dataset bias and perceptual bias both need to be considered in the critical analysis of machine vision systems and propose to understand critical machine vision as an important transdisciplinary challenge, situated at the interface of computer science and visual studies/Bildwissenschaft. (shrink)

Doxasticism about our awareness of normative (i.e. justifying) reasons – the view that we can recognise reasons for forming attitudes or performing actions only by means of normative judgements or beliefs – is incompatible with the following triad of claims: -/- (1) Being motivated (i.e. forming attitudes or performing actions for a motive) requires responding to and, hence, recognising a relevant reason. -/- (2) Infants are capable of being motivated. -/- (3) Infants are incapable of normative judgement or belief. -/- (...) It should be clear that (3) is true, given that infants lack the required reflective and conceptual capacities. So doxasticists have to reject either (1) or (2) (or both). But this forced choice may be understood as a dilemma for doxasticism. On the hand, doxasticists may adopt a Kantian approach and reject (2), precisely because they think that motivation presupposes the doxastic recognition of reasons, and because infants lack the capacity to doxastically recognise reasons. But this choice seems to wrongly reduce the responses of infants to mere reflexes or instinctive reactions. On the other hand, doxasticists may choose a Humean route and deny (1) by espousing a purely causal or teleological account of motivation. But this would mean detrimentally ignoring the normative nature of (some instances of) motivation. -/- One elegant way of avoiding this dilemma is to give up doxasticism and instead endorse experientialism – the view that we enjoy some experiential access to reasons, which is independent of, and perhaps more fundamental than, our capacity to form normative judgements and beliefs. In this talk, I would like to provide an argument for the existence of such a non-doxastic form of access to reasons. More specifically, I aim to defend the claim that our basic awareness of reasons is phenomenal in nature. What this means is that it forms part of our access from the inside to those of our mental episodes that provide us with access to reasons. In other words, when we introspectively attend to reason-giving mental episodes and what they are about, we have the impression of the presence of a reason for us. My defence of this experientialist alternative to doxasticism will primarily focus on perceptual reasons for first-order beliefs about the external world. (shrink)

A libertarian theory of justice holds that persons are self-owners and have the Hohfeldian moral power to justly acquire property rights in initially unowned external resources. Different variants of libertarianism can be distinguished according to their stance on the famous Lockean proviso. The proviso requires, in Locke’s words, to leave ‘enough and as good’ for others, and thus specifies limits on the acquisition of property. Left-libertarians accept an egalitarian interpretation of the proviso, ‘right-libertarians’ either reject any kind of proviso or (...) accept rather weak versions of it. In be-tween there is room for moderate interpretations of the proviso, and in particular for a sufficientarian interpretation: a ‘sufficiency proviso.’ The resulting theory of justice can be called ‘moderate libertarianism.’ In this article I make a case for moderate libertarianism, so understood. I argue that moderate libertarianism has advantages over both left- and right-libertarianism because it better coheres with the most plausible rationale for endorsing a libertarian theory of justice in the first place. (shrink)

During the last two decades, several different anti-physicalist arguments based on an epistemic or conceptual gap between the phenomenal and the physical have been proposed. The most promising physicalist line of defense in the face of these arguments – the Phenomenal Concept Strategy – is based on the idea that these epistemic and conceptual gaps can be explained by appeal to the nature of phenomenal concepts rather than the nature of non-physical phenomenal properties. Phenomenal concepts, on this proposal, involve unique (...) cognitive mechanisms, but none that could not be fully physically implemented. David Chalmers has recently presented a Master Argument to show that the Phenomenal Concept Strategy – not just this or that version of it, but any version of it – fails. Chalmers argues that the phenomenal concepts posited by such theories are either not physicalistically explicable, or they cannot explain our epistemic situation with regard to qualia. I argue that it is his Master Argument that fails. My claim is his argument does not provide any new reasons to reject the Phenomenal Concept Strategy. I also argue that, although the Phenomenal Concept Strategy is successful in showing that the physicalist is not rationally compelled to give up physicalism in the light of the anti-physicalist arguments, the anti-physicalist is not rationally compelled to give up the anti-physicalist argument in the light of the Phenomenal Concept Strategy either. (shrink)

Martin Heideggers Abendgespräch in einem russischen Kriegsgefangenenlager zwischen einem Jüngeren und einem Älteren ist datiert auf den 8. Mai 1945, den Tag, an dem der Nationalsozialismus besiegt wurde. Der Schlüssel zum Verständnis des Textes ist ein Zitat aus dem klassischen daoistischen Buch Zhuangzi. Warum wendet sich Heidegger an diesem Tag der chinesischen Philosophie zu? Für den Philosophen und Sinologen Fabian Heubel birgt das Abendgespräch die einzigartige Gelegenheit, Heideggers Öffnung für östliches Denken kritisch zu erörtern. Zugleich zeigt sich die Kommunikationsverweigerung zwischen (...) Heidegger und Adorno in neuem Licht, indem das Buch beide mit Hilfe daoistischen paradoxen Denkens ins Gespräch kommen lässt. Im Kommunizieren dieser drei Momente tritt eine transkulturelle Kritik hervor, die durch geschichtliches Bewusstsein von Nöten gezeichnet ist. Heideggers Kehre nach Osten ist gescheitert. Andererseits gibt es keinen philosophischen Weg nach China, der an seinem Denken vorbeiführt."-- Back cover. (shrink)

The subject of mental processes or mental states is usually assumed to be an individual, and hence the boundaries of mental features – in a strict or metaphorical sense – are naturally regarded as reaching no further than the boundaries of the individual. This chapter addresses various philosophical developments in the 20th and 21st century that questioned this natural assumption. I will frame this discussion by fi rst presenting a historically infl uential commitment to the individualistic nature of the mental (...) in Descartes’ theory. I identify various elements in the Cartesian conception of the mind that were subsequently criticized and rejected by various externalist theories, advocates of the extended mind hypothesis and defenders of embodied cognition. Then I will indicate the main trends in these critiques. (shrink)

The hitherto neglected Pandechion epistemonicon, Ulisse Aldrovandi’s extant manuscript encyclopaedia, indicates that Renaissance naturalists did not necessarily apply the humanist jack-of-all-trades, the commonplace book, in their own field without considerably altering its form. Over many years the Italian natural historian tested and recombined different techniques to arrive at the form of paper technology that he considered to be the most fit for his purposes. Not all of these techniques were taught at school or university. Rather, Aldrovandi drew on administrative practices (...) as well as on the bookkeeping practices of early modern merchants that he knew first-hand. Reconstructing the formation and use of the Pandechion this article contributes to the historiography of learned reading and information management in Renaissance Europe. (shrink)

Immanuel Kant's Critique of Judgment is widely recognized as a founding document of modern aesthetics, but its legacy has fallen into disrepute. In this book Katalin Makkai calls for the rediscovery of Kant's aesthetics, showing that its centerpiece, his investigation of the judgment of taste, paints a compelling portrait of our relationships with works of art that we love. At its heart is a scene of aesthetic encounter in which one feels oneself to be 'animated' - brought to life (...) - by an object, finding there to be something in one's experience of it, beyond what there is to know about it, that one wants to explore and articulate. Tracing Kant's insight that to judge is to reveal one's sense of what bears judging, and hence of what matters, Makkai situates Kant's aesthetics within his larger study, begun in the first Critique, of judgment's fundamental role in the life of the mind. (shrink)

The implicational fragment of the logic of relevant implication, $R_{\to}$ is one of the oldest relevance logics and in 1959 was shown by Kripke to be decidable. The proof is based on $LR_{\to}$ , a Gentzen-style calculus. In this paper, we add the truth constant $\mathbf{t}$ to $LR_{\to}$ , but more importantly we show how to reshape the sequent calculus as a consecution calculus containing a binary structural connective, in which permutation is replaced by two structural rules that involve $\mathbf{t}$ (...) . This calculus, $LT_\to^{\text{\textcircled{$\mathbf{t}$}}}$ , extends the consecution calculus $LT_{\to}^{\mathbf{t}}$ formalizing the implicational fragment of ticket entailment . We introduce two other new calculi as alternative formulations of $R_{\to}^{\mathbf{t}}$ . For each new calculus, we prove the cut theorem as well as the equivalence to the original Hilbert-style axiomatization of $R_{\to}^{\mathbf{t}}$ . These results serve as a basis for our positive solution to the long open problem of the decidability of $T_{\to}$ , which we present in another paper. (shrink)

A sequent calculus for the positive fragment of entailment together with the Church constants is introduced here. The single cut rule is admissible in this consecution calculus. A topological dual gaggle semantics is developed for the logic. The category of the topological structures for the logic with frame morphisms is proven to be the dual category of the variety, that is defined by the equations of the algebra of the logic, with homomorphisms. The duality results are extended to the logic (...) of entailment that includes a De Morgan negation. (shrink)