Until not too many years ago, all logics except classical logic (and, perhaps, intuitionistic logic too) were considered to be things esoteric. Today this state of a airs seems to have completely been changed. There is a growing interest in many types of nonclassical logics: modal and temporal logics, substructural logics, paraconsistent logics, non-monotonic logics { the list is long. The diversity of systems that have been proposed and studied is so great that a need is felt by many researchers (...) to try to put some order in the present logical jungle. Thus Cl91], Ep90] and Wo88] are three recent books in which an attempt is made to develop a general theoretical framework for the study of logics. On the more pragmatic side, several systems have been developed with the goal of providing a computerized logical framework in which many di erent logical systems can be implemented in a uniform way. An example is the Edinburgh LF( HHP91]). (shrink)

The aim of the current study was to monitor the changes that individual participants experienced as a result of taking part in a peace education program. The findings of prior analyses led to the understanding that participating in a peace program does not always ensure positive changes and may even cause a regression in attitudes. The present study was conducted in two stages. In the first stage, the researchers learned about the processes that participants underwent during a peace education program (...) and accordingly, a reinforcement program to restore/rehabilitate any negative attitudes was formed. In the second stage, the effectiveness over time of this reinforcement program was evaluated. The study’s findings show that engaging in reflection about the workshop content, especially when it is oriented towards positive thinking, is effective in reinforcing attitudes among participants who underwent a positive change in attitudes, and at the same time helps to rehabilitate attitudes among those participants who underwent a negative change. It is recommended that future peace education programs include at least three parts: preliminary preparation, the program itself, and follow-up/reinforcement activity after completion of the program. (shrink)

I argue that the debate about the reason-giving character of perception, and, derivatively, the contemporary debate about the nature of the conceptual content of perception, is best viewed as a confrontation with refined versions of the following three independently plausible, yet mutually inconsistent, propositions: Perceptual apprehension Some perceptions provide reasons directly Exclusivity Only beliefs provide reasons directly Bifurcation No perception is a belief I begin with an evaluation and refinement of each proposition so as to crystallize the source of the (...) difficulties that dominate our thinking about the reason-giving character of perception. I argue that the contemporary literature is broadly split between those denying Bifurcation and those denying Perceptual apprehension. Though Exclusivity, too, has been target to criticism, its grip on our thinking has all too often been underestimated. As a result, a proper denial or modification of Exclusivity is yet wanting. Overcoming Exclusivity involves a considerable challenge that has not been adequately acknowledged or met—to develop a substantive account of nonconceptual apprehension. Getting a clearer understanding of the nature, the source, and possible resolution of this challenge is the primary aim of this paper. (shrink)

Why are children better language learners than adults despite being worse at a range of other cognitive tasks? Here, we explore the role of multiword sequences in explaining L1–L2 differences in learning. In particular, we propose that children and adults differ in their reliance on such multiword units in learning, and that this difference affects learning strategies and outcomes, and leads to difficulty in learning certain grammatical relations. In the first part, we review recent findings that suggest that MWUs play (...) a facilitative role in learning. We then discuss the implications of these findings for L1–L2 differences: We hypothesize that adults are both less likely to extract MWUs and less capable of benefiting from them in the process of learning. In the next section, we draw on psycholinguistic, developmental, and computational findings to support these predictions. We end with a discussion of the relation between this proposal and other accounts of L1–L2 difficulty. (shrink)

According to doxastic accounts of trust, trusting a person to \(\varPhi \) involves, among other things, holding a belief about the trusted person: either the belief that the trusted person is trustworthy or the belief that she actually will \(\varPhi \) . In recent years, several philosophers have argued against doxastic accounts of trust. They have claimed that the phenomenology of trust suggests that rather than such a belief, trust involves some kind of non-doxastic mental attitude towards the trusted person, (...) or a non-doxastic disposition to rely upon her. This paper offers a new account of reasons for trust and employs the account to defend a doxastic account of trust. The paper argues that reasons for trust are preemptive reasons for action or belief. Thus the Razian concept of preemptive reasons, which arguably plays a key role in our understanding of relations of authority, is also central to our understanding of relations of trust. Furthermore, the paper argues that acceptance of a preemptive account of reasons for trust supports the adoption of a doxastic account of trust, for acceptance of such an account both neutralizes central objections to doxastic accounts of trust and provides independent reasons supporting a doxastic account. (shrink)

What must laypersons understand about science to allow them to make sound decisions on science-related issues? Relying on recent developments in social epistemology, this paper argues that scientific education should have the goal not of bringing laypersons' understanding of science closer to that of expert insiders, but rather of cultivating the kind of competence characteristic of “competent outsiders” (Feinstein 2011). Moreover, it argues that philosophers of science have an important role to play in attempts to promote this kind of understanding, (...) but that to successfully fulfill this role, they will have to approach central questions in the field differently. (shrink)

Modest pessimism about philosophical progress is the view that while philosophy may sometimes make some progress, philosophy has made, and can be expected to make, only very little progress (where the extent of philosophical progress is typically judged against progress in the hard sciences). The paper argues against recent attempts to defend this view on the basis of the pervasiveness of disagreement within philosophy. The argument from disagreement for modest pessimism assumes a teleological conception of progress, according to which the (...) attainment of true answers to the big philosophical questions, or knowledge of them, is the primary goal of philosophy. The paper argues that this assumption involves a misconception of the goal of philosophy: if philosophy has a primary goal, its goal is the understanding of philosophical problems rather than knowledge of answers to philosophical questions. Moreover, it is argued that if the primary goal of philosophy is such understanding, then widespread disagreement within philosophy does not indicate that philosophy makes little progress. (shrink)

The paper discusses Linda Zagzebski's account of epistemic authority. Building on Joseph Raz's account of political authority, Zagzebski argues that the basic contours of epistemic authority match those Raz ascribes to political authority. This, it is argued, is a mistake. Zagzebski is correct in identifying the pre-emptive nature of reasons provided by an authority as central to our understanding of epistemic authority. However, Zagzebski ignores important differences between practical and epistemic authority. As a result, her attempt to explain the rationality (...) of belief on authority by applying an analogue of Raz's Normal Justification Thesis to the domain of belief fails. A successful explanation of the rationality of belief on authority will need to be attuned to the differences between political and epistemic authorities. (shrink)

This chapter gives an account of epistemic trust. It argues that trust in general is a matter of declining to take precautions against the trustee’s failing to come through, and that this amounts in the epistemic case to declining to rely on evidence for the testified proposition, instead relying solely on the testifier. But if this is so, how can trust play a positive role in securing knowledge? The key, it is argued, lies in recognizing that trust is preemptive: Trusting (...) someone entails believing that she is trustworthy, and this belief preempts other evidence about whether she will come through. In other words, this belief gives the truster himself a good reason to desist from relying on evidence other than the trustee’s word. But if trust is preemptive, how is it compatible with epistemic responsibility, which seems to involve relying on your own evidence? Because, it is claimed, preempting your own evidence in favor of the testifier’s say-so enables your belief to be supported by her evidence – which, we may assume, is superior to your own. Far from forfeiting epistemic responsibility, then, epistemic trust on the preemptive account gives you justificatory access to a swathe of evidence that you would not otherwise have had. (shrink)

In this article, Arnon explores the link between implicit learning, statistical learning and language development. She focuses on two central themes, namely the issue of age invariance and the question of variation in learning outcomes. Arnon suggests that the two literatures are studying a fundamentally similar phenomenon and argues in favor of a closer alignment. However, she also raises important methodological concerns.

I present an account of what it is to trust a speaker, and argue that the account can explain the common intuitions which structure the debate about the transmission view of testimony. According to the suggested account, to trust a speaker is to grant her epistemic authority on the asserted proposition, and hence to see her opinion as issuing a second order, preemptive reason for believing the proposition. The account explains the intuitive appeal of the basic principle associated with the (...) transmission view of testimony: the principle according to which, a listener can normally obtain testimonial knowledge that p by believing a speaker who testifies that p only if the speaker knows that p. It also explains a common response to counterexamples to this principle: that these counterexamples do not involve normal cases of testimonial knowledge. (shrink)

Proponents of mechanistic explanation all acknowledge the importance of organization. But they have also tended to emphasize specificity with respect to parts and operations in mechanisms. We argue that in understanding one important mode of organization—patterns of causal connectivity—a successful explanatory strategy abstracts from the specifics of the mechanism and invokes tools such as those of graph theory to explain how mechanisms with a particular mode of connectivity will behave. We discuss the connection between organization, abstraction, and mechanistic explanation and (...) illustrate our claims by looking at an example from recent research on so-called network motifs. (shrink)

One fundamental divide among philosophers studying the nature of trust concerns the relation between trust and belief. According to doxastic accounts of trust, trust entails a belief about the trustee: either the belief that she is trustworthy with respect to what she is trusted to do, or that she will do what she is trusted to do. Non-doxastic accounts deny that trusting entails holding such a belief. The chapter describes and evaluates the main considerations which have been cited for and (...) against doxastic accounts of trust. It argues that a preemptive reasons account of trust neutralizes some of the key objections to doxastic accounts, and that considerations favoring a doxastic account appear to be stronger than those favoring non-doxastic accounts. The chapter also suggests that the debate about the nature of trust, and the mental state required for trusting can benefit from linking it with the debate about the value of trust. (shrink)

'Volgens de Duitse denker Carl Schmitt is zonder vijandbeeld geen politiek mogelijk,' schreven Coen Simon en Frank Meester aan Arnon Grunberg. Zij vroegen hem Het begrip politiek van Carl Schmitt (1888-1985) te lezen om na te gaan wat hij ons nu nog te zeggen heeft. Hoeveel natiestaat hebben wij nodig? Hoeveel vijanden? Waartoe dient politiek? En is een samenleving zonder oorlog en geweld mogelijk? Aan de hand van Schmitt en denkers als Walter Benjamin en Jacques Derrida probeert Grunberg antwoord (...) te geven op die vragen. 'Onze cultuur heeft de vegetarische slager voortgebracht en zal uiteindelijk ook de geweldloze oorlog produceren. Hoe die er precies uit zal zien is onduidelijk, maar Schmitts vermoeden dat die oorlog om de oorlog eens en voor altijd uit te roeien gruwelijk zal zijn lijkt me gerechtvaardigd,' aldus Grunberg. Maar ook stelt hij dat er geen rechtvaardigheid kan bestaan als het geweld wordt afgezworen. In Vriend & vijand legt Grunberg de vinger op zowel de zere plekken van de parlementaire democratie als de kritiek erop. Vrienden en vijanden van deze democratie mogen dit essay niet aan zich voorbij laten gaan"--Back cover. (shrink)

Recently, various philosophers have argued that we can obtain knowledge via the imagination. In particular, it has been suggested that we can come to know concrete, empirical matters of everyday significance by appropriately imagining relevant scenarios. Arguments for this thesis come in two main varieties: black box reliability arguments and constraints-based arguments. We suggest that both strategies are unsuccessful. Against black-box arguments, we point to evidence from empirical psychology, question a central case-study, and raise concerns about a (claimed) evolutionary rationale (...) for the imagination's reliability. Against the constraints-based account, we argue that to the extent that it works, this does not give rise to knowledge that is distinctively from the imagination. We conclude by suggesting that the imagination's role in raising possibilities, traditionally seen as part of the context of discovery, can in fact play a role in justification, including as a bulwark against certain sorts of skepticism. (shrink)

Evolutionary debunking arguments appeal to selective etiologies of human morality in an attempt to undermine moral realism. But is morality actually the product of evolution by natural selection? Although debunking arguments have attracted considerable attention in recent years, little of it has been devoted to whether the underlying evolutionary assumptions are credible. In this paper, we take a closer look at the evolutionary hypotheses put forward by two leading debunkers, namely Sharon Street and Richard Joyce. We raise a battery of (...) considerations, both empirical and theoretical, that combine to cast doubt on the plausibility of both hypotheses. We also suggest that it is unlikely that there is in the vicinity a plausible alternative hypothesis suitable for the debunker’s cause. (shrink)

Within the contemporary epistemology of testimony, it is widely assumed that testimonial scepticism can be dismissed without engaging with possible reasons or arguments supporting the view. This assumption of dismissibility both underlies the debate between reductionist and non-reductionist views of testimony and is responsible for the neglect of testimonial scepticism within contemporary epistemology. This paper argues that even given liberal assumptions about what may constitute valid grounds for the dismissal of a sceptical view, the assumption that testimonial scepticism is dismissible (...) should be rejected. For even if familiar sceptical positions and scepticism about testimonial justification can be dismissed on such grounds, scepticism about testimonial knowledge cannot. (shrink)

On many science-related policy questions, the public is unable to make informed decisions, because of its inability to make use of knowledge obtained by scientists. Philip Kitcher and James Fishkin have both suggested therefore that on certain science-related issues, public policy should not be decided on by actual democratic vote, but should instead conform to the public’s counterfactual informed democratic decision. Indeed, this suggestion underlies Kitcher’s specification of an ideal of a well-ordered science. This article argues that this suggestion misconstrues (...) the normative significance of CIDDs. At most, CIDDs might have epistemic significance, but no authority or legitimizing force. (shrink)

I present an account of what it is to trust a speaker, and argue that the account can explain the common intuitions which structure the debate about the transmission view of testimony. According to the suggested account, to trust a speaker is to grant her epistemic authority on the asserted proposition, and hence to see her opinion as issuing a second order, preemptive reason for believing the proposition. The account explains the intuitive appeal of the basic principle associated with the (...) transmission view of testimony: the principle according to which, a listener can normally obtain testimonial knowledge that p by believing a speaker who testifies that p only if the speaker knows that p. It also explains a common response to counterexamples to this principle: that these counterexamples do not involve normal cases of testimonial knowledge. (shrink)

According to the evidential view of testimony (EVT), the epistemic value of testimony is its value as evidence. Richard Moran has argued that because testimony is deliberately produced with the intention of making audiences form a belief, its value as evidence for the attested proposition is diminished; as a result, EVT cannot explain why we regard testimony as such a significant source of knowledge. I argue that this argument against EVT fails, because there is no reason to think that the (...) deliberate nature of testimony diminishes its value as evidence. (shrink)

Idealization and abstraction are central concepts in the philosophy of science and in science itself. My goal in this paper is suggest an account of these concepts, building on and refining an existing view due to Jones Idealization XII: correcting the model. Idealization and abstraction in the sciences, vol 86. Rodopi, Amsterdam, pp 173–217, 2005) and Godfrey-Smith Mapping the future of biology: evolving concepts and theories. Springer, Berlin, 2009). On this line of thought, abstraction—which I call, for reasons to be (...) explained, abstractness—involves the omission of detail, whereas idealization consists in a deliberate mismatch between a description and the world. I will suggest that while the core idea underlying these authors’ view is correct, they make several assumptions and stipulations that are best avoided. For one thing, they tie abstractness too close to truth. For another, they do not allow sufficient room to the difference between idealization and error. Taking these points into account leads to a refined account of the distinction, in which abstractness is seen in terms of relative richness of detail, and idealization is seen as closely connected with the knowledge and intentions of idealizers. I lay out these accounts in turn, and then discuss the relationship between the two concepts, and several other upshots of the present way of construing the distinction. (shrink)

Modeling is an important scientific practice, yet it raises significant philosophical puzzles. Models are typically idealized, and they are often explored via imaginative engagement and at a certain “distance” from empirical reality. These features raise questions such as what models are and how they relate to the world. Recent years have seen a growing discussion of these issues, including a number of views that treat modeling in terms of indirect representation and analysis. Indirect views treat the model as a bona (...) fide object, specified by the modeler and used to represent and reason about some portion of the concrete empirical world. On some indirect views, model systems are abstract entities, such as mathematical structures, while on other views they are concrete hypothetical things. Here I assess these views and offer a novel account of models. I argue that regarding models as abstracta results in some significant tensions with the practice of modeling, especially in areas where non-mathematical models are common. Furthermore, viewing models as concrete hypotheticals raises difficult questions about model-world relations. The view I argue for treats models as direct, albeit simplified, representations of targets in the world. I close by suggesting a treatment of model-world relations that draws on a recent work by Stephen Yablo concerning the notion of partial truth. (shrink)

We suggest two precise abstract definitions of the notion of ‘relevance logic’ which are both independent of any proof system or semantics. We show that according to the simpler one, R → source is the minimal relevance logic, but R itself is not. In contrast, R and many other logics are relevance logics according to the second definition, while all fragments of linear logic are not.

Humans are capable of extracting recurring patterns from their environment via statistical learning (SL), an ability thought to play an important role in language learning and learning more generally. While much work has examined statistical learning in infants and adults, less work has looked at the developmental trajectory of SL during childhood to see whether it is fully developed in infancy or improves with age, like many other cognitive abilities. A recent study showed modality‐based differences in the effect of age (...) during childhood: While visual SL improved with age, auditory SL did not. This finding was taken as evidence for modality‐based differences in SL. However, since that study used auditory linguistic stimuli (syllables), the differential effect of age may have been driven by stimulus type (linguistic vs. non‐linguistic) rather than modality. Here, we ask whether age will affect performance similarly in the two modalities when non‐linguistic auditory stimuli are used (familiar sounds instead of syllables). We conduct a large‐scale study of children's performance on visual and non‐linguistic auditory SL during childhood (ages 5–12 years). The results show a similar effect of age in both modalities: Unlike previous findings, both visual and non‐linguistic auditory SL improved with age. These findings highlight the stimuli‐sensitive nature of SL and suggest that modality‐based differences may be stimuli‐dependent, and that age‐invariance may be limited to linguistic stimuli. (shrink)

I distinguish three theses associated with the new mechanistic philosophy – concerning causation, explanation and scientific methodology. Advocates of each thesis are identified and relationships among them are outlined. I then look at some recent work on natural selection and mechanisms. There, attention to different kinds of New Mechanism significantly affects of what is at stake.

The Hodgkin–Huxley (HH) model of the action potential is a theoretical pillar of modern neurobiology. In a number of recent publications, Carl Craver ([2006], [2007], [2008]) has argued that the model is explanatorily deficient because it does not reveal enough about underlying molecular mechanisms. I offer an alternative picture of the HH model, according to which it deliberately abstracts from molecular specifics. By doing so, the model explains whole-cell behaviour as the product of a mass of underlying low-level events. The (...) issue goes beyond cellular neurobiology, for the strategy of abstraction exhibited in the HH case is found in a range of biological contexts. I discuss why it has been largely neglected by advocates of the mechanist approach to explanation. 1 Introduction2 A Primer on the HH Model2.1 The basic qualitative picture2.2 The quantitative model3 Interlude: What Did Hodgkin and Huxley Think?4 Craver’s View4.1 Mechanistic explanation4.2 Sketches4.3 Craver's view: The HH model as a mechanism sketch5 An Alternative View of the HH Model5.1 Another look at the equations5.2 The discrete-gating picture5.3 The road paved by Hodgkin and Huxley5.4 Summary and comparison to Craver6 Conclusion: The HH Model and Mechanistic Explanation6.1 Sketches and abstractions6.2 Why has aggregative abstraction been overlooked? (shrink)

Many biological investigations are organized around a small group of species, often referred to as ‘model organisms’, such as the fruit fly Drosophila melanogaster. The terms ‘model’ and ‘modelling’ also occur in biology in association with mathematical and mechanistic theorizing, as in the Lotka–Volterra model of predator-prey dynamics. What is the relation between theoretical models and model organisms? Are these models in the same sense? We offer an account on which the two practices are shown to have different epistemic characters. (...) Theoretical modelling is grounded in explicit and known analogies between model and target. By contrast, inferences from model organisms are empirical extrapolations. Often such extrapolation is based on shared ancestry, sometimes in conjunction with other empirical information. One implication is that such inferences are unique to biology, whereas theoretical models are common across many disciplines. We close by discussing the diversity of uses to which model organisms are put, suggesting how these relate to our overall account. 1 Introduction2 Volterra and Theoretical Modelling3 Drosophila as a Model Organism4 Generalizing from Work on Model Organisms5 Phylogenetic Inference and Model Organisms6 Further Roles of Model Organisms6.1 Preparative experimentation6.2 Model organisms as paradigms6.3 Model organisms as theoretical models6.4 Inspiration for engineers6.5 Anchoring a research community7 Conclusion. (shrink)

Evolutionary debunking arguments (EDAs) have attracted extensive attention in meta-ethics, as they pose an important challenge to moral realism. Mogensen (2015) suggests that EDAs contain a fallacy, by confusing two distinct forms of biological explanation – ultimate and proximate. If correct, the point is of considerable importance: evolutionary genealogies of human morality are simply irrelevant for debunking. But we argue that the actual situation is subtler: while ultimate claims do not strictly entail proximate ones, there are important evidential connections between (...) the two. Attending to these connections clears ground for a new and improved EDA. However, it also brings into view some possible problems with EDAs that have been largely neglected so far. (shrink)

In a recent article, Steel, Buchak and Eyal argue that current levels of uncertainty do not present a good reason to bar controlled human infection trials of COVID-19 vaccines from proceeding. We argue that their argumentation for this conclusion is flawed. SBE are mistaken about the effects which different forms of ignorance have on participants’ ability to provide valid informed consent. Decision-makers considering whether to allow such trials, we argue, must ultimately consider the likelihood that consent to participation in such (...) trials under current conditions would be valid, and whether this likelihood is high enough to permit such trials. This is a question that SBE completely ignore. We conclude that there indeed are valid concerns about conducting CHI trials given the current state of knowledge about COVID-19, concerns which SBE fail to address. (shrink)

The logic $G3^{<}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$ was introduced in Robles and Mendéz as a paraconsistent logic which is based on Gödel’s 3-valued matrix, except that Kleene–Łukasiewicz’s negation is added to the language and is used as the main negation connective. We show that $G3^{<}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$ is exactly the intersection of $G3^{\{1\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$ and $G3^{\{1,0.5\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$, the two truth-preserving 3-valued logics which are based on the same truth tables. We then construct a Hilbert-type system which has for $\to $ as its sole rule of inference, and is (...) strongly sound and complete for $G3^{<}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$. Then we show how, by adding one axiom or one new rule of inference, we get strongly sound and complete systems for $G3^{\{1\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$ and $G3^{\{1,0.5\}}_{{{}^{\scriptsize{-}}}\!\!\textrm{L}}$. Finally, we provide quasi-canonical Gentzen-type systems which are sound and complete for those logics and show that they are all analytic, by proving the cut-elimination theorem for them. (shrink)

What should the goals of scientific inquiry be? What questions should scientists investigate, and how should our resources be distributed between different lines of investigation? Philip Kitcher has suggested that we should answer these questions by appealing to an ideal based on the consideration of hypothetical democratic deliberations under ideal circumstances. The paper argues that we have no reason to adopt this ideal. The paper examines both traditional arguments for democracy and Kitcher's own reasons for adopting this ideal, as presented (...) in Kitcher (2001) and in Kitcher (2011b), and argues that none of these supports adoption of Kitcher's proposed ideal. (shrink)

A logic \ is called self-extensional if it allows to replace occurrences of a formula by occurrences of an \-equivalent one in the context of claims about logical consequence and logical validity. It is known that no three-valued paraconsistent logic which has an implication can be self-extensional. In this paper we show that in contrast, there is exactly one self-extensional three-valued paraconsistent logic in the language of \ for which \ is a disjunction, and \ is a conjunction. We also (...) investigate the main properties of this logic, determine the expressive power of its language, and provide a cut-free Gentzen-type proof system for it. (shrink)

Moral realism is often taken to have common sense and initial appearances on its side. Indeed, by some lights, common sense and initial appearances underlie all the central positive arguments for moral realism. We offer a kind of debunking argument, taking aim at realism’s common sense standing. Our argument differs from familiar debunking moves both in its empirical assumptions and in how it targets the realist position. We argue that if natural selection explains the objective phenomenology of moral deliberation and (...) judgement, then this undermines arguments from that phenomenology. This results in a simpler, and in some ways more direct, challenge to realism. It is also less vulnerable to the main objections that have been leveled against such arguments. If accepted, our conclusion should make a real difference to the dialectic in this area. It means that neither realism nor its denial is the default, to-be-refuted, position. (shrink)

Non-deterministic matrices are multiple-valued structures in which the value assigned by a valuation to a complex formula can be chosen non-deterministically out of a certain nonempty set of options. We consider two different types of semantics which are based on Nmatrices: the dynamic one and the static one . We use the Rasiowa-Sikorski decomposition methodology to get sound and complete proof systems employing finite sets of mv-signed formulas for all propositional logics based on such structures with either of the above (...) types of semantics. Later we demonstrate how these systems can be converted into cut-free ordinary Gentzen calculi which are also sound and complete for the corresponding non-deterministic semantics. As a by-product, we get new semantic characterizations for some well-known logics. (shrink)

A proof is presented showing that there is no paraconsistent logics with a standard implication which have a three-valued characteristic matrix, and in which the replacement principle holds.