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

Alzheimer’s Disease (AD) and Autism Spectrum Disorder (ASD) represent two distinct but equally impactful challenges in the field of neurology and cognitive health. AD is a degenerative neurological condition characterized by its progressive nature, typically affecting individuals in later stages of life. The hallmark features include cognitive impairment, mem- ory deterioration, and alterations in behavior. In contrast, ASD is a developmental disorder typically diagnosed in childhood, marked by difficulties in social interaction, communication, and repetitive behaviors. This paper explores the potential (...) of the time-frequency feature extraction model known as the Left-Right Fast Fourier Transform (LR-FFT) in the context of these two disorders. While AD and ASD differ significantly in their onset, presentation, and demographic affected, both necessitate early and accurate diagnosis to enable timely intervention and tailored treatment strategies. Our research yields promising results, with classification accuracies reaching 88.26% for AD and 99.86% for ASD, demonstrating the LR-FFT’s potential to enhance diagnostic accuracy. By contributing to improved differentiation between these complex neurological conditions, this work aims to advance our understanding and management of AD and ASD, ultimately benefiting patients, their families, and healthcare practitioners. (shrink)

Administrative—judgment on the nature of judgment—conflict between Judges in judicial practice—claimant challenges the judicial capacity of respondent —claimant open and fluid in judicial style—respondent certain and authoritative in judicial style—insights from Psi Division on the role of judgment in the universe—whether respondent is a good judge—whether judgment closes down meaning—whether respondent is inhuman—whether judges are inhuman—whether judging is horrific—insight from twentieth century fiction on the place of humans in the universe—horror of HP Lovecraft—suppression of horrific cosmic context within judicial institution—suppression (...) for the good of society. (shrink)

Chief Judge Achilles and Judge Hera – uniqueness of proceedings – the nature of judicial decision-making – the judicial order of Mega-city One – source of judicial power – judicial styles – qualities required for judicial office – context of judicial action – requirement of reflection – interpretation and meaning in enforcement of law – adjudicative models – law as horrific – legal theories – Hans Kelsen – Justice Hercules – Jacques DerridaJudge Howard – critical assessment of judicial order of (...) Mega-city One – Hans Kelsen, positivism and democracy – merging of law fondatrice and law conservatrice – the “soul of the law” – fracture of the Rule of Law – fascism – comparisons with fascist regimes of twentieth Century Europe – signifiers in judicial uniform – consequences of dissent – reasons for, and consequences of, resignationChief Judge AchillesJudge HeraJudgement delivered 3 March 2138.Grand Hall of Justice, Mega-city One. (shrink)

Selon Schiller, jouer, c’est agir en étant dégagé de toute contrainte et de toute obligation, et donc tirer grand plaisir de sa liberté par rapport aux nécessités. C’est ce sentiment de liberté rattachant le jeu au phénomčne esthétique de beauté qui fait sa grande valeur éducationnelle. La qualité que nous appelons beauté procure le męme plaisir que le jeu. Dans une belle śuvre d’art, la matičre n’est pas dominée par la forme ou vice-versa. Une śuvre d’art est un jeu libre (...) entre forme et substance, entre beauté et contrainte, et représente de ce fait le summum de l’activité ludique. Les jeux sont des pas sur la voie de la beauté, car ils éduquent ceux qui jouent au plaisir de la liberté de création. Contrairement ŕ la position de Schiller, Maria Montessori rejette le jeu comme moyen d’éducation. Elle pense que les enfants doivent travailler pour trouver leur voie ŕ travers les difficultés de la réalité. Or, l’analyse de ses méthodes révčle la présence de nombreux éléments de la liberté que Schiller attribue au jeu. Les enfants peuvent choisir les choses avec lesquelles ils « travaillent ». Ils ne sont pas obligés de les utiliser exactement de la maničre que l’éducateur leur montre. Et, ce qui est le plus important, les enfants prennent un grand plaisir ŕ exécuter leur « travail ». Dans cet article, l’auteur interprčte d’abord les réflexions de Schiller sur l’éducation ŕ travers le jeu, oů l’accent est mis sur l’imagination. Dans la seconde partie, l’auteur discute la question de savoir s’il est justifié de prétendre que Maria Montessori rejette l’imagination comme moyen d’éducation. (shrink)

We prove a number of results in effective randomness, using methods in which Π⁰₁ classes play an essential role. The results proved include the fact that every PA Turing degree is the join of two random Turing degrees, and the existence of a minimal pair of LR degrees below the LR degree of the halting problem.

Let ω be the set of natural numbers. For functions f, g: ω → ω, we say f is dominated by g if f < g for all but finitely many n ∈ ω. We consider the standard “fair coin” probability measure on the space 2ω of in-finite sequences of 0's and 1's. A Turing oracle B is said to be almost everywhere dominating if, for measure 1 many X ∈ 2ω, each function which is Turing computable from X is (...) dominated by some function which is Turing computable from B. Dobrinen and Simpson have shown that the almost everywhere domination property and some of its variant properties are closely related to the reverse mathematics of measure theory. In this paper we exposit some recent results of Kjos-Hanssen, Kjos-Hanssen/Miller/Solomon, and others concerning LR-reducibility and almost everywhere domination. We also prove the following new result: If B is almost everywhere dominating, then B is superhigh, i. e., 0″ is truth-table computable from B ′, the Turing jump of B. (shrink)

A well known fact is that every Lebesgue measurable set is regular, i.e., it includes an F$_{\sigma}$ set of the same measure. We analyze this fact from a metamathematical or foundational standpoint. We study a family of Muchnik degrees corresponding to measure-theoretic regularity at all levels of the effective Borel hierarchy. We prove some new results concerning Nies's notion of LR-reducibility. We build some $\omega$-models of RCA$_0$which are relevant for the reverse mathematics of measure-theoretic regularity.

We say that A ≤LR B if every B-random number is A-random. Intuitively this means that if oracle A can identify some patterns on some real γ. In other words. B is at least as good as A for this purpose. We study the structure of the LR degrees globally and locally (i.e., restricted to the computably enumberable degrees) and their relationship with the Turing degrees. Among other results we show that whenever α in not GL₂ the LR degree of (...) α bounds $2^{\aleph _{0}}$ degrees (so that, in particular, there exist LR degrees with uncountably many predecessors) and we give sample results which demonstrate how various techniques from the theory of the c.e. degrees can be used to prove results about the c.e. LR degrees. (shrink)

Local Recurrency Theory (LR) holds that recurrent loops of neural activity localized to the visual cortex are necessary and sufficient for visual consciousness (if certain background conditions obtain). LR’s popularity has recently waned in favor of theories holding that higher-level types of processing are necessary for consciousness (for example, the Global Neuronal Workspace Theory and Higher-order Theory). This has been in part because of empirical evidence thought to disconfirm LR. However, these competing theories now face challenges of their own, often (...) coming in the form of evidence showing that higher-level brain areas (that is, in the prefrontal cortex) are probably not essential for consciousness. Given growing challenges to LR's competitors, it would be timely to re-assess the prospects for LR. This article carries out such an investigation, first laying out the theory precisely, then going on to survey the evidence presented against it. What will be found is that none of the evidence necessarily undermines LR, but instead just fosters its theoretical enrichment. The overall conclusion: LR remains among our most promising neuroscientific theories of visual consciousness. (shrink)

Several scholars advance the ‘LR-LP thesis’: the claim that American Legal Realism presupposes Legal Positivism. Brian Leiter and Frederick Schauer, prominent scholars of Realism, delimit that thesis to a Razian version of Exclusive Legal Positivism (‘ELP’). This article nevertheless argues that Leiter and Schauer’s respective accounts of Legal Realism are difficult to square with Razian ELP. Indeed, the Realist hypotheses about alternative drivers of official decision, concerning ‘working’ rules, ‘real’ rules, and ‘situation-types’, if correct, actually threaten Razian ELP. -/- Problems (...) arise for the LR-LP thesis (as delimited to Razian ELP) irrespective of whether those three Realist alternative drivers are classified as legal or non-legal norms. If they are non-legal, merits-based norms, then (a) those alternative drivers do much more work within official decision than ELP suggests is the case for those sorts of norms, and (b), Inclusive Legal Positivism may better, and might even be required, to explain them. Alternatively, if those Realist alternative drivers are better understood as source-based legal norms, then they cannot fulfil (or even be claimed by the law to fulfil) certain core functions that ELP attributes to legal norms. (shrink)

There is a plethora of confirmation measures in the literature. Zalabardo considers four such measures: PD, PR, LD, and LR. He argues for LR and against each of PD, PR, and LD. First, he argues that PR is the better of the two probability measures. Next, he argues that LR is the better of the two likelihood measures. Finally, he argues that LR is superior to PR. I set aside LD and focus on the trio of PD, PR, and LR. (...) The question I address is whether Zalabardo succeeds in showing that LR is superior to each of PD and PR. I argue that the answer is negative. I also argue, though, that measures such as PD and PR, on one hand, and measures such as LR, on the other hand, are naturally understood as explications of distinct senses of confirmation. (shrink)

A full separation theorem for the derivable rules of intuitionistic linear logic without bounds, 0 and exponentials is proved. Several structural consequences of this theorem for subreducts of (commutative) residuated lattices are obtained. The theorem is then extended to the logic LR+ and its proof is extended to obtain the finite embeddability property for the class of square increasing residuated lattices.

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

We show that the class of strongly jump-traceable c.e. sets can be characterised as those which have sufficiently slow enumerations so they obey a class of well-behaved cost functions, called benign. This characterisation implies the containment of the class of strongly jump-traceable c.e. Turing degrees in a number of lowness classes, in particular the classes of the degrees which lie below incomplete random degrees, indeed all LR-hard random degrees, and all ω-c.e. random degrees. The last result implies recent results of (...) Diamondstone's and Ng's regarding cupping with superlow c.e. degrees and thus gives a use of algorithmic randomness in the study of the c.e. Turing degrees. (shrink)

Wittgenstein's approach to religion is an important part of any assessment of the significance of his thought as a whole for educational thinking and practice. As we have seen, although his view of religion is elusive and stands in need of definitive evaluation, it offers a number of insights and challenges.Whilst Wittgenstein's approach conflicts in important respects with the LR view of education in religion, because that view is based on important social and cultural realities which are significant for Wittgensteinian (...) principles, it is not supplanted. The Wittgensteinian approach both supplies important perspectives which will enrich the LR view, whilst giving support to a greater pluralism in the way in which education in religion is conceived, including forms of substantial religious upbringing and schooling. (shrink)

In the recent literature on confirmation there are two leading approaches to the provision of a probabilistic measure of the degree to which a hypothesis is confirmed by evidence. The first is to construe the degree to which evidence E confirms hypothesis H as a function that is directly proportional to p and inversely proportional to p . I shall refer to this as the probability approach. The second approach construes the notion as a function that is directly proportional to (...) the true-positive rate – the probability of the evidence if the hypothesis is true, p – and inversely proportional to the false-positive rate – the probability of the evidence if the hypothesis is false, p . These reverse conditional probabilities – of the evidence on the truth or falsehood of the hypothesis – are sometimes known as likelihoods. I shall refer to the approach to confirmation that uses them as the likelihood approach.For each of these approaches, there are two obvious options as to how to define the confirmation function. The first is to define it as the difference between the magnitude that is treated as increasing confirmation or p ) and the magnitude that is treated as decreasing confirmation or p ). The second is to define confirmation as the quotient of these two magnitudes.This yields four different measures of confirmation, represented in the following table: Differences RatiosProbabilities PD = p – p1 PR = Graphic2Likelihoods LD = p – p3 LR = Graphic4All these measures agree on whether or not E provides some support for H. Intuitively, we want to say that E provides some support for H just in case learning that E is true would make us assign a higher probability to H, i.e. when p(H …. (shrink)

We demonstrate that an unlexicalized PCFG can parse much more accurately than previously shown, by making use of simple, linguistically motivated state splits, which break down false independence assumptions latent in a vanilla treebank grammar. Indeed, its performance of 86.36% (LP/LR F1) is better than that of early lexicalized PCFG models, and surprisingly close to the current state-of-theart. This result has potential uses beyond establishing a strong lower bound on the maximum possible accuracy of unlexicalized models: an unlexicalized PCFG is (...) much more compact, easier to replicate, and easier to interpret than more complex lexical models, and the parsing algorithms are simpler, more widely understood, of lower asymptotic complexity, and easier to optimize. (shrink)

Intellectual humility (IH) is often conceived as the recognition of, and appropriate response to, your own intellectual limitations. As far as we are aware, only a handful of studies look at interventions to increase IH – e.g. through journalling – and no study so far explores the extent to which having high or low IH can be predicted. This paper uses machine learning and natural language processing techniques to develop a predictive model for IH and identify top terms and features (...) that indicate degrees of IH. We trained our classifier on the dataset from an existing psychological study on IH, where participants were asked to journal their experiences with handling social conflicts over 30 days. We used Logistic Regression (LR) to train a classifier and the Linguistic Inquiry and Word Count (LIWC) dictionaries for feature selection, picking out a range of word categories relevant to interpersonal relationships. Our results show that people who differ on IH do in fact systematically express themselves in different ways, including through expression of emotions (i.e., positive, negative, and specifically anger, anxiety, sadness, as well as the use of swear words), use of pronouns (i.e., first person, second person, and third person) and time orientation (i.e., past, present, and future tenses). We discuss the importance of these findings for IH and the value of using such techniques for similar psychological studies, as well as some ethical concerns and limitations with the use of such semi-automated classifications. (shrink)

Reasons transmit. If one has a reason to attain an end, then one has a reason to effect means for that end: reasons are transmitted from end to means. I argue that the likelihood ratio (LR) is a compelling measure of reason transmission from ends to means. The LR measure is superior to other measures, can be used to construct a condition specifying precisely when reasons transmit, and satisfies intuitions regarding end-means reason transmission in a broad array of cases.

There are different Bayesian measures to calculate the degree of confirmation of a hypothesis H in respect of a particular piece of evidence E. Zalabardo (Analysis 69:630–635, 2009) is a recent attempt to defend the likelihood-ratio measure (LR) against the probability-ratio measure (PR). The main disagreement between LR and PR concerns their sensitivity to prior probabilities. Zalabardo invokes intuitive plausibility as the appropriate criterion for choosing between them. Furthermore, he claims that it favours the ordering of pairs evidence/hypothesis generated by (...) LR. We will argue, however, that the intuitive non-numerical example provided by Zalabardo does not show that prior probabilities do not affect the degree of confirmation. On account of this, we conclude that there is no compelling reason to endorse LR qua measure of degree of confirmation. On the other side, we should not forget some technicalities which still benefit PR. (shrink)

The field of left–right (LR) patterning—the study of molecular mechanisms that yield directed morphological asymmetries in otherwise symmetrical organisms—is in disarray. On one hand is the undeniably elegant hypothesis that rotary beating of inclined cilia is the primary symmetry‐breaking step: they create an asymmetric extracellular flow across the embryonic midline. On the other hand lurk many early symmetry‐breaking steps that, even in some vertebrates, precede the onset of ciliary flow. We highlight an intracellular model of LR patterning where gene expression (...) is initiated by physiological asymmetries that arise from subcellular asymmetries (e.g. motor‐protein function along oriented cytoskeletal tracks). A survey of symmetry breaking in eukaryotes ranging from protists to vertebrates suggests that intracellular cytoskeletal elements are ancient and primary LR cues. Evolutionarily, quirky effectors like ciliary motion were likely added later in vertebrates. In some species (like mice), developmentally earlier cues may have been abandoned entirely. Late‐developing asymmetries pose a challenge to the intracellular model, but early mid‐plane determination in many groups increases its plausibility. Multiple experimental tests are possible. BioEssays 29: 271–287, 2007. © 2007 Wiley Periodicals, Inc. (shrink)

To the standard propositional modal system of provability logic constants are added to account for the arithmetical fixed points introduced by Bernardi-Montagna in [5]. With that interpretation in mind, a system LR of modal propositional logic is axiomatized, a modal completeness theorem is established for LR and, after that, a uniform arithmetical (Solovay-type) completeness theorem with respect to PA is obtained for LR.