In this paper we present a modal logic framework to reason about the expertise of information sources. A source is considered an expert on a proposition φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document} if they are able to correctly refute φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document} in any possible world where φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document} is false. Closely connected with expertise is a notion of (...) soundness of information: φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document} is said to be “sound” if it is true up to lack of expertise of the source. That is, any statement logically weaker than φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document} on which the source has expertise must in fact be true. This is relevant for modelling situations in which sources make claims beyond their domain of expertise. Particular attention is paid to the connection between expertise and knowledge: we show that expertise and soundness admit precise interpretations in terms of S4 and S5 epistemic logic, under certain conditions. We go on to extend the framework to multiple sources, defining two notions of collective expertise. These also have epistemic interpretations via distributed and common knowledge from multi-agent epistemic logic. On the technical side, we give several sound and complete axiomatisations of various classes of expertise models. (shrink)

In the study of the arithmetic degrees the $\omega \text {-REA}$ sets play a role analogous to the role the r.e. degrees play in the study of the Turing degrees. However, much less is known about the arithmetic degrees and the role of the $\omega \text {-REA}$ sets in that structure than about the Turing degrees. Indeed, even basic questions such as the existence of an $\omega \text {-REA}$ set of minimal arithmetic degree are open. This paper makes progress on (...) this question by demonstrating that some promising approaches inspired by the analogy with the r.e. sets fail to show that no $\omega \text {-REA}$ set is arithmetically minimal. Finally, it constructs a $\prod ^0_{2}$ singleton of minimal arithmetic degree. Not only is this a result of considerable interest in its own right, constructions of $\prod ^0_{2}$ singletons often pave the way for constructions of $\omega \text {-REA}$ sets with similar properties. Along the way, a number of interesting results relating arithmetic reducibility and rates of growth are established. (shrink)

We extend work of H. Friedman, L. Harrington and P. Welch to the third level of the projective hierarchy. Our main theorems say that (under appropriate background assumptions) the possibility to select definable elements of non-empty sets of reals at the third level of the projective hierarchy is equivalent to the disjunction of determinacy of games at the second level of the projective hierarchy and the existence of a core model (corresponding to this fragment of determinacy) which must then (...) contain all real numbers. The proofs use Sacks forcing with perfect trees and core model techniques. (shrink)

Recent experimental data from proteomics and genomics are interpreted here in ways that challenge the predominant viewpoint in biology according to which the four evolutionary processes, including mutation, recombination, natural selection and genetic drift, are sufficient to explain the origination of species. The predominant viewpoint appears incompatible with the finding that the sequenced genome of each species contains hundreds, or even thousands, of unique genes - the genes that are not shared with any other species. These unique genes and proteins, (...) singletons, define the very character of every species. Moreover, the distribution of protein families from the sequenced genomes indicates that the complexity of genomes grows in a manner different from that of self-organizing networks: the dominance of singletons leads to the conclusion that in living organisms a most unlikely phenomenon can be the most common one. In order to provide proper rationale for these conclusions related to the singletons, the paper first treats the frequency of functional proteins among random sequences, followed by a discussion on the protein structure space, and it ends by questioning the idea that protein domains represent conserved units of evolution. (shrink)

We investigate and extend the notion of a good approximation with respect to the enumeration ${({\mathcal D}_{\rm e})}$ and singleton ${({\mathcal D}_{\rm s})}$ degrees. We refine two results by Griffith, on the inversion of the jump of sets with a good approximation, and we consider the relation between the double jump and index sets, in the context of enumeration reducibility. We study partial order embeddings ${\iota_s}$ and ${\hat{\iota}_s}$ of, respectively, ${{\mathcal D}_{\rm e}}$ and ${{\mathcal D}_{\rm T}}$ (the Turing degrees) into (...) ${{\mathcal D}_{\rm s}}$ , and we show that the image of ${{\mathcal D}_{\rm T}}$ under ${\hat{\iota}_s}$ is precisely the class of retraceable singleton degrees. We define the notion of a good enumeration, or singleton, degree to be the property of containing the set of good stages of some good approximation, and we show that ${\iota_s}$ preserves the latter, as also other naturally arising properties such as that of totality or of being ${\Gamma^0_n}$ , for ${\Gamma \in \{\Sigma,\Pi,\Delta\}}$ and n > 0. We prove that the good enumeration and singleton degrees are immune and that the good ${\Sigma^0_2}$ singleton degrees are hyperimmune. Finally we show that, for singleton degrees a s < b s such that b s is good, any countable partial order can be embedded in the interval (a s, b s). (shrink)

We combine two techniques of set theory relating to minimal degrees of constructibility. Jensen constructed a minimal real which is additionally a Π 1 2 singleton. Groszek built an initial segment of order type 1 + α * , for any ordinal α. This paper shows how to force a Π 1 2 singleton such that the c-degrees beneath it, all represented by reals, are of type 1 + α * , for many ordinals α. We also examine the definability (...) α needs to be so represented by a real. (shrink)

We consider implicit definability over the natural number system $\mathbb{N},+,\times,=$. We present a new proof of two theorems of Leo Harrington. The first theorem says that there exist implicitly definable subsets of $\mathbb{N}$ which are not explicitly definable from each other. The second theorem says that there exists a subset of $\mathbb{N}$ which is not implicitly definable but belongs to a countable, explicitly definable set of subsets of $\mathbb{N}$. Previous proofs of these theorems have used finite- (...) or infinite-injury priority constructions. Our new proof is easier in that it uses only a nonpriority oracle construction, adapted from the standard proof of the Friedberg jump theorem. (shrink)

We investigate an enrichment of the propositional modal language L with a "universal" modality ■ having semantics x ⊧ ■φ iff ∀y(y ⊧ φ), and a countable set of "names" - a special kind of propositional variables ranging over singleton sets of worlds. The obtained language ℒ $_{c}$ proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment ℒ(⍯) of ℒ, where ⍯ is an additional modality with the semantics x ⊧ ⍯φ (...) iff Vy(y ≠ x → y ⊧ φ). Model-theoretic characterizations of modal definability in these languages are obtained. Further we consider deductive systems in ℒ $_{c}$ . Strong completeness of the normal ℒ $_{c}$ logics is proved with respect to models in which all worlds are named. Every ℒ $_{c}$ -logic axiomatized by formulae containing only names (but not propositional variables) is proved to be strongly frame-complete. Problems concerning transfer of properties ([in]completeness, filtration, finite model property etc.) from ℒ to ℒ $_{c}$ are discussed. Finally, further perspectives for names in multimodal environment are briefly sketched. (shrink)

Full meet contraction, that was devised by Carlos Alchourrón and David Makinson in the early 1980' s, has often been overlooked since it is not in itself a plausible contraction operator. However, it is a highly useful building-block in the construction of composite contraction operators. In particular, all plausible contraction operators can be reconstructed so that the outcome of contracting a belief set K by a sentence p is defined as K ∼ f, where ∼ is full meet contraction and (...) f a sentential selector, i.e. a function to and from sentences. This paper investigates the logic of full meet contraction. Seven properties of this operation are presented that contribute to making it useful as a building-block: Full meet contraction is a purely logical operation. It retains finitebasedness of the belief set. It is the inclusion-maximal contraction that removes all sentences that can contribute to implying the input sentence. It is the inclusion-maximal contraction that removes all non-tautologous consequences of the input sentence. Almost all contractions can be reconstructed as full meet contraction. Full meet contraction allows for recovery of the input sentence. Full meet contraction provides a unified account of multiple and singleton contraction. La llamada full meet contraction, creada por Carlos Alchourrón y David Makinson en los comienzos de los ' 80, ha sido a menudo desestimada puesto que ella no constituye un operador de contracción plausible. De todas formas ella es altamente útil en la construcción de operadores de contracción compuestos. En particular, todos los operadores de contracción plausibles pueden ser reconstruidos de forma tal que la contracción de un conjunto de creencias K por una sentencia p sea definida como K ∼ f, donde ∼ es una full meet contraction y f un selector de sentencias, i.e., una función de sentencias a sentencias. En este trabajo investigamos la lógica de la full meet contraction. Se presentan siete propiedades de esta operación que contribuyen a hacerla útil como building-block: Full meet contraction es una operación puramente lógica. Ella retiene la finit- basednes del conjunto de creencias. Ella es la máxima-inclusiva de las contracciones que elimina todas las sentencias que pueden contribuir a implicar la input-sentence. Es la contracción maximal inclusiva que elimina todas las consecuencias no tautológicas de la input-sentence. Casi todas las contracciones pueden ser reconstruidas como full-meet contractions. Full meet contraction permite la recuperación de la input-sentence. Full meet contracción da cuenta en forma unificada de las contracciones múltiples y singulares. (shrink)

We briefly overview some of the historical landmarks on the path leading to the reduction of the number of logical connectives in classical logic. Relying on the duality inherent in Boolean algebras, we introduce a new operator ( Nallor ) that is the dual of Schönfinkel’s operator. We outline the proof that this operator by itself is sufficient to define all the connectives and operators of classical first-order logic ( Fol ). Having scrutinized the proof, we pinpoint the theorems of (...) Fol that are needed in the proof. Using the insights gained from the proof, we show that there are four binary operators that each can serve as the only undefined logical constant for Fol . Finally, we show that from every n -ary connective that yields a functionally complete singleton set of connectives two Schönfinkel-type operators are definable, and all the latter are so definable. (shrink)

Let I be an ideal of subsets of a Polish space X, containing all singletons and possessing a Borel basis. Assuming that I does not satisfy ccc, we consider the following conditions (B), (M) and (D). Condition (B) states that there is a disjoint family F $\subseteq$ P(X) of size c, consisting of Borel sets which are not in I. Condition (M) states that there is a Borel function f: X → X with $f^{-1}[\{x\}] \not\in$ I for each x (...) ∈ X. Provided that X is a group and I is invariant, condition (D) states that there exist a Borel set B $\not\in$ I and a perfect set P $\subseteq$ X for which the family $\{B + x: x \in P\}$ is disjoint. The aim of the paper is to study whether the reverse implications in the chain (D) $\Rightarrow$ (M) $\Rightarrow$ (B) $\Rightarrow$ not-ccc can hold. We build a σ-ideal on the Cantor group witnessing (M) & ¬ (D) (Section 2). A modified version of that σ-ideal contains the whole space (Section 3). Some consistency results on deriving (M) from (B) for "nicely" defined ideals are established (Sections 4 and 5). We show that both ccc and (M) can fail (Theorems 1.3 and 5.6). Finally, some sharp versions of (M) for invariant ideals on Polish groups are investigated (Section 6). (shrink)

We consider a set-theoretic version of mereology based on the inclusion relation ⊆ and analyze how well it might serve as a foundation of mathematics. After establishing the non-definability of ∈ from ⊆, we identify the natural axioms for ⊆-based mereology, which constitute a finitely axiomatizable, complete, decidable theory. Ultimately, for these reasons, we conclude that this form of set-theoretic mereology cannot by itself serve as a foundation of mathematics. Meanwhile, augmented forms of set-theoretic mereology, such as that obtained by (...) adding the singleton operator, are foundationally robust. (shrink)

We consider countably additive, nonnegative, extended real-valued measures which vanish on singletons. Such a measure is universal on a set X iff it is defined on all subsets of X and is semiregular iff every set of positive measure contains a subset of positive finite measure. We study the problem of existence of a universal semiregular measure on X which is invariant under a given group of bijections of X. Moreover we discuss some properties of universal, semiregular, invariant measures (...) on groups. (shrink)

We work in λH, the untyped λ-calculus in which all unsolvables are identified. We resolve a conjecture of Barendregt asserting that the range of a definable map is either infinite or a singleton. This is refuted by constructing a λ-term Ξ such that ΞM = ΞΙ ⟺ ΞM ≠ ΞΩ. The construction generalizes to ranges of any finite size, and to some other sensible lambda theories.

Domestic violence is one of the most common forms of violence against women. Domestic violence during pregnancy is associated with adverse perinatal and maternal outcomes. We aimed to assess whether domestic violence was associated with mode of delivery, low birthweight and preterm birth in two sites in Nepal. In this prospective cohort study we consecutively recruited 2004 pregnant women during antenatal care at two hospitals between June 2015 and September 2016. The Abuse Assessment Screen was used to assess fear and (...) violence. Having ever experienced either fear or violence was defined as any domestic violence. Obstetric outcomes were obtained from hospital records for 1381 women, selecting singleton pregnancies only. Mode of delivery was assessed as birth by cesarean section or not. A birthweight of less than 2500 g was defined as low birthweight and preterm birth as birth before completion of 37 weeks gestation. Descriptive and multiple logistic regression analyses were performed to assess associations. Twenty percent of the women reported any domestic violence. Among all 1381 women, 37.6% gave birth by cesarean section. Of those women who delivered by cesarean section, 84.7% had an emergency cesarean section. Less than 10% of the babies were born prematurely and 13.5% were born with low birthweight. We found no significant association between exposure to any domestic violence during pregnancy and risk of a low birthweight baby or birth by cesarean section. However, having experienced both violence and fear was significantly associated with giving birth to a preterm infant [aOR 2.33 ]. Domestic violence is common in Nepal. This is a potential risk factor for severe morbidity and mortality in newborns. We found that the risk of having a preterm baby was higher for pregnant women who experienced both fear and violence. This should be recognized by the health sector. In this study, no significant differences were found in the rate of cesarean section nor low birthweight for women who had experienced any domestic violence compared to those who did not. (shrink)

The purpose of this paper is to defend a particular kind of cinematic realism, anti-illusionism, which is the thesis that cinematic motion is real. Following a brief introduction to realism and cinema in Section 1, I analyse Berys Gaut’s taxonomy of cinematic realism and define anti-illusionism in Section 2. Section 3 contrasts the anti-illusionist theories of Gregory Currie and Trevor Ponech with the illusionist theories of Andrew Kania and Gaut. I reconceptualize the debate in terms of Tom Gunning’s cinematic animation (...) in Section 4, focusing on the question of cinematic singletons. In Section 5 I argue that cinematic singletons both exist and undergo objective displacement—and thus for anti-illusionism. I conclude, in Sections 6–7, with responses to potential objections to my argument from Kania and Gaut. (shrink)

This paper continues joint work of the authors with P. Clote, R. Soare and S. Wainer (Annals of Pure and Applied Logic, vol. 31 (1986), pp. 145--163). An element x of the Cantor space 2 ω is said have rank α in the closed set P if x is in $D^\alpha(P)\backslash D^{\alpha + 1}(P)$ , where D α is the iterated Cantor-Bendixson derivative. The rank of x is defined to be the least α such that x has rank α in (...) some Π 0 1 set. The main result of the five-author paper is that for any recursive ordinal λ + n (where λ is a limit and n is finite), there is a point with rank λ + n which is Turing equivalent to O (λ + 2n) . All ranked points constructed in that paper are Π 0 2 singletons. We now construct a ranked point which is not a Π 0 2 singleton. In the previous paper the points of high rank were also of high hyperarithmetic degree. We now construct ▵ 0 2 points with arbitrarily high rank. We also show that every nonrecursive RE point is Turing equivalent to an RE point of rank one and that every nonrecursive ▵ 0 2 point is Turing equivalent to a hyperimmune point of rank one. We relate Clote's notion of the height of a Π 0 1 singleton in the Baire space with the notion of rank. Finally, we show that every hyperimmune point x is Turing equivalent to a point which is not ranked. (shrink)

Background: Randomized controlled trials have been criticized for their inability to identify and differentiate the causal mechanisms that generate the outcomes they measure. One solution is the development of realist trials that combine the empirical precision of trials' outcome data with realism's theoretical capacity to identify the powers that generate outcomes. Main Body: We review arguments for and against this position and conclude that critical realist trials are viable. Using the example of an evaluation of the educational effectiveness of virtual (...) reality simulation, we explore whether Partial Least Squares Structural Equation Modelling can move statistical analysis beyond correlational analysis to support realist identification of the mechanisms that generate correlations. Conclusion: We tentatively conclude that PLS-SEM, with its ability to identify ‘points of action’, has the potential to provide direction for researchers and practitioners in terms of how, for whom, when, where and in what circumstances an intervention has worked. (shrink)

Reading Beauvoir's “Must We Burn Sade?” alongside the chapter called “Sexual Initiation” in The Second Sex, I argue that the problem with Sade is not his perversity, but his perpetual virginity. In The Second Sex, Beauvoir advances a new understanding of sexual initiation as a physical and spiritual movement toward the other, disqualifying any purely physical machination as sufficient to initiate one into “authentic erotic reality.” Sade's refusal of Eros as described in “Must We Burn Sade?” demonstrates that the Marquis's (...) commitment to his characteristic Sadism in fact condemned him to a barren promiscuity, a trenchant and joyless virginity that he elected to perpetuate. Finally, I argue that we should reread Sadism not as a perversion but as based on the Greek model of the “virgin ailment.” As such, Sadism may turn out to be a more genuine and widespread threat than we ordinarily acknowledge. (shrink)

This book details the underlining philosophical approaches to ethical theories and how these can be used to structure an approach to day-to-day ethical issues, and thereby resolve them. It provides an understanding of the ethical theories which underpin decisions in health care by first laying the foundation with a philosophical framework and then going on to develop this into an examination of contemporary health care dilemmas and professional issues. Not available in the U.S.

Contemporary theories of Virtue Ethics are often presented as being in opposition to Kantian Ethics and Consequentialism. It is argued that Virtue Ethics takes as fundamental the question, “What sort of character would a virtuous person have?” and that Kantian Ethics and Consequentialism take as fundamental the question, “What makes an action right?” I argue that this opposition is misconceived. The opposition is rather between Virtue Ethics and Kantian Ethics on the one hand and Consequentialism on the other. The former (...) two are concerned with, respectively, the development of a virtuous character and a good will, whereas Consequentialism is essentially a doctrine that just provides a justification of the right option without specifying how this is to be achieved. Furthermore, I show that Consequentialism, interpreted as a justificatory doctrine, is both an impoverished doctrine and one that cannot be enriched by taking a “pick and mix” approach to other ethical theories in the way that Consequentialists advocate. I argue that there is at least one reason to prefer Kantian Ethics: Kantian Ethics necessarily avoids the objection of selfcenteredness, whereas the avoidance of this objection is only contingent in the case of Virtue Ethics. (shrink)

The Dutch microbiologist/biochemist Albert Jan Kluyver was an early proponent of the idea of biochemical unity, and how that concept might be demonstrated through the careful study of microbial life. The fundamental relatedness of living systems is an obvious correlate of the theory of evolution, and modern attempts to construct phylogenetic schemes support this relatedness through comparison of genomes. The approach of Kluyver and his scientific descendants predated the tools of modern molecular biology by decades. Kluyver himself is poorly recognized (...) today, yet his influence at the time was profound. Through lens of today however, it has been argued that the focus by Kluyver and others to create taxonomic and phylogenetic schemes using morphology and biochemistry distorted and hindered progress of the discipline of microbiology, because of a perception that the older approaches focused too much on a reductionist worldview. This essay argues that in contrast the careful characterization of fundamental microbial metabolism and physiology by Kluyver made many of the advances of the latter part of the twentieth century possible, by offering a framework which in many respects anticipated our current view of phylogeny, and by directly and indirectly training a generation of scientists who became leaders in the explosive growth of biotechnology. (shrink)

Gaze behavior is an important component of children’s language, cognitive, and sociocultural development. This is especially true for young deaf children acquiring a signed language—if they are not looking at the language model, they are not getting linguistic input. Deaf caregivers engage their deaf infants and toddlers using visual and tactile strategies to draw in, support, and promote their child’s visual attention; we argue that these caregiver actions create a developmental niche that establishes the visual modality capital their child needs (...) for successful sign language learning. But most deaf children do not have deaf signing parents and they will need to rely on adult signing teachers if they are to acquire a signed language at an early age. This study examines classroom interactions between a Deaf teacher, her teacher’s aide, and six deaf preschoolers to document the teachers’ “everyday practices” as they socialize the gaze behavior of these children. Utilizing a detailed behavioral and linguistic analysis of two video-recorded book-sharing contexts, we present data summarizing the teacher’s attention-getting actions directed toward the children and the discourse-embedded cues that signal the teacher’s expectations for student participation in the signed conversation. We observed that the teacher’s behaviors differed according to the parent status of the deaf preschooler suggesting that Deaf children of Deaf parents arrive to the preschool classroom with well-developed self-regulation of their attention or gaze. The teachers also used more physical and explicit cueing with the deaf children of hearing parents—possibly to promote their ability to leverage the visual modality for sign language acquisition. We situate these socialization patterns within a framework that integrates notions of intuitive or indigenous practices, developmental niche, and modality capital. Implications for early childhood deaf education are also discussed. (shrink)

As the first of its kind this collection draws together cutting edge scholarship in the field, focusing on the theory and practice of yoga in contemporary times ...