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)

We present a general approach to quantified modal logics that can simulate most other approaches. The language is based on operators indexed by terms which allow to express de re modalities and to control the interaction of modalities with the first-order machinery and with non-rigid designators. The semantics is based on a primitive counterpart relation holding between n-tuples of objects inhabiting possible worlds. This allows an object to be represented by one, many, or no object in an accessible world. Moreover (...) by taking as primitive a relation between n-tuples we avoid some shortcoming of standard individual counterparts. Finally, we use cut-free labelled sequent calculi to give a proof-theoretic characterisation of the quantified extensions of each first-order definable propositional modal logic. In this way we show how to complete many axiomatically incomplete quantified modal logics. (shrink)

Recoge las bases y peculiaridades de las concepciones pedagógicas de Manuel Bartolomé Cossío, sus ideas acerca de la enseñanza y las innovaciones introducidas en el sistema educativo.

Norms conferring public or private powers, i.e., the competence to issue other norms, play a very important rôle in law. But there is no agreement among legal philosophers about the nature of such norms. There are two main groups of theories, those that regard them as a kind of norms of conduct (either commands or permissions) and those that regard them as non-reducible to other types of norms. I try to show that reductionist theories are not quite acceptable; neither the (...) command-variety (Kelsen, Alf Ross inOn Law and Justice), nor the permission-variety (von Wright, Kanger, Lindahl) provide a satisfactory account of competence norms.Among the authors who maintain that competence norms are different from (and hence not reducible to) norms of conduct are Hart, Ross inDirectives and Norms, and Searle. Ross and Searle distinguish between regulative and constitutive rules as two radically different kinds of rules and classify competence norms among constitutive rules. This distinction runs parallel to von Wright's distinction between rules that are prescriptions and determinative rules. While the first regulate actions (by commanding, prohibiting, or permitting them), determinative rules define certain concepts. To view competence norms as (partial) definitions of certain legal concepts (like those of legislator, judge, etc.) seems to open interesting perspectives and to shed light on at least one aspect of these elusive norms. (shrink)

Partial proceedings of the 17th World Congress, International Association for Philosophy of Law and Social Philosophy, Bologna, 1995.

In the context of bounded arithmetic we consider some general replacement schemes and construct models for them. A new proof of a conservation result between and is derived.

This paper reports a psychological study of human categorization that looked at the procedures used by expert scientists when dealing with puzzling items. Five professional botanists were asked to specify a category from a set of positive and negative instances. The target category in the study was defined by a feature that was unusual, hence situations of uncertainty and puzzlement were generated. Subjects were asked to think aloud while solving the tasks, and their verbal reports were analyzed. A number of (...) problem solving strategies were identified, and subsequently integrated in a model of knowledge‐guided inductive categorization. Our model proposes that expert knowledge influences the subjects' reasoning in more complex ways than suggested by earlier investigations of scientific reasoning. As in previous studies, domain knowledge influenced our subjects' hypothesis generation and testing; but, additionally, it played a central role when subjects revised their hypotheses. (shrink)