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)

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)

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 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)

Se busca rastrear la imagen que Platón tiene de Heráclito y articularla con la estructura argumentativa del Cratilo, para comprender las necesidades textuales a las que responde la doctrina del flujo perpetuo, es decir, la discusión sobre la corrección (ὀρθότης) del nombre. Gracias a la inclusión del testimonio heraclíteo, resulta posible rastrear la presunta consolidación de la tesis sobre los nombres primarios y los secundarios como el eje de la separación entre dos planos de realidad (uno estable y uno móvil) (...) y de la teoría de las Ideas -es decir, como la base de la epistemología platónica presente en los diálogos de madurez-. The article seeks to trace the image Plato has of Heraclitus and connect it with the argumentative structure of the Cratylus in order to understand the textual needs that give rise to the doctrine of perpetual flux, that is, the discussion regarding the correctness (ὀρθότης) of names. The inclusion of Heraclitus's testimony makes it possible to trace the alleged consolidation of the thesis regarding primary and secondary names as the axis of separation between two levels of reality (one stable, the other, changing) and the theory of Ideas -that is, as the basis of Plato's epistemology as set forth in the late dialogues-. (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)

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.

Artificial intelligence is a useful predictive tool for a wide variety of fields of knowledge. Despite this, the educational field is still an environment that lacks a variety of studies that use this type of predictive tools. In parallel, it is postulated that the levels of self-esteem in the university environment may be related to the strategies implemented to solve problems. For these reasons, the aim of this study was to analyze the levels of self-esteem presented by teaching staff and (...) students at university and to design an algorithm capable of predicting these levels on the basis of their coping strategies, resilience, and sociodemographic variables. For this purpose, the Rosenberg Self-Esteem Scale, the Perceived Stress Scale, and the Brief Resilience Scale were administered. The results showed a relevant role of resilience and stress perceived in predicting participants’ self-esteem levels. The findings highlight the usefulness of artificial neural networks for predicting psychological variables in education. (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)

This paper presents a method to compute a posteriori probability intervals when the initial conditional information is also given with probability intervals. The right way to make an exact computation is with the associated convex set of probabilities. Probability trees are used to represent these initial conditional convex sets because they greatly save the space required. This paper proposes a simulated annealing algorithm, which uses probability trees to represent the convex sets in order to compute the a posteriori intervals.

Se ha sostenido tradicionalmente que los predicados atribuidos a Dios y a las criaturas son análogos. Pero, ¿qué es la analogía? Varios filósofos han pensado que la analogía debe ser considerada como una forma de ambigüedad. Argumentamos aquí que los predicados atribuidos a Dios y a las criaturas no son ambiguos o vagos. Siguiendo algunas sugerencias de McDaniel, proponemos una concepción de la analogía donde el fenómeno semántico está asociado con el carácter más o menos natural de la propiedad o (...) propiedades que instancian las entidades que satisfacen el predicado análogo. Un predicado "θ" es análogo si y sólo si, la propiedad Θ, que algo instancia, si y sólo si es θ, es menos natural que cualquier propiedad Ξ tal que todo lo que instancie Ξ, instancia Θ. Además, se requiere que las entidades de las cuales el término análogo es predicado deban ser ontológica o epistémicamente dependientes unas de otras. || It has been traditionally sustained that predicates attributed to God and to the creatures are analogical predicates. But, what is analogy? Several philosophers have thought that analogy should be taken as a form of ambiguity. Here we argue that predicates attributed to God and to creatures are neither ambiguous nor vague. Following some suggestions given by McDaniel, we propose a view of analogy in which the semantic phenomenon is associated with the more or less natural character of the property or properties that the entities that satisfy the analogous predicate instantiate. A predicate "θ" is analogous if and only if the property Θ, which something instantiates, if and only if it is θ, is less natural that any property Ξ so that anything that instantiates Ξ, instantiates Θ. Furthermore, it is required that the entities of which the analogous term is predicated should be either ontologically or epistemically dependent on each other. (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)

Risk taking is a component of the decision-making process in situations that involve uncertainty and in which the probability of each outcome – rewards and/or negative consequences – is already known. The influence of cognitive and emotional processes in decision making may affect how risky situations are addressed. First, inaccurate assessments of situations may constitute a perceptual bias in decision making, which might influence RT. Second, there seems to be consensus that a proneness bias exists, known as risk proneness, which (...) can be defined as the propensity to be attracted to potentially risky activities. In the present study, we take the approach that risk perception and risk proneness affect RT behaviours. The study hypothesises that locus of control, emotion regulation, and executive control act as perceptual biases in RT, and that personality, sensation seeking, and impulsivity traits act as proneness biases in RT. The results suggest that locus of control, emotion regulation and executive control influence certain domains of RT, while personality influences in all domains except the recreational, and sensation seeking and impulsivity are involved in all domains of RT. The results of the study constitute a foundation upon which to build in this research area and can contribute to the increased understanding of human behaviour in risky situations. (shrink)

In this paper I argue that many scholars involved in the contemporary free will debates have underappreciated the philosophical appeal of agent causation because the resources of contemporary emergentism have not been adequately introduced into the discussion. Whereas I agree that agent causation’s main problem has to do with its intelligibility, particularly with respect to the issue of how substances can be causally relevant, I argue that the notion of substance causation can be clearly articulated from an emergentist framework. According (...) to my proposal, a free agent is _a causally powerful substance that emerges in an anomic way from her constitutive mental events_, downwardly constraining, selecting and, in this way, having control on them. As we shall see, this particular concept of agent causation not only makes sense of the deep insight behind agent libertarianism, but it also provides us with the resources to solve some of the main objections that have been raised against it. It is true that here I cannot develop a complete defense of the evidential credentials of emergentism. Still, even if the considerations that follow do not serve to convince detractors of agent causal libertarian accounts of free will, they do suggest that libertarian agent causation is more promising than is typically acknowledged. (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)

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)

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.

The COVID-19 global health emergency has greatly impacted the educational field. Faced with unprecedented stress situations, professors, students, and families have employed various coping and resilience strategies throughout the confinement period. High and persistent stress levels are associated with other pathologies; hence, their detection and prevention are needed. Consequently, this study aimed to design a predictive model of stress in the educational field based on artificial intelligence that included certain sociodemographic variables, coping strategies, and resilience capacity, and to study the (...) relationship between them. The non-probabilistic snowball sampling method was used, involving 337 people from the university education community in south-eastern Spain. The Perceived Stress Scale, Stress Management Questionnaire, and Brief Resilience Scale were administered. The Statistical Package for the Social Sciences was used to design the architecture of artificial neural networks. The results found that stress levels could be predicted by the synaptic weights of coping strategies and timing of the epidemic, with a predictive capacity of over 80% found in the neural network model. Additionally, direct and significant associations were identified between the use of certain coping strategies, stress levels, and resilience. The conclusions of this research are essential for effective stress detection, and therefore, early intervention in the field of educational psychology, by discussing the influence of resilience or lack thereof on the prediction of stress levels. Identifying the variables that maintain a greater predictive power in stress levels is an effective strategy to design more adjusted prevention programs and to anticipate the needs of the community. (shrink)

Challenges to Legal Theory offers the reader a fascinating journey though a variety of multi-disciplinary topics, ranging from law and literature, and law and religion, to legal philosophy and constitutional law. The collection reflects some of the challenges that the field of legal theory currently faces. It is compiled by a selection of international and Spanish scholars, whose essays are made available in English translation for the first time. The volume is based on a collection of essays, published in Spanish, (...) in honour of Professor José Iturmendi Morales, of Complutense University, Madrid, and brings the rich scholarship of pre-eminent Spanish scholars of law and legal theory to an international audience. (shrink)

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)

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)