The latest Omicron variant of the novel coronavirus has itself created a novel situation—bringing attention to the topic of healthcare rationing among hospitalized pediatric patients. This may be the first time that many pediatricians, nurses, parents, and public health officials have been compelled to engage in uncomfortable discussions about the allocation of medical care/resources. Simply put, finite budgets, resources, and a dwindling healthcare workforce do not permit all patients to receive unlimited medical care. Triage and bedside rationing decisions (...) are happening in a range of difficult everyday circumstances both implicitly and explicitly, but in ways not recognized by even the best ethically framed intentions. Clinicians and hospital administrators have largely been left on their own “to flatten the rationing curve” in hopes that resources never have to be explicitly rationed at their facility. Unfortunately, the downstream result is a misinformed and distrustful public (i.e. parents, guardians, and caregivers) filled with people who are already burdened with inflammatory pseudoscience narratives and deficits in health literacy. This paper aims to elevate a more thoughtful conversation about healthcare rationing by analyzing some existing ethical principles/framework developed for rationing decision making during previous emergency responses and drawing from the day-to-day clinical perspectives of a frontline pediatric acute care/hospitalist. (shrink)

The current COVID-19 pandemic and the previous SARS/MERS outbreaks of 2003 and 2012 have resulted in a series of major global public health crises. We argue that in the interest of developing effective and safe vaccines and drugs and to better understand coronaviruses and associated disease mechenisms it is necessary to integrate the large and exponentially growing body of heterogeneous coronavirus data. Ontologies play an important role in standard-based knowledge and data representation, integration, sharing, and analysis. Accordingly, we initiated the (...) development of the community-based Coronavirus Infectious Disease Ontology in early 2020. -/- As an Open Biomedical Ontology (OBO) library ontology, CIDO is open source and interoperable with other existing OBO ontologies. CIDO is aligned with the Basic Formal Ontology and Viral Infectious Disease Ontology. CIDO has imported terms from over 30 OBO ontologies. For example, CIDO imports all SARS-CoV-2 protein terms from the Protein Ontology, COVID-19-related phenotype terms from the Human Phenotype Ontology, and over 100 COVID-19 terms for vaccines (both authorized and in clinical trial) from the Vaccine Ontology. CIDO systematically represents variants of SARS-CoV-2 viruses and over 300 amino acid substitutions therein, along with over 300 diagnostic kits and methods. CIDO also describes hundreds of host-coronavirus protein-protein interactions (PPIs) and the drugs that target proteins in these PPIs. CIDO has been used to model COVID-19 related phenomena in areas such as epidemiology. The scope of CIDO was evaluated by visual analysis supported by a summarization network method. CIDO has been used in various applications such as term standardization, inference, natural language processing (NLP) and clinical data integration. We have applied the amino acid variant knowledge present in CIDO to analyze differences between SARS-CoV-2 Delta and Omicron variants. CIDO's integrative host-coronavirus PPIs and drug-target knowledge has also been used to support drug repurposing for COVID-19 treatment. -/- CIDO represents entities and relations in the domain of coronavirus diseases with a special focus on COVID-19. It supports shared knowledge representation, data and metadata standardization and integration, and has been used in a range of applications. (shrink)

The COVID-19 pandemic generated overflow of healthcare systems in several countries. As the ethical debates focused on prioritisation for access to care with scarce medical resources, numerous recommendations were created. Late 2021, the emergence of the Omicron variant whose transmissibility was identified but whose vaccine sensitivity was still unknown, reactivated debates. Fears of the need to prioritise patients arose, particularly in France. Especially, a debate began about the role of vaccination status in the prioritisation strategy. The Ethics Committee (...) (EC) of the University Hospital of Bordeaux (UHB), France, identified prioritisation criteria in the literature (some recommended, such as being a healthcare worker (HCW) or having consented to research, while others were discouraged, such as age with a threshold effect or vaccination status). A survey was sent within the institution in January 2022 to explore frontline physicians' adherence to these prioritisation criteria. The decision making conditions were also surveyed. In 15 days, 78/165 (47.3%) frontline physicians responded, and more widely 1286/12946 (9.9%) professionals. A majority of frontline physicians were opposed to prioritising HCWs (54/75, 72%) and even more opposed to participating in research (69/76, 89.6%). Conversely, the results were very balanced for non-recommended criteria (respectively 39/77, 50.7% and 34/69 49.3% in favour for age with a threshold effect and for vaccination status). Decisions were considered to be multi-professional and multi-disciplinary for 65/76, 85.5% and 53/77, 68.8% of frontline physicians. Responders expressed opposition to extending decision-making to representatives of patients, civil society or HCWs not involved in care. Prioritisation recommendations in case of scarce medical resources were not necessarily approved by the frontline physicians, or by the other HCWs. This questions the way ethical recommendations should be communicated and discussed at a local scale, but it also questions these recommendations themselves. The article also reports the experience of seeking HCWs opinions on a sensitive ethical debate in a period of crisis. (shrink)

With the coronavirus pandemic and the Omicron variant once again forcing countries into lockdown, this essay seeks to outline a Foucauldian critique of various legal measures taken by the Danish government to cope with COVID-19 during the first year and a half of the pandemic. The essay takes a critical look at the extra-legal measures employed by the Danish government, as the Danish politicians attempted to halt the spread of the, now almost forgotten, Cluster 5 COVID-19 variant. (...) This situation will serve as a critical point from where to start using Foucault’s writings on life and biopolitics in order to expose various legally problematic governmental decisions that became visible during the handling of COVID-19 in general and the Cluster 5 mutation in particular. Reframing the pandemic within Foucault’s concept of biopolitics, this essay concludes that the state of exception has led to an increase in biopolitical logic, where some lives have come to matter more than others. As a critical counterpoint to this logic, the conclusion suggests that the notion of biocommunism could provide a suitable reconfiguration of communism. A reconfiguration that could mitigate some of the issues related to biopolitics is uncovered earlier in the essay. (shrink)

In ‘Does zero-COVID neglect health disparities?’ we made the case that strict zero-COVID policies implemented during the coronavirus 2019 disease (COVID-19) pandemic raise health equity concerns so serious that these policies are not ethically sustainable.1 Zero-COVID, which has dominated many Pacific Rim societies, sets zero deaths from COVID-19 as a goal, and aims to reach it by forcefully containing transmission through short-term lockdowns, followed by stringent find, test, trace and isolate methods. Since the paper appeared in 2021, the Omicron (...) variant and subvariants took hold, making a strict zero goal unattainable and leading many countries to abandon it. Careful ethical analysis of zero-COVID’s impact remains crucially important, however, not only because the novel coronavirus continues to surprise us, but also to ensure lessons learnt from this pandemic are carried forward to future pandemics. In ‘Zero-COVID and health inequities’,2 Schaefer argues that it is possible to pursue zero-COVID yet offset any negative impacts on disadvantaged groups. Citing Singapore, where zero-COVID led to outbreaks in crowded and unsanitary migrant workers dormitories, Schaefer notes the government offset these effects, setting up less densely populated ‘quick build dormitories’ that caused daily case counts to drop, even while zero-COVID remained …. (shrink)

As we journey into the fourth year of the COVID-19 pandemic, a majority of Americans express relief at a “return to normal,” experience pandemic fatigue, or embrace the idea of living with COVID-19 in much the same way we live with the seasonal flu. But transition to a new phase of life with SARS-CoV-2 does not diminish the importance of vaccination. The US Centers for Disease Control and the Food and Drug Administration recently recommended another round of booster dose for (...) persons age 5 and up, or an initial series for those not previously vaccinated, with an updated bivalent formula that protects against both the original virus strain and Omicron subvariants that are now the dominant source of infection. By most accounts most of the population has been or will become infected with SARS-CoV-2. Suboptimal uptake of the COVID-19 vaccines among the approximately 25 million adolescents in the United States is a significant obstacle to population coverage, public health, and the health and well-being of adolescents. A major cause of low adolescent uptake is parental vaccine hesitancy. This article discusses parental vaccine hesitancy and argues that permitting independent adolescent consent to COVID-19 vaccination should be an ethical and policy priority as we continue to confront the threat of Omicron and other variants of the coronavirus. We discuss the central role of the pediatric healthcare team in caring for adolescent patients who disagree with their parents about vaccination. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:On the NoseDavid F. Bell (bio)I recently underwent a COVID test. As the technician inserted the rather ominous cotton-tipped probe into my nostril, she told me that it was going to feel as if she were tickling my brain. Indeed… This experience, shared by many during the past three years, and likely multiple times, prompted me to think about my nose. Not since cocaine reentered American mainstream culture in (...) the 1970s and '80s—and found its way into countless movies that reflect the trend—has the nose been so central to a certain state of public life. It's difficult to find a film dealing with American culture from that period and beyond, from Scarface to The Wolf of Wall Street, in which there is not a scene depicting characters snorting the obligatory line or spoon of cocaine. Yes, snorting, sniffing, sneezing, ingesting the line through the nose and finishing leftover dust by collecting it with a moist finger, rubbing it lovingly against the front gum of the mouth. Freud's "Über Coca" looms ominously in the background, the work of a phase in Freud's professional career complicated by his obscure relationships with Parke-Davis (now a subsidiary of Pfizer) and Merck, pharmaceutical companies that supplied him with early samples to tickle his nose (Freud; Merkel). The Sacklers of the moment. In our day, Pfizer wants to transform our noses into defenses against the virus rather than conduits toward mind-altering dreams. In the wake of the Freud and William Halsted cocaine addictions chronicled by Howard Merkel, the irony of the contemporary link between Pfizer and the nose is patent.The nose: that orifice through which the virus creeps, the first stage in breathing, the first filter for air-borne pollutants. Recently, important immunological analyses of COVID have focused on the question of viral load, how much virus is necessary to overcome the nose's filtering function and reach the deeper airways leading to the lungs. The processes triggered by any of the major vaccines prepare antibody blueprints and actual antibodies that can be dispatched to the linings of the nose to counter the virus as soon as the body detects its presence. The Delta, Omicron, and subsequent variants remind us that the virus has mechanisms to challenge this response, namely, increased viral load that intensifies transmissibility and the potential to overwhelm antibodies. It seems, however, that [End Page 231] so-called breakthrough infections are still well controlled by the body's vaccinated immune system. Hysteria about the dangers of such incursions is partially a product of biased and often incorrect or incomplete media coverage of the COVID vaccine, which has terrified the vaccinated and fueled the skepticism of the unvaccinated.The virus tries to overpower and confuse the filtering nose in another way, more immediately apparent to our conscious selves. As many as eighty-five percent of COVID infections result in the loss of smell, generally recovered in about two to three weeks in sickened people who overcome the infection. About five percent of COVID victims, however, have not recovered their sense of smell six months or more after they have shed the virus.1 What might it mean to lose one's sense of smell? In our vision-oriented culture, both sound (the ear) and smell (the nose) have been less recognized as primary defense mechanisms than in other cultures. When one hears a sound, the first reaction is to prepare for a threat, before the sonic source is seen or understood. Orientation in the world, knowing from which direction the sound emanates, is key to preparing the body for an encounter with an unknown phenomenon: "To sound (an alarm) means to warn. Isn't any emerging sound understood as a warning? Any unexpected sonic occurrence is seen as an indication of something that is to come and that must be clarified rapidly" (Deshays 34). By the same token, to sample surroundings by sniffing what is in the air signals whether one should inhale or somehow try to hold one's breath in search of cleaner, more palatable air. Without olfaction, we are at potentially heightened risk of asphyxiation. We are more likely to... (shrink)

Set in the immediate context of the recent UN conference on climate change in Glasgow and the sudden emergence of the variant, Omicron, this paper involves discussion of the present state of discourse concerning globalization in the broadest sense. It begins by contrasting the approaches and substance of two specific books: Globalization Matters by Manfred Steger and Paul James and Grave New World by Stephen King. The difference between the two books is brought into sharp relief by the (...) economism of the book by King and the multidimensionality of the volume by Steger and James. More generally, these recent books are chosen because they are almost complete opposites, the central difference being the adamant optimism about globalization in Globalization Matters and the extreme pessimism and negativity in Grave New World. It is also very important to emphasize the wide ranging and penetrative character of Globalization Matters compared with the latter. Also invoked is recent and very significant work by Dipesh Chakrabarty. Two themes are claimed here to be neglected, namely global history and the concept of glocalization. Attention is also drawn to the crucial omission of the fact that much of globalization talk began in the fields of religious study and theology. The disparity between these two latter fields of study and mainstream social science and conventional history is given attention. The contributions of other crucial commentators to the overall debate, Lovelock and Latour, are also invoked. The focus by Steger and James, on the one hand, and Chakrabarty on the other, on the Anthropocene is given attention. Overall, the article concludes by placing the global-local problematic at the centre of what is called here globalization discourse. (shrink)

This study aims to explore librarians’ motivating styles in virtual information literacy instruction sessions based on participating students’ perception. The research method use a quantitative approach, involving a survey method was applied for this study. The survey was conducted involving a sample of 250 students who had attended the virtual information literacy sessions at the selected library. The questionnaire was distributed electronically using Google Form and it comprised of open-ended questions to provide responses regarding the motivation provided by librarians in (...) virtual literacy instruction. The study identified three stages of the virtual information literacy instructions in which librarians applied different motivational styles. The three learning processes: Greeting and Welcome, Core, and Wrap up, each provided evidence of motivating styles. The findings of this investigation are useful to practicing librarians as they can focus on motivating students during the virtual information literacy instruction. (shrink)

This article argues that the much-maligned ‘notational variants’ of a given formal linguistic theory play a role similar to alternative numerical measurement scales. Thus, they can be used to identify the invariant components of the grammar; i.e., those features that do not depend on the choice of empirically equivalent representation. Treating these elements as the ‘meaningful’ structure of language has numerous consequences for the philosophy of science and linguistics. I offer several such examples of how linguistic theorizing can profit from (...) adopting a measurement-theoretic viewpoint. The first concerns a measurement-theoretic response to a famous criticism of Quine's. Others follow from issues of simplicity in the current biolinguistics program. An unexpected similarity with behaviorist practices is also uncovered. I then argue that managable and useful steps can be taken in this area. (shrink)

The tableaux-constructions have a number of properties which advantageously distinguish them from equivalent axiomatic systems . The proofs in the form of tableaux-constructions have a full accordance with semantic interpretation and subformula property in the sense of Gentzen’s Hauptsatz. Method of tatleaux-construction gives a good substitute of Gentzen’s methods and thus opens a good perspective for the investigations of theoretical as well as applied aspects of logical calculi. It should be noted that application of tableau method in modal, tense, relevant (...) and other non-classical logics is connected with serious difficulties. Tableaux variants are constructed only for a few normal modal systems. As to relevant and paraconsistent logic, the absence of its tableau variants may be considered as a question of special interest. We shall formulate the tableaux for propositional modal system S4.1, S4.2, S4.3, S4.4 and relevant R∗ and E ∗ using Beth’s tableaux construction with indexed formulas. (shrink)

An efficient variant of the double-negation translation explains the relationship between Shoenfield’s and G¨odel’s versions of the Dialectica interpretation.

Capitalist dynamics in knowledge production are not limited to situations in which economic interests influence researchers’ practices. Building on laboratory studies and the French “pragmatic” tradition in sociology, this article proposes an approach to tackle more pervasive capitalist logics at work in contemporary research and their consequences. It uses the term epistemic capitalism to denote the accumulation of capital, as worth made durable, through the act of doing research, in and beyond academia. In doing so, it conceptualizes capitalism primarily not (...) as a system of circulation and accumulation of monetary value but rather as a cultural way of producing, attributing, and accumulating specific forms of worth, which need not be monetary. Empirically, the article studies variants in epistemic capitalism by addressing the differing role of the accumulation of different forms of capital and the regimes connected to it in two institutional settings in Austria, academic life science laboratories and biotechnology start-up companies. Concluding, it argues that analytically dissociating the concept of capitalism from its link to economic value allows a finer-grained cultural analysis of the importance and effects of processes of accumulation in contemporary research. It ends with discussing the normative implications of these findings for debates about the commercialization of academia. (shrink)

First we give an overview about variants of visibility and related problems. Then we prove that some guarding and covering problems are NP-hard for ortho-polygons with holes, using a so-called vertex cover technique.

Focus on the way in which cultural variants affect other variants' probabilities of transmission in modeling and empirical work can enrich Kline's conceptualization of teaching. For example, the problem of communicating complex cumulative culture is an adaptive problem; teaching methods that manage transmission so that acquisition of some cultural variants increases the probability of acquiring others, provide a partial solution.

This paper examines different forms in which?Third Serbia? is being discursively constructed. This concept has recently been offered within the public arena as the alternative to the former division into?First? and?Second? Serbia. Although the name is the same,?Third Serbia? is not one but many. They all share an explicit call for overcoming cleavages and extremes, which are perceived as overdrawn, artificial, and/or removed from genuine concerns and interests of Serbian society. There is also a moral claim contained in this, since (...) what is offered is presented as better and more correct than the previous dichotomy. The various facets of?Third Serbia?, their similarities and divergences, will be explored based on the analysis of a corpus of texts from daily and weekly press in which this signifier is found. (shrink)

Among the types of strings which are technically ungrammatical but fully intelligible, dialect variants form a special class. They can be viewed as generated by alternate transformations within the grammar; the means by which they are interpreted is therefore identical with the means by which interpretations are assigned to well-formed strings. Such language-specific rules thus differ from the universal procedures by which other types of ungrammatical strings are apparently derived.

Brain‐derived neurotrophic factor (BDNF) is the most‐abundant neurotrophin in the brain. In mammals, it is synthesized as a precursor called proBDNF, which is proteolytically cleaved to generate mature BDNF. The BDNF gene is located on chromosome 11p13, and a functional single nucleotide polymorphism (SNP) of this gene has been shown to produce a valine (Val)‐to‐methionine (Met) substitution in the proBDNF protein at codon 66 (Val66Met). Several papers suggest that this SNP is related to decreased hippocampal volume and hippocampus‐mediated memory performance (...) in humans. Recently, Chen et al.1 generated a variant BDNF mouse (BDNFMet/Met) that reproduces the phenotypic hallmarks in humans with a variant Met allele. In the behavioral analysis, BDNFMet/Met mice show increased anxiety‐related behaviors. This mini‐review examines the impact of Met substitution of proBDNF on anxiety‐related behaviors. BioEssays 29: 116–119, 2007. © 2007 Wiley Periodicals, Inc. (shrink)

In this paper, we introduce anaffective variant of the Simon paradigm. Three experiments are reported in which nouns and adjectives with a positive, negative, or neutral affective meaning were used as stimuli. Depending on the grammatical category of the presented word (i.e. noun or adjective), participants had to respond as fast as possible by saying a predetermined positive or negative word. In Experiments 1 and 2, the words POSITIVE and NEGATIVE were required as responses, in Experiment 3, FLOWER and (...) CANCER were used as response words. Despite the fact that participants were explicitly instructed to ignore the affective meaning of the presented words, reaction times were faster when the affective connotation of the presented word and the correct response was the same than when it differed. The results lendfurther support tothe hypothesis that stimulus valence can be processed automatically. We also argue that the affective Simon paradigm can be used as a flexible tool for the study of affective-processing and discuss how other variants of the Simon paradigm can be developed to stimulate research on other aspects of information-processing. (shrink)

This paper presents detailed formalizations of ontological arguments in a simple modal natural deduction calculus. The first formal proof closely follows the hints in Scott’s manuscript about Gödel’s argument and fills in the gaps, thus verifying its correctness. The second formal proof improves the first one, by relying on the weaker modal logic KB instead of S5 and by avoiding the equality relation. The second proof is also technically shorter than the first one, because it eliminates unnecessary detours and uses (...) Axiom 1 for the positivity of properties only once. The third and fourth proofs formalize, respectively, Anderson’s and Bjørdal’s variants of the ontological argument, which are known to be immune to modal collapse. (shrink)

This is the first part of a two-part article on semantic compositionality, that is, the principle that the meaning of a complex expression is determined by the meanings of its parts and the way they are put together. Here we provide a brief historical background, a formal framework for syntax and semantics, precise definitions, and a survey of variants of compositionality. Stronger and weaker forms are distinguished, as well as generalized forms that cover extra-linguistic context dependence as well as linguistic (...) context dependence. In the second article, we survey arguments for and arguments against the claim that natural languages are compositional, and consider some problem cases. It will be referred to as Part II. (shrink)

Genetic research into ageing, longevity and late-onset disease is becoming increasingly common. Yet, there is a paucity of knowledge related to clinical actionability and the return of pathogenic variants to otherwise healthy elderly individuals. Whether or not genetic research in the elderly should be managed differently from standard practices adapted for younger populations has not yet been defined. In this article, we provide an overview of ethical and practical challenges in preparing for a genetic study of over 14 000 healthy (...) Australians aged 70 years or older enrolled in the ASPirin in Reducing Events in the Elderly Healthy Ageing Biobank. At the time of consent, all participants in this study were free of life-threatening illness, cardiovascular disease or cognitive impairment. ASPREE is thus a cohort of healthy elderly individuals with seemingly minimal burden of genetic disease recruited without ascertainment bias. The cohort presents a unique opportunity to address the penetrance of known pathogenic variants in a population without disease symptoms; however, it also raises a number of ethical concerns regarding the interpretation and disclosure of variants with known clinical actionability. Some of the challenges include how to manage the interpretation, disclosure and actioning of pathogenic variants found in otherwise healthy elderly adults without disease symptoms, whether or not to disclose findings for the benefit of family members rather than elderly consented donors themselves, how to manage the return of genetic findings to the elderly individuals who are now in severe cognitive decline or terminal illness, how to ensure quality of information and clinical service upon disclosure of results to this demographic and how to prepare for the insurance implications of disclosing genetic information under Australian law. We discuss these and other dilemmas and propose a defensible plan of management. Trial registration number ISRCTN83772183. (shrink)

The occurrence of a new strain of SARS-CoV-2 cannot be ruled out. Therefore, this study seeks to investigate the possible effects of a hypothetical imperfect anti-COVID-19 vaccine on the control of not only the first variant of SARS-CoV-2 but also the second variant of SARS-CoV-2. We further examine the rates and a, escape of quarantined infectious individuals from isolation centers. The control R c and basic reproduction numbers R 0 are computed which gives assess to obtain asymptotic stability (...) of disease-free equilibrium point globally and the existence of a unique persistent equilibrium solution. Numerical results reveal that people infected with the second strain who are vaccinated with an imperfect vaccine are under control but the prevalence of the second variant enhances the prevalence of the first variant. Thus, discovering a vaccine that is effective for the prevention of variant 2 is necessary for the control of COVID-19. Numerical results also reveal that increase in the rate at which individuals infected with the first variant escape the isolation center gives rise to the population infected with the first variant and lowers the peak of the population infected with the second variant. This is probably because individuals infected with the second variant appear to be more careful with their lives and get vaccinated more than individuals infected with the first variant. (shrink)

The mechanism(s) by which the thymidine analogue 5‐bromodeoxyuridine (BUdR) specifically inhibits the expression of differentiated functions is poorly understood, as are the ways in which cells regulate processes exhibiting probabilistic aspects. I have developed a theoretical model for the regulation of the decision of myogenic cells to differentiate that can explain both of the above phenomena. This model provided a strategy for isolating myoblast variants that had amplified the expression of the factors regulating the decision to differentiate. These myoblasts served (...) as the source of mRNA for making and screening a cDNA library in order to isolate these factors. The successful cloning of these genes should represent a major advance in our understanding of the molecular basis for the major coordinated changes in gene expression that accompany cell differentiation. (shrink)

Various connexive FDE-based modal logics are studied. Some of these logics contain a conditional that is both connexive and strict, thereby highlighting that strictness and connexivity of a conditional do not exclude each other. In particular, the connexive modal logics cBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document}, cKN4, scBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document}, scKN4, cMBL, and scMBL are introduced semantically by means of classes of Kripke models. The logics cBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} (...) \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document} and cKN4 are connexive variants of the FDE-based modal logics BK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document} and KN4 with a weak and a strong implication, respectively. The system cMBL is a connexive variant of the modal bilattice logic MBL. The latter is a modal extension of Arieli and Avron’s logic of logical bilattices and is characterized by a class of Kripke models with a four-valued accessibility relation. In the systems scBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document}, scKN4, and scMBL, the conditional is both connexive and strict. Sound and complete tableau calculi for all these logics are presented and used to show that the entailment relations of the systems under consideration are decidable for finite premise set. Moreover, the logics cBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {cBK}^-$$\end{document} and cMBL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {cMBL}$$\end{document} are shown to be algebraizable. The algebraizability of cMBL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {cMBL}$$\end{document} is derived from proving cMBL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {cMBL}$$\end{document} to be definitionally equivalent to MBL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {MBL}$$\end{document}. All connexive modal logics studied in this paper are decidable, paraconsistent, and inconsistent but non-trivial logics. (shrink)

Kreisel’s conjecture is the statement: if, for all$n\in \mathbb {N}$,$\mathop {\text {PA}} \nolimits \vdash _{k \text { steps}} \varphi (\overline {n})$, then$\mathop {\text {PA}} \nolimits \vdash \forall x.\varphi (x)$. For a theory of arithmeticT, given a recursive functionh,$T \vdash _{\leq h} \varphi $holds if there is a proof of$\varphi $inTwhose code is at most$h(\#\varphi )$. This notion depends on the underlying coding.${P}^h_T(x)$is a predicate for$\vdash _{\leq h}$inT. It is shown that there exist a sentence$\varphi $and a total recursive functionhsuch that$T\vdash (...) _{\leq h}\mathop {\text {Pr}} \nolimits _T(\ulcorner \mathop {\text {Pr}} \nolimits _T(\ulcorner \varphi \urcorner )\rightarrow \varphi \urcorner )$, but, where$\mathop {\text {Pr}} \nolimits _T$stands for the standard provability predicate inT. This statement is related to a conjecture by Montagna. Also variants and weakenings of Kreisel’s conjecture are studied. By the use of reflexion principles, one can obtain a theory$T^h_\Gamma $that extendsTsuch that a version of Kreisel’s conjecture holds: given a recursive functionhand$\varphi (x)$a$\Gamma $-formula (where$\Gamma $is an arbitrarily fixed class of formulas) such that, for all$n\in \mathbb {N}$,$T\vdash _{\leq h} \varphi (\overline {n})$, then$T^h_\Gamma \vdash \forall x.\varphi (x)$. Derivability conditions are studied for a theory to satisfy the following implication: if, then$T\vdash \forall x.\varphi (x)$. This corresponds to an arithmetization of Kreisel’s conjecture. It is shown that, for certain theories, there exists a functionhsuch that$\vdash _{k \text { steps}}\ \subseteq\ \vdash _{\leq h}$. (shrink)