We give examples of calculi that extend Gentzen’s sequent calculusLKby unsound quantifier inferences in such a way that derivations lead only to true sequents, and proofs therein are nonelementarily shorter thanLK-proofs.

We prove a number of results on the determinacy of σ-projective sets of reals, i.e., those belonging to the smallest pointclass containing the open sets and closed under complements, countable unions, and projections. We first prove the equivalence between σ-projective determinacy and the determinacy of certain classes of games of variable length <ω^2 (Theorem 2.4). We then give an elementary proof of the determinacy of σ-projective sets from optimal large-cardinal hypotheses (Theorem 4.4). Finally, we show how to generalize the proof (...) to obtain proofs of the determinacy of σ-projective games of a given countable length and of games with payoff in the smallest σ-algebra containing the projective sets, from corresponding assumptions (Theorem 5.1, Theorem 5.4). (shrink)

We determine the consistency strength of determinacy for projective games of length ω^2. Our main theorem is that $\Pi _{n + 1}^1$-determinacy for games of length ω^2 implies the existence of a model of set theory with ω + n Woodin cardinals. In a first step, we show that this hypothesis implies that there is a countable set of reals A such that M_n(A), the canonical inner model for n Woodin cardinals constructed over A, satisfies $A = R$ and the (...) Axiom of Determinacy. Then we argue how to obtain a model with ω + n Woodin cardinal from this. We also show how the proof can be adapted to investigate the consistency strength of determinacy for games of length ω^2 with payoff in $R^R\Pi _1^1$ or with σ-projective payoff. (shrink)

For every countable wellordering $\alpha $ greater than $\omega $, it is shown that clopen determinacy for games of length $\alpha $ with moves in $\mathbb {N}$ is equivalent to determinacy for a class of shorter games, but with more complicated payoff. In particular, it is shown that clopen determinacy for games of length $\omega ^2$ is equivalent to $\sigma $ -projective determinacy for games of length $\omega $ and that clopen determinacy for games of length $\omega ^3$ is equivalent (...) to determinacy for games of length $\omega ^2$ in the smallest $\sigma $ -algebra on $\mathbb {R}$ containing all open sets and closed under the real game quantifier. (shrink)

Extending Aanderaa’s classical result that $\pi ^{1}_{1} < \sigma ^{1}_{1}$, we determine the order between any two patterns of iterated $\Sigma ^{1}_{1}$ - and $\Pi ^{1}_{1}$ -reflection on ordinals. We show that this order of linear reflection is a prewellordering of length $\omega ^{\omega }$. This requires considering the relationship between linear and some non-linear reflection patterns, such as $\sigma \wedge \pi $, the pattern of simultaneous $\Sigma ^{1}_{1}$ - and $\Pi ^{1}_{1}$ -reflection. The proofs involve linking the lengths of (...) $\alpha $ -recursive wellorderings to various forms of stability and reflection properties satisfied by ordinals $\alpha $ within standard and non-standard models of set theory. (shrink)

Let Mn♯ denote the minimal active iterable extender model which has n Woodin cardinals and contains all reals, if it exists, in which case we denote by Mn the class-sized model obtained by iterating the topmost measure of Mn class-many times. We characterize the sets of reals which are Σ1-definable from R over Mn, under the assumption that projective games on reals are determined:1. for even n, Σ1Mn=⅁RΠn+11;2. for odd n, Σ1Mn=⅁RΣn+11.This generalizes a theorem of Martin and Steel for L, (...) that is, the case n=0. As consequences of the proof, we see that determinacy of all projective games with moves in R is equivalent to the statement that Mn♯ exists for all n∈N, and that determinacy of all projective games of length ω2 with moves in N is equivalent to the statement that Mn♯ exists and satisfies AD for all n∈N. (shrink)

The variety \(\mathbb{DHMSH}\) of dually hemimorphic semi-Heyting algebras was introduced in 2011 by the second author as an expansion of semi-Heyting algebras by a dual hemimorphism. In this paper, we focus on the variety \(\mathbb{DHMSH}\) from a logical point of view. The paper presents an extensive investigation of the logic corresponding to the variety of dually hemimorphic semi-Heyting algebras and of its axiomatic extensions, along with an equally extensive universal algebraic study of their corresponding algebraic semantics. Firstly, we present a (...) Hilbert-style axiomatization of a new logic called "Dually hemimorphic semi-Heyting logic" (\(\mathcal{DHMSH}\), for short), as an expansion of semi-intuitionistic logic \(\mathcal{SI}\) (also called \(\mathcal{SH}\)) introduced by the first author by adding a weak negation (to be interpreted as a dual hemimorphism). We then prove that it is implicative in the sense of Rasiowa and that it is complete with respect to the variety \(\mathbb{DHMSH}\). It is deduced that the logic \(\mathcal{DHMSH}\) is algebraizable in the sense of Blok and Pigozzi, with the variety \(\mathbb{DHMSH}\) as its equivalent algebraic semantics and that the lattice of axiomatic extensions of \(\mathcal{DHMSH}\) is dually isomorphic to the lattice of subvarieties of \(\mathbb{DHMSH}\). A new axiomatization for Moisil's logic is also obtained. Secondly, we characterize the axiomatic extensions of \(\mathcal{DHMSH}\) in which the "Deduction Theorem" holds. Thirdly, we present several new logics, extending the logic \(\mathcal{DHMSH}\), corresponding to several important subvarieties of the variety \(\mathbb{DHMSH}\). These include logics corresponding to the varieties generated by two-element, three-element and some four-element dually quasi-De Morgan semi-Heyting algebras, as well as a new axiomatization for the 3-valued Łukasiewicz logic. Surprisingly, many of these logics turn out to be connexive logics, only a few of which are presented in this paper. Fourthly, we present axiomatizations for two infinite sequences of logics namely, De Morgan Gödel logics and dually pseudocomplemented Gödel logics. Fifthly, axiomatizations are also provided for logics corresponding to many subvarieties of regular dually quasi-De Morgan Stone semi-Heyting algebras, of regular De Morgan semi-Heyting algebras of level 1, and of JI-distributive semi-Heyting algebras of level 1. We conclude the paper with some open problems. Most of the logics considered in this paper are discriminator logics in the sense that they correspond to discriminator varieties. Some of them, just like the classical logic, are even primal in the sense that their corresponding varieties are generated by primal algebras. (shrink)

We prove a topological completeness theorem for the modal logic $$\textsf{GLP}$$ GLP containing operators $$\{\langle \xi \rangle :\xi \in \textsf{Ord}\}$$ { ⟨ ξ ⟩ : ξ ∈ Ord } intended to capture a wellordered sequence of consistency operators increasing in strength. More specifically, we prove that, given a tall-enough scattered space X, any sentence $$\phi $$ ϕ consistent with $$\textsf{GLP}$$ GLP can be satisfied on a polytopological space based on finitely many Icard topologies constructed over X and corresponding to the (...) finitely many modalities that occur in $$\phi $$ ϕ. (shrink)

The thesis is guided by the question: What is the subject matter of Heidegger’s philosophy in the period of Being and Time? I start by arguing that Heidegger’s formulation of the question of being is ambiguous because the term ‘being’ is open to at least two interpretations. I claim that this ambiguity has motivated two types of reading of Heidegger’s early work. On the first reading, Heidegger’s philosophy is understood as attempting to infer metaphysical claims (claims about what-is, or being (...) in a traditionally metaphysical sense) on the basis of claims about the structure of Dasein’s understanding. This reading typically renders Heidegger an idealist. On the second reading, Heidegger’s philosophy is taken to have no metaphysical ambitions, and thereby to be limited to elucidating the structure of Dasein’s understanding. I argue that both types of reading are inadequate and diagnose them as grounded in a Cartesian presupposition that Heidegger rejects. On the basis of direct textual evidence and a number of theoretical considerations I assert that although the second type of reading is right in that the primary object of Heidegger’s philosophy is the conditions of understanding and that the idealist reading is wrong, it is a mistake to deny that Heidegger’s philosophy has metaphysical implications. I claim that Heidegger’s exposition of the conditions of understanding involves a larger picture from the outset, a picture that delineates the relation between understanding and entities, and locates the objective in relation to Dasein. On this picture, 1) empirical entities are unqualifiedly independent of Dasein, 2) we have direct cognitive access to these entities as they are in themselves, and 3) there is no a priori unintelligible entities or aspects of entities. I address a number of potential objections to this way of interpreting Heidegger’s work. (shrink)

This article questions the prevailing opinion that Domitian's prohibition of castration was intended as a protective measure devised to check masters’ abuses on their slaves, as part of a larger trend towards more enlightened attitudes towards slavery among the Romans. While brutal, castration was the only type of mutilation which increased the monetary value of slaves. Banning it curtailed slaves’ chances of social climbing and narrowed their channels towards positions of power. The emasculation ban is, instead, better understood as one (...) of the many measures directed towards the control of the sexual behaviour and the sumptuary practices of the Roman elite. Introduced as a censorial decree, the ban gave Domitian the opportunity to act as the upholder of Republican traditions at the same time as he impinged on the private lives of his subjects and put senators and equestrians under his thumb. The article also argues that, contrary to what is usually argued, the constant re-enforcement of the prohibition to castrate by Domitian's successors is an indication of the effectiveness of the Roman legal machinery and its capacity to reach the most distant corners of the Roman empire. (shrink)

We determine the number of non‐isomorphic semi‐Heyting algebras on an n‐element chain, where n is a positive integer, using a recursive method. We then prove that the numbers obtained agree with those determined in [1]. We apply the formula to calculate the number of non‐isomorphic semi‐Heyting chains of a given size in some important subvarieties of the variety of semi‐Heyting algebras that were introduced in [5]. We further exploit this recursive method to calculate the numbers of non‐isomorphic semi‐Heyting chains with (...) n elements such that removing the mth element () we are left with a subalgebra. We also solve a related problem posed in [1] of determining the number of ways a semi‐Heyting chain with elements can be extended to a n element semi‐Heyting chain by adding a new element in the mth place. Finally we combine these results by finding a second way to calculate the numbers that provides some extra information. (shrink)

An algebra A = ⟨A, ∨, ∧, →, 0, 1⟩ is a semi-Heyting algebra if ⟨A, ∨, ∧, 0, 1⟩ is a bounded lattice, and it satisfies the identities: x ∧ ≈ x ∧ y, x ∧ ≈ x ∧ [ → ], and x → x ≈ 1.

How did cultural factors participate in the event of October in Chile? How were these factors related to each other? What implications did they have for collective action and social life? The purpose of the article is to carry out a cultural reading of the October event. To do this, a dialogue is proposed between cultural sociology and cultural studies, applied to the October protest movement, resorting to interpretive research tools. The appropriation of Plaza Italia, in Santiago, by the protesters, (...) is used in an illustrative way to highlight the cultural elements and their interactions. Among the findings, the production of meaning based on motifs and frames stands out, the production of its own symbolism and iconography and the deployment of performances that allow defining the Plaza itself as an artifact of protest. Then certain scopes of the above for civil society are discussed. It concludes with a projection of the work and a brief reflection on the relationship between social sciences and humanities to deploy an interpretive strategy of empirical research. (shrink)

Summary A brief state of the art for Phlegon of Tralles’ De Mirabilia 3 anti-Roman prophecies is followed by a reassessment of four of its components: the historical identification of the Roman protagonist “Publius”, Naupaktos as the main stage for the prophecies, the multiple meanings of the Red Wolf as well as the Oak Tree, and the Roman military retreat. By analyzing these specific elements, it will be argued that these presages were not only associated with events during the Antiochean (...) and Mithridatic Wars, but were also related with historical experiences from the First Macedonian Conflict. (shrink)

The variety \ of implication zroupoids and a constant 0) was defined and investigated by Sankappanavar :21–50, 2012), as a generalization of De Morgan algebras. Also, in Sankappanavar :21–50, 2012), several subvarieties of \ were introduced, including the subvariety \, defined by the identity: \, which plays a crucial role in this paper. Some more new subvarieties of \ are studied in Cornejo and Sankappanavar that includes the subvariety \ of semilattices with a least element 0. An explicit description of (...) semisimple subvarieties of \ is given in Cornejo and Sankappanavar. It is a well known fact that there is a partial order ) induced by the operation ∧, both in the variety \ of semilattices with a least element and in the variety \ of De Morgan algebras. As both \ and \ are subvarieties of \ and the definition of partial order can be expressed in terms of the implication and the constant, it is but natural to ask whether the relation \ on \ is actually a partial order in some subvariety of \ that includes both \ and \. The purpose of the present paper is two-fold: Firstly, a complete answer is given to the above mentioned problem. Indeed, our first main theorem shows that the variety \ is a maximal subvariety of \ with respect to the property that the relation \ is a partial order on its members. In view of this result, one is then naturally led to consider the problem of determining the number of non-isomorphic algebras in \ that can be defined on an n-element chain -chains), n being a natural number. Secondly, we answer this problem in our second main theorem which says that, for each \, there are exactly n nonisomorphic \-chains of size n. (shrink)

Education is essential to life, and the epidemic affected everything. Parents want to get their kids the most important teaching. However, since COVID-19 has affected schools and other institutions, providing education has become the most significant issue. Online learning pedagogy uses technology to provide high-quality learning environments for student-centered learning. Further, this study explores the experiences and challenges faced by Filipino tertiary students regarding the lack of gadgets amidst online learning. Employing the Interpretative Phenomenological Analysis, the findings of this study (...) were: Some college students still have difficulty with online learning. Attending online classes is difficult, especially for students with limited resources. Smartphones, other gadgets, and internet connections play a significant role in online classrooms because they are the ones that students utilize while learning online, which is essential for successful participation in online higher education as well as for solving a variety of other difficulties in the new normal. Further, College students face similar health challenges. Having an online learning setup is not just about students' struggles with learning resources but also about their health issues. When our respondents used their smartphones for an extended period, they reported eye aches and blurred vision. They also said that some of their body parts, such as their legs and back, are aching, and feel pressured because they tend to overthink things in their surroundings, which causes them incredible difficulty in performing their best in attending online classes. Even though college students continue to suffer from a lack of learning resources during online sessions, they do their best to manage their needs and the scarcity of learning resources. Students have unique coping methods for dealing with difficulties in online classes. (shrink)

SummaryThis paper examines the role of health knowledge in the association between mothers' education and use of maternal and child health services in Ghana. The study uses data from a nationally representative sample of female respondents to the 2008 Ghana Demographic and Health Survey. Ordered probit regression models evaluate whether women's health knowledge helps to explain use of three specific maternal and child health services: antenatal care, giving birth with the supervision of a trained professional and complete child vaccination. The (...) analyses reveal that mothers' years of formal education are strongly associated with health knowledge; health knowledge helps explain the association between maternal education and use of health services; and, net of a set of stringent demographic and socioeconomic controls, mothers' health knowledge is a key factor associated with use of health services. (shrink)

Cancer is a singular cellular state, the emergence of which destabilises the homeostasis reached through the evolution to multicellularity. We present the idea that the onset of the cellular disobedience to the metazoan functional and structural architecture, known as the cancer phenotype, is triggered by changes in the cell's external environment that occur with ageing: what ensues is a breach of the social contract of multicellular life characteristic of metazoans. By integrating old ideas with new evidence, we propose that with (...) ageing the environmental information that maintains a multicellular organisation is eroded, rewiring internal processes of the cell, and resulting in an internal shift towards an ancestral condition resulting in the pseudo‐multicellular cancer phenotype. Once that phenotype emerges, a new local social contract is built, different from the homeostatic one, leading to tumour formation and the foundation of a novel local ecosystem. (shrink)

In this work, our aim is to investigate the impact of a non-Kolmogorov predator-prey-subsidy model incorporating nonlinear prey refuge and the effect of fear with Holling type II functional response. The model arises from the study of a biological system involving arctic foxes, lemmings, and seal carcasses. The positivity and asymptotically uniform boundedness of the solutions of the system have been derived. Analytically, we have studied the criteria for the feasibility and stability of different equilibrium points. In addition, we have (...) derived sufficient conditions for the existence of local bifurcations of codimension 1. It is also observed that there is some time lag between the time of perceiving predator signals through vocal cues and the reduction of prey’s birth rate. So, we have analyzed the dynamical behaviour of the delayed predator-prey-subsidy model. Numerical computations have been performed using MATLAB to validate all the analytical findings. Numerically, it has been observed that the predator, prey, and subsidy can always exist at a nonzero subsidy input rate. But, at a high subsidy input rate, the prey population cannot persist and the predator population has a huge growth due to the availability of food sources. (shrink)

Background: Heart rate variability (HRV) has been considered as a measure of heart-brain interaction and autonomic modulation, and it is modified by cognitive and attentional tasks. In cognitive tasks, HRV was reduced in participants who achieved worse results. This could indicate the possibility of HRV predicting cognitive performance, but this association is still unclear in a high cognitive load sport such as chess Objective: To analyse modifications on HRV and subjective perception of stress, difficulty and complexity in different chess problem (...) tasks. Design: HRV was assessed at baseline. During the chess problems, HRV was also monitored, and immediately after chess problems the subjective stress, difficulty and complexity were also registered. Method: A total of 16 male chess players, age: 35.19 (13.44) and ELO: 1927.69 (167.78) were analysed while six chess problem solving tasks with different level of difficulty were conducted (two low level, two medium level and two high level chess problems). Participants were classified according to their results into two groups: high performance or low performance. Results: Friedman test showed a significant effect of tasks in HRV indexes and perceived difficulty, stress and complexity in both high and low performance groups. A decrease in HRV was observed in both groups when chess problems difficulty increased. In addition, HRV was significantly higher in the high performance group than in the low performance group during chess problems. Conclusions: An increase in autonomic modulation was observed to meet the cognitive demands of the problems, being higher while the difficulty of the tasks increased. Non-linear HRV indexes seem to be more reactive to tasks difficulty, being an interesting and useful tool in chess training. (shrink)

El siguiente escrito muestra el breve pero enjundioso intercambio epistolar entre quizás los dos filósofos cristianos más importantes del siglo XX: Étienne Gilson y Jacques Maritain. Las cartas están centradas en torno a algunas de las tantas temáticas que inquietaron a los tomistas del siglo pasado –la intuición de Dios, el primer objeto de la inteligencia, la función propia del intelecto humano, entre otras– y que aun muestran su plena actualidad en el debate contemporáneo. Ofrecemos la primera traducción al español (...) de las cartas enviadas en el año 1923 –inicio de una fructífera correspondencia entre ambos filósofos–, con ocasión de la publicación de la segunda edición de _El tomismo_, uno de los libros más emblemáticos de Gilson. (shrink)

Within the polemic work which was developed by Eastern Christians it is necessary to underline the transmission of the whole of the religious conceptions, the kinds of argumentation and defence of the dogma, the elaboration of the discourse, the debate techniques used, the vocabulary which was adapted and generated, the rewriting developed from the Biblical material and Quranic criticism, as well as the refutations of the Muslim ideas, and the huge information which is inside the intrachristian polemics. Theology is the (...) most important element to describe the abridged knowledge which is in all of the treatises which make whole the polemic typology. This element allows us to rebuild the rich and involved tram which forms the 'theological knowledge' of the different Ch1istian churches and the several Muslim trends too. This, polemics help to clarify the processes which shape the ideology of the different human groups in conflict. (shrink)

One of the modern features in Maimonides’ exegesis is the interpretation of the figurative and symbolic concepts which can be found in the Biblical text. To this respect, the task developed by the Cordovan writer place the texts before new hermeneutic possibilities of analysis which offer original readings from his interpretation.

When recalling autobiographical events, people not only retrieve event details but also the feelings they experienced. The current study examined whether people are able to consistently recall the intensity of past feelings associated with two consequential and negatively valenced events, i.e. the 9/11 attack (N = 769) and the COVID-19 pandemic (N = 726). By comparing experienced and recalled intensities of negative feelings, we discovered that people systematically recall a higher intensity of negative feelings than initially reported – overestimating the (...) intensity of past negative emotional experiences. The COVID-19 dataset also revealed that individuals who experienced greater improvement in emotional well-being displayed smaller biases in recalling their feelings. Across both datasets, the intensity of remembered feelings was correlated with initial feelings and current feelings, but the impact of the current feelings was stronger in the COVID-19 dataset than in the 9/11 dataset. Our results demonstrate that when recalling negative autobiographical events, people tend to overestimate the intensity of prior negative emotional experiences with their degree of bias influenced by current feelings and well-being. (shrink)

Similarity profiled association mining from time stamped transaction databases is an important topic of research relatively less addressed in the field of temporal data mining. Mining temporal patterns from these time series databases requires choosing and applying similarity measure for similarity computations and subsequently pruning temporal patterns. This research proposes a novel z-space based interest measure named as Krishna Sudarsana for time-stamped transaction databases by extending interest measure Srihass proposed in previous research. Krishna Sudarsana is designed by using the product (...) based fuzzy Gaussian membership function and performs similarity computations in z-space to determine the similarity degree between any two temporal patterns. The interest measure is designed by considering z-values between z = 0 and z = 3.09. Applying the Krishna Sudarsana requires moving the threshold value given by user to a different transformation space which is a defined as a function of standard deviation. In addition to proposing interest measure, new expressions for standard deviation and equivalent z-space threshold are derived for similarity computations. For experimental evaluation, we considered Naïve, Sequential and Spamine algorithms that applies Euclidean distance function and compared performance of these three approaches to Z-Spamine algorithm that uses Krishna Sudarsana by choosing various test cases. Experiment results proved the performance of the proposed approach is better to Sequential approach that uses snapshot database scan strategy and Spamine approach that uses lattice based database scan strategy. (shrink)

A single mother is a person who is accountable for raising their children alone because they do not have a husband or live-in partner. Single mothers claim to have no co-parenting relationships at all, comparing single parents to those who are married, cohabiting, or without children, single parents experience the worst work-life balance. A single parent may feel overwhelmed by the demands of juggling child care, a career, paying bills, and maintaining household responsibilities. Single-parent households frequently deal with several extra (...) obligations and possible complications that other families would not. The study also emphasizes the difficulties and coping mechanisms faced by contractual single parents as well as their lived experiences. The study's findings, which were based on an Interpretative Phenomenological Analysis, were as follows: (1) Work-life balance can be difficult for single parents. They struggle to keep their jobs while taking care of their family because they are the only ones in charge of the children. (2) Single contractual mothers face particular difficulties due to a lack of resources for basic expenses. (3) Contractual single women lean on their kids, the good people in their lives, and their faith in God to get through problems. (shrink)

DBS Think Tank IX was held on August 25–27, 2021 in Orlando FL with US based participants largely in person and overseas participants joining by video conferencing technology. The DBS Think Tank was founded in 2012 and provides an open platform where clinicians, engineers and researchers can freely discuss current and emerging deep brain stimulation technologies as well as the logistical and ethical issues facing the field. The consensus among the DBS Think Tank IX speakers was that DBS expanded in (...) its scope and has been applied to multiple brain disorders in an effort to modulate neural circuitry. After collectively sharing our experiences, it was estimated that globally more than 230,000 DBS devices have been implanted for neurological and neuropsychiatric disorders. As such, this year’s meeting was focused on advances in the following areas: neuromodulation in Europe, Asia and Australia; cutting-edge technologies, neuroethics, interventional psychiatry, adaptive DBS, neuromodulation for pain, network neuromodulation for epilepsy and neuromodulation for traumatic brain injury. (shrink)

ABSTRACTThe social content of affective stimuli has been proposed as having an influence on cognitive processing and behaviour. This research was aimed, therefore, at studying whether automatic exogenous attention demanded by affective pictures was related to their social value. We hypothesised that affective social pictures would capture attention to a greater extent than non-social affective stimuli. For this purpose, we recorded event-related potentials in a sample of 24 participants engaged in a digit categorisation task. Distracters were affective pictures varying in (...) social content, in addition to affective valence and arousal, which appeared in the background during the task. Our data revealed that pictures depicting high social content captured greater automatic attention than other pictures, as reflected by the greater amplitude and shorter latency of anterior P2, and anterior and posterior N2 components of the ERPs. In addition, social content also provoked greater allocation of processing resour... (shrink)