Formal topology is today an established topic in the development of constructive mathematics and constructive proofs for many classical results of general topology have been obtained by using this approach. Here we analyze one of the main concepts in formal topology, namely, the notion of formal point. We will contrast two classically equivalent definitions of formal points and we will see that from a constructive point of view they are completely different. Indeed, according to the first definition the formal points (...) of the formal topology of the real numbers can be indexed by a set whereas this is not possible according to the second one. (shrink)

In the literature, the nature of the relationships between memory processes and summary evaluations is still a debate. According to some theoretical approaches (e.g., “two-memory hypothesis”; Anderson, 1989) retrospective evaluations are based on the impression formed while attending to the to-be-assessed stimuli(on-line judgment) – no functional dependence between information retrieval and judgment is implied. Conversely, several theories entail that judgment must depend, at least in part, on memory processes (e.g., Dougherty, Gettys, & Ogden, 1999; Schwarz, 1998; Tversky & Kahneman, 1973). (...) The present study contributes to this debate by addressing two important issues. First, it shows how more comprehensive memory measures than those used previously (e.g., Hastie & Park, 1986) are necessary in order to detect a relationship between memory and retrospective evaluations. Secondly, it demonstrates how memory strategies influence the relationship between memory and judgment. Participants recalled lists of words, after having assessed each of them for their pleasantness. Results showed a clear association between memory and judgment, which was mediated by the individual strategies participants used to recall the items. (shrink)

In this paper a proof of the normal form theorem for the closed terms of Girard's system F is given by using a computability method à la Tait. It is worth noting that most of the standard consequences of the normal form theorem can be obtained using this version of the theorem as well. From the proof-theoretical point of view the interest of the proof is that the definition of computable derivation here used does not seem to be well founded. (...) MSC: 03F05, 03B15. (shrink)

This article suggests developing the concept of spiritual ecology into that of balanced spiritual ecosystems. Philosophies, theologies, education systems, political parties, and gender-based and ethnic identity politics need to be critiqued both from within and without so that they can finally contribute to the creation, maintenance and flourishing of balanced spiritual ecosystems.Contribution: Spiritual ecology is a concept on which converge different worldviews. This article recommends using balanced spiritual ecosystems, instead. The new concept could provoke further reflection on how our -ontologies (...) and communities co-exist and whether they do it organically and spiritually. This article befits HTS’s interest in ‘theology and nature’. (shrink)

We show that the variety of Heyting algebras has finitary unification type. We also show that the subvariety obtained by adding it De Morgan law is the biggest variety of Heyting algebras having unitary unification type. Proofs make essential use of suitable characterizations (both from the semantic and the syntactic side) of finitely presented projective algebras.

We show that some common varieties of modal K4-algebras have finitary unification type, thus providing effective best solutions for equations in free algebras. Applications to admissible inference rules are immediate.

The pandemic period has placed the organizations in a state of great tension. It has generated a situation of confusion, lack of rules, and production-related criticalities that have called into question the very existence of many productive realities. This article aims to highlight the dimensions of care and ethics put in place by HR managers in COVID-19. The objective that animated the authors have focused on the HRM level of medium and large companies in Italy to highlight the protective actions (...) toward people and the organization in the period COVID 19, highlighting what were the ethical values and actions of care put in place. In this article, we wanted to give voice to managers who had management tasks in their organizations by asking them to tell us how they dealt with the challenges imposed by the emergency. In the research, we start from a way of understanding workplaces understood as a “process of ongoing social relationship” within which the HR function is dedicated to the care of the quality of relationships. HR managers have to manage a complex role of mediating between the interests of people and employers by trying to find good mediations. (shrink)

By using some classical reasoning we show that any countably presented formal topology, namely, a formal topology with a countable axiom set, is spatial.

Abstract.Formal topologies are today an established topic in the development of constructive mathematics. One of the main tools in formal topology is inductive generation since it allows to introduce inductive methods in topology. The problem of inductively generating formal topologies with a cover relation and a unary positivity predicate has been solved in [CSSV]. However, to deal both with open and closed subsets, a binary positivity predicate has to be considered. In this paper we will show how to adapt to (...) this framework the method used to generate inductively formal topologies with a unary positivity predicate; the main problem that one has to face in such a new setting is that, as a consequence of the lack of a complete formalization, both the cover relation and the positivity predicate can have proper axioms. (shrink)

Este texto reflete sobre o memoricídio, consequente à presunção racial branca, como vestígio de operações para o genocídio dos corpos e das mentes negras a partir da Peleja de Inácio da Catingueira contra Romano. Sob o jogo discursivo da humilhação, já se encontrava a vontade brutal de destruição de qualquer traço, perspectiva, visão remanescente de saberes e culturas africanas ou descendentes, fossem de cunho material, simbólico, reflexivo, imagético, expressivo, na língua, no corpo. No embate, Inácio, negro, escravizado, já rebaixado sob (...) a égide do sistema escravocrata, embate-se contra a tentativa presunçosa de aniquilamento perpetrada por seu oponente. (shrink)

Este texto reflete sobre o memoricídio, consequente à presunção racial branca, como vestígio de operações para o genocídio dos corpos e das mentes negras a partir da Peleja de Inácio da Catingueira contra Romano. Sob o jogo discursivo da humilhação, já se encontrava a vontade brutal de destruição de qualquer traço, perspectiva, visão remanescente de saberes e culturas africanas ou descendentes, fossem de cunho material, simbólico, reflexivo, imagético, expressivo, na língua, no corpo. No embate, Inácio, negro, escravizado, já rebaixado sob (...) a égide do sistema escravocrata, embate-se contra a tentativa presunçosa de aniquilamento perpetrada por seu oponente. (shrink)

By means of models in toposes of C-sets (where C is a small category), necessary conditions are found for the minimum quantified extension of a propositional (intermediate, modal) logic to be complete with respect to Kripke semantics; in particular, many well-known systems turn out to be incomplete.

We prove a generalization of the hyper-game theorem by using an abstract version of inductively generated formal topology. As applications we show proofs for Cantor theorem, uncountability of the set of functions from N to N and Gödel theorem which use no diagonal argument.

Vision is the main entrance for environmental input to the human brain. Even if vision is our most used sensory modality, its importance is not limited to environmental exploration. Rather it has strong links to motor competences, further extending to cognitive and social aspects of human life. These multifaceted relationships are particularly important in developmental age and become dramatically evident in presence of complex deficits originating from visual aberrancies. The present review summarizes the available neuropsychological evidence on the development of (...) visual competences, with a particular focus on the associated visuo-motor integration skills in health and disease. With the aim of supporting future research and interventional settings, the goal of the present review is to constitute a solid base to help the translation of neuropsychological hypotheses into straightforward empirical investigations and rehabilitation/training protocols. This approach will further increase the impact, ameliorate the acceptance, and ease the use and implementation of lab-derived intervention protocols in real-life situations. (shrink)

O Argumento da Terra Gêmea Moral (ATGM) é o desafio semântico central para o Realismo Moral Naturalista (RMN). À fim de evitar tal problema, os defensores do RMN têm articulado uma série de réplicas ao ATGM. Neste artigo, abordo algumas dessas réplicas e defendo a tese de que elas não refutam o ATGM. Considero duas propostas em específico: o Argumento da Tradução, de D. Copp, e o Argumento do Fim da Investigação Moral, de A. Viggiano. Apresento essas objeções, mostro em (...) que sentido pretendem responder ao ATGM e argumento que cada uma delas é vulnerável a vários problemas. Concluo que os ataques de Copp e Viggiano ao ATGM devem ser recusados e que o desafio semântico ao RMN persiste. (shrink)

We show that (contrary to the parallel case of intuitionistic logic, see [7], [4]) there does not exist a translation fromS42 (the propositional modal systemS4 enriched with propositional quantifiers) intoS4 that preserves provability and reduces to identity for Boolean connectives and.

The logicD-J of the weak exluded middle with constant domains is proved to be incomplete with respect to Kripke semantics, by introducing models in presheaves on an arbitrary category. Additional incompleteness results are obtained for the modal systems with nested domains extendingQ-S4.1.

Sufficient syntactic conditions for canonicity in intermediate and intuitionistic modal logics are given. We present a new technique which does not require semantic first-order reduction and which is constructive in the sense that it works in an intuitionistic metatheory through a model without points which is classically isomorphic to the usual canonical model.

In this paper we present a general theory of normal forms, based on a categorial result for the free monoid construction. We shall use the theory mainly for proposictional modal logic, although it seems to have a wider range of applications. We shall formally represent normal forms as combinatorial objects, basically labelled trees and forests. This geometric conceptualization is implicit in and our approach will extend it to other cases and make it more direct: operations of a purely geometric and (...) combinatorial nature will be introduced in order to give a mathematical description of the basic logical/algebraic constructions .We begin by recalling the above-mentioned categorial construction: we need a careful inspection of it because in the various examples considered later we plan to deduce from it in a uniform way the normal forms and the description of finitely generated free algebras. This method always works whenever we can describe the category of algebras corresponding to the logic under consideration as a T-objects category. When this simple description seems not to be available, still the general theory might be of some interest, because a description of the category of algebras as a T-objects category plus equation is possible .The central part of the paper is more advanced and specific: we show how the general approach presented here can provide some insights even in the basic case of the modal system K. Section 4 contains a contribution to the theory of normal forms, namely the description of the uniform substitution. This result will enable us to give a duality theorem for the category of finitely generated free modal algebras and in Section 5 to provide a characterization of the collections of normal forms which happen to be normal forms for a logic, thus giving a description of the lattice of modal logics.Section 6 deals with some applications: we shall show how to use normal forms in order to prove for the modal system K the definability of higher-order propositional quantifiers and of the tense operator F .As to the prerequisites, the paper is almost self-contained. The reader is only assumed to have familiarity with standard techniques in algebraic logic ). Knowledge of the basic facts about adjoint functors is required too, see e.g. McLane or the appendix. (shrink)

We characterize (both from a syntactic and an algebraic point of view) the normal K4-logics for which unification is filtering. We also give a sufficient semantic criterion for existence of most general unifiers, covering natural extensions of K4.2⁺ (i.e., of the modal system obtained from K4 by adding to it, as a further axiom schemata, the modal translation of the weak excluded middle principle).

We investigate finitarity of unification types in locally finite varieties of Heyting algebras, giving both positive and negative results. We make essential use of finite dualities within a conceptualization for E-unification theory 733–752) relying on the algebraic notion of a projective object.

The recent cycle of social struggles against precarity in Italy has been characterized by an extensive use of images representing precarious workers. This contribution explores this in the case of the Euro Mayday Parade (EMP) protest campaign. The subversion of existing popular culture traditions was the main objective of the activists’ newly created icons such as San Precario, Serpica Naro and other visual tools. The visual work on gender in the EMP seemed to fill a gap between theoretical work on (...) the feminization of affective and immaterial labour and the less predominant presence of gender. Visual icons seem to have been at least as successful as text messages in publicizing the precarity discourse and their production deserves further attention. (shrink)

We provide a new and elementary proof of strong normalization for the lambda calculus of intersection types. It uses no strong method, like for instance Tait-Girard reducibility predicates, but just simple induction on type complexity and derivation length and thus it is obviously formalizable within first order arithmetic. To obtain this result, we introduce a new system for intersection types whose rules are directly inspired by the reduction relation. Finally, we show that not only the set of strongly normalizing terms (...) of pure lambda calculus can be characterized in this system, but also that a straightforward modification of its rules allows to characterize the set of weakly normalizing terms. (shrink)

A. M. Pitts in [Pi] proved that HA op fp is a bi-Heyting category satisfying the Lawrence condition. We show that the embedding $\Phi: HA^\mathrm{op}_\mathrm{fp} \longrightarrow Sh(\mathbf{P_0,J_0})$ into the topos of sheaves, (P 0 is the category of finite rooted posets and open maps, J 0 the canonical topology on P 0 ) given by $H \longmapsto HA(H,\mathscr{D}(-)): \mathbf{P_0} \longrightarrow \text{Set}$ preserves the structure mentioned above, finite coproducts, and subobject classifier, it is also conservative. This whole structure on HA op (...) fp can be derived from that of Sh(P 0 ,J 0 ) via the embedding Φ. We also show that the equivalence relations in HA op fp are not effective in general. On the way to these results we establish a new kind of duality between HA op fp and a category of sheaves equipped with certain structure defined in terms of Ehrenfeucht games. Our methods are model-theoretic and combinatorial as opposed to proof-theoretic as in [Pi]. (shrink)

This paper explores how some Italian HR managers narrate the changes imposed by the COVID-19 threat in the workplace. Events since December 2019 have presented exceptional circumstances to which HR managers have reacted in very different ways. This study explored how HR managers came to introduce organizational changes aimed at coping with the emergency, as well as how employees were involved in those organizational changes. The article is based on a thematic analysis of some interviews with Italian HR managers whose (...) companies decided to switch working from home on a massive scale. We wanted to offer some reflections on the actions taken by a few HR managers and Italian companies to keep working at a time when most workers were forced to respect the lockdown. (shrink)

Radiation therapy therapists face challenging daily tasks that leave them prone to high attrition and burnout and subsequent deficits in performance. Here, we employed an accelerated alpha-theta neurofeedback protocol that is implementable in a busy medical workplace to test if 12 RTTs could learn the protocol and exhibit behavior and brain performance-related benefits. Following the 3-week protocol, participants showed a decrease in subjective cognitive workload and a decrease in response time during a performance task, as well as a decrease in (...) desynchrony of the alpha electroencephalogram band. Additionally, novel microstate analysis for neurofeedback showed a significant decrease in global field power following neurofeedback. These results suggest that the RTTs successfully learned the protocol and improved in perceived cognitive workload following 3 weeks of neurofeedback. In sum, this study presents promising behavioral improvements as well as brain performance-related evidence of neurophysiological changes following neurofeedback, supporting the feasibility of implementing neurofeedback in a busy workplace and encouraging the further study of neurofeedback as a tool to mitigate burnout. (shrink)

Pretende-se abordar como os argumentos luteranos ─ de natureza constitucional das "magistraturas inferiores" e de direito privado ─ acerca do direito de resistência, desenvolvidos no final da década de 1520 e início de 1530, foram recepcionados no _Segundo Tratado Sobre o Governo Civil_, de John Locke, escrito no século XVII. O argumento de direito privado compreende que todo governante que abandona as boas ações e se dedica a cometer atos tirânicos se despoja de sua autoridade e, consequentemente, deve ser tratado (...) como uma pessoa privada, portanto, sujeita ao lícito revide, o que configura uma espécie de legítima defesa. O argumento constitucional das "magistraturas inferiores" afirma a possibilidade de órgãos intermediários entre o governante e o povo estarem legitimados para oferecer resistência às tiranias. Em John Locke, ambos os argumentos objetivam a solução do problema da tirania para se obter liberdade política e religiosa. (shrink)