The problem is addressed of establishing the satisfiability of prenex formulas involving a single universal quantifier, in diversified axiomatic set theories. A rather general decision method for solving this problem is illustrated through the treatment of membership theories of increasing strength, ending with a subtheory of Zermelo-Fraenkel which is already complete with respect to the ∀*∀ class of sentences. NP-hardness and NP-completeness results concerning the problems under study are achieved and a technique for restricting the universal quantifier is presented.

Being able to state the principles which lie deepest in the foundations of mathematics by sentences in three variables is crucially important for a satisfactory equational rendering of set theories along the lines proposed by Alfred Tarski and Steven Givant in their monograph of 1987. The main achievement of this paper is the proof that the 'kernel' set theory whose postulates are extensionality. (E), and single-element adjunction and removal. (W) and (L), cannot be axiomatized by means of three-variable sentences. This (...) highlights a sharp edge to be crossed in order to attain an 'algebraization' of Set Theory. Indeed, one easily shows that the theory which results from the said kernel by addition of the null set axiom, (N), is in its entirety expressible in three variables. (shrink)

As is well-known, the Bernays-Schönfinkel-Ramsey class of all prenex ∃*∀* -sentences which are valid in classical first-order logic is decidable. This paper paves the way to an analogous result which the authors deem to hold when the only available predicate symbols are ∈ and =, no constants or function symbols are present, and one moves inside a (rather generic) Set Theory whose axioms yield the well-foundedness of membership and the existence of infinite sets. Here semi-decidability of the satisfiability problem for (...) the BSR class is proved by following a purely semantic approach, the remaining part of the decidability result being postponed to a forthcoming paper. (shrink)

This book presents a set of historical recollections on the work of Martin Davis and his role in advancing our understanding of the connections between logic, computing, and unsolvability. The individual contributions touch on most of the core aspects of Davis’ work and set it in a contemporary context. They analyse, discuss and develop many of the ideas and concepts that Davis put forward, including such issues as contemporary satisfiability solvers, essential unification, quantum computing and generalisations of Hilbert’s tenth problem. (...) The book starts out with a scientific autobiography by Davis, and ends with his responses to comments included in the contributions. In addition, it includes two previously unpublished original historical papers in which Davis and Putnam investigate the decidable and the undecidable side of Logic, as well as a full bibliography of Davis’ work. As a whole, this book shows how Davis’ scientific work lies at the intersection of computability, theoretical computer science, foundations of mathematics, and philosophy, and draws its unifying vision from his deep involvement in Logic. (shrink)

As proved recently, the satisfaction problem for all prenex formulae in the set-theoretic Bernays-Shönfinkel-Ramsey class is semi-decidable over von Neumann's cumulative hierarchy. Here that semi-decidability result is strengthened into a decidability result for the same collection of formulae.

This paper introduces the logics of super-strict implications, where a super-strict implication is a strengthening of C.I. Lewis' strict implication that avoids not only the paradoxes of material implication but also those of strict implication. The semantics of super-strict implications is obtained by strengthening the (normal) relational semantics for strict implication. We consider all logics of super-strict implications that are based on relational frames for modal logics in the modal cube. it is shown that all logics of super-strict implications are (...) connexive logics in that they validate Aristotle's Theses and (weak) Boethius's Theses. A proof-theoretic characterisation of logics of super-strict implications is given by means of G3-style labelled calculi, and it is proved that the structural rules of inference are admissible in these calculi. It is also shown that validity in the S5-based logic of super-strict implications is equivalent to validity in G. Priest's negation-as-cancellation-based logic. Hence, we also give a cut-free calculus for Priest's logic. (shrink)

Background: COVID-19 has taken many lives worldwide and due to this, millions of persons are in grief. When the grief process lasts longer than 6 months, the person is in risk of developing Complicated Grief Disorder. The CGD is related to serious health consequences. To reduce the probability of developing CGD a preventive intervention could be applied. In developing countries like Mexico, the psychological services are scarce, self-applied interventions could provide support to solve this problem and reduce the health impact (...) even after the pandemic has already finished.Aims: To design and implement a self-applied intervention composed of 12 modules focused on the decrease of the risk of developing CGD, and increasing the life quality, and as a secondary objective to reduce the symptomatology of anxiety, depression, and increase of sleep quality. The Intervention Duelo COVID follows the principles of User Experience and is designed according to the needs and desires of a sample of the objective participants, to increase the adherence to the self-applied intervention, considered one of the main weaknesses of online interventions.Methods: A Randomized Controlled Trial will be conducted from the 22nd of December of 2020 to the first of June 2021. The participants will be assigned to an intervention with elements of Cognitive Behavioral Therapy, Acceptance and Commitment Therapy, Mindfulness and Positive Psychology. The control group will be a wait-list condition, that will receive the intervention 1.5–2 months after the pre-measurement were taken. The Power Size Calculation conducted through G*Power indicated the need for a total of 42 participants, which will be divided by 21 participants in each group. The platform will be delivered through responsive design assuring with this that the intervention will adapt to the screen size of cellphones, tablets, and computers.Ethics and Dissemination: The study counts with the approval of the Research Ethics Committee of the Autonomous University of Ciudad Juárez, México, and it is registered in Clinical Trials. The article is sent and registered in clinical trials before the recruitment started. The results will be reported in future conferences, scientific publications, and media. (shrink)

Hasta el final de su vida, y durante más de diez años, Publio Virgilio Marón (70-19 a.C.) estuvo dedicado a la composición de la Eneida, unánimemente reconocida como el más perfecto exponente del clasicismo romano. Virgilio pretendió con ella ofrecer al público romano la gran epopeya de sus orígenes, que sirviera al tiempo como justificación y exaltación del nuevo régimen impuesto por el emperador Augusto. El resultado sería esta magistral combinación entre el pasado legendario de Roma y su historia reciente. (...) Más allá de las evidentes funciones políticas y sus distintos niveles temáticos, la Eneida nos ofrece la gesta de un héroe exiliado de su patria. Tras la quema de Troya a manos de los griegos, Eneas parte hacia una tierra extraña, en la que había de encontrar su nuevo hogar. En su viaje por mar, el hijo de Venus arrostrará numerosas dificultades hasta llegar a su destino en la costa italiana, e incluso allí se verá obligado a entablar una guerra contra los pueblos itálicos, para conseguir al fin fundar una ciudad llamada a convertirse en cabeza del mundo. (shrink)

How has the concept of democracy been understood, manifested, reimagined and represented through the ages? In a work that spans 2,500 years these fundamental questions are addressed by 66 experts, each contributing their overview of a theme applied to a period in history. With the help of a broad range of case material they illustrate the physical, social and cultural contexts of democracy in Western culture from antiquity to the present. Individual volume editors ensure the cohesion of the whole, and (...) to make it as easy as possible to use, chapter themes are identical across each of the volumes. Superbly illustrated, the full six-volume set combines to present the most comprehensive and authoritative survey available on democracy throughout history. The six volumes cover: 1 - Antiquity (500 BCE-565 CE); 2 - Medieval Age (565-1450); 3 - Renaissance (1450-1650); 4 - Age of Enlightenment (1650-1800); 5 - Age of Empire (1800-1920); 6 Modern Age (1920-present) The ten themes are: Sovereignty; Liberty and the Rule of Law; The 'Common Good'; Economic and Social Democracy; Religion and the Principles of Political Obligation; Citizenship and Gender; Ethnicity, Race and Nationalism; Democratic Crises, Revolutions and Civil Resistance; International Relations; Beyond the Polis. The page extent for the pack is approximately 2016pp. Each volume opens with Notes on Contributors and an Introduction and concludes with Notes, Bibliography, and an Index. The Cultural Histories Series A Cultural History of Democracy is part of The Cultural Histories Series. Titles are available both as printed hardcover sets for libraries needing just one subject or preferring a one-off purchase and tangible reference for their shelves, or as part of a fully-searchable digital library available to institutions by annual subscription or on perpetual access (see www.bloomsburyculturalhistory.com). (shrink)

Dai saggi raccolti in questo volume da Garin emergono le linee di una storia della civiltà del Rinascimento italiano. Lo studio dello stretto intreccio tra vita intellettuale e vita politica, soprattutto nella Firenze fra Tre e Quattrocento, costituisce il punto di partenza per una nuova interpretazione di questo periodo. Le origini dell'Umanesimo vanno cercate nel rapporto fra la tradizione di libertà e democrazia della repubblica fiorentina e l'immagine ideale della repubblica come erede di Roma.

Sulla dignità umana -- Bioetica senza fondamento? -- Una sovranità limitata per la ricerca scientifica: ossimoro o truismo -- Ius quia iussum e ius quia iustum (considerazioni su alcuni passi del libro della genesi) -- La pace come problema -- A proposito di religioni, identità nazionali e diritto -- Su costituzioni e costituzionalismo -- A proposito del trattato politico di Spinoza -- A proposito dei lineamenti fondamentali di filosofia del diritto di Hegel -- A proposito degli elementi di scienza politica (...) di Mosca -- Su Michels -- Su luigi einaudi 'italiano del tutto particolare' -- Guerra e pace secondo cotta -- Una postilla non scientifica (ovvero: un dittico contro Schmitt). (shrink)

1. Le fe por la palabra -- 2. Topía y Utopía -- 3. Luz en la caverna.