An efficient variant of the double-negation translation explains the relationship between Shoenfield’s and G¨odel’s versions of the Dialectica interpretation.

Various connexive FDE-based modal logics are studied. Some of these logics contain a conditional that is both connexive and strict, thereby highlighting that strictness and connexivity of a conditional do not exclude each other. In particular, the connexive modal logics cBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document}, cKN4, scBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document}, scKN4, cMBL, and scMBL are introduced semantically by means of classes of Kripke models. The logics cBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} (...) \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document} and cKN4 are connexive variants of the FDE-based modal logics BK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document} and KN4 with a weak and a strong implication, respectively. The system cMBL is a connexive variant of the modal bilattice logic MBL. The latter is a modal extension of Arieli and Avron’s logic of logical bilattices and is characterized by a class of Kripke models with a four-valued accessibility relation. In the systems scBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document}, scKN4, and scMBL, the conditional is both connexive and strict. Sound and complete tableau calculi for all these logics are presented and used to show that the entailment relations of the systems under consideration are decidable for finite premise set. Moreover, the logics cBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {cBK}^-$$\end{document} and cMBL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {cMBL}$$\end{document} are shown to be algebraizable. The algebraizability of cMBL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {cMBL}$$\end{document} is derived from proving cMBL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {cMBL}$$\end{document} to be definitionally equivalent to MBL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {MBL}$$\end{document}. All connexive modal logics studied in this paper are decidable, paraconsistent, and inconsistent but non-trivial logics. (shrink)

L’article de Karl Popper « Indeterminism in Quantum Physics and in Classical Physics » est tombé injustement dans l’oubli. Popper jugeait le déterminisme faux : l’avenir est ouvert. En principe, remplacer la variante de Laplace de la pré-détermination par une prédétermination prévisible permet de rendre scienti-fique, donc réfutable, le déterminisme « scientifique ». Popper a affirmé qu’il l’avait réfuté. Maintenant, un système métaphysique peut avoir une extension – au sens mathématique – qui le rend explicatif et testable. Si une extension (...) existe, alors elle n’est pas unique, et de nombreuses autres extensions alterna-tives existent. La preuve de Popper n’est alors pas concluante. (shrink)

Capitalist dynamics in knowledge production are not limited to situations in which economic interests influence researchers’ practices. Building on laboratory studies and the French “pragmatic” tradition in sociology, this article proposes an approach to tackle more pervasive capitalist logics at work in contemporary research and their consequences. It uses the term epistemic capitalism to denote the accumulation of capital, as worth made durable, through the act of doing research, in and beyond academia. In doing so, it conceptualizes capitalism primarily not (...) as a system of circulation and accumulation of monetary value but rather as a cultural way of producing, attributing, and accumulating specific forms of worth, which need not be monetary. Empirically, the article studies variants in epistemic capitalism by addressing the differing role of the accumulation of different forms of capital and the regimes connected to it in two institutional settings in Austria, academic life science laboratories and biotechnology start-up companies. Concluding, it argues that analytically dissociating the concept of capitalism from its link to economic value allows a finer-grained cultural analysis of the importance and effects of processes of accumulation in contemporary research. It ends with discussing the normative implications of these findings for debates about the commercialization of academia. (shrink)

This article argues that the much-maligned ‘notational variants’ of a given formal linguistic theory play a role similar to alternative numerical measurement scales. Thus, they can be used to identify the invariant components of the grammar; i.e., those features that do not depend on the choice of empirically equivalent representation. Treating these elements as the ‘meaningful’ structure of language has numerous consequences for the philosophy of science and linguistics. I offer several such examples of how linguistic theorizing can profit from (...) adopting a measurement-theoretic viewpoint. The first concerns a measurement-theoretic response to a famous criticism of Quine's. Others follow from issues of simplicity in the current biolinguistics program. An unexpected similarity with behaviorist practices is also uncovered. I then argue that managable and useful steps can be taken in this area. (shrink)

Focus on the way in which cultural variants affect other variants' probabilities of transmission in modeling and empirical work can enrich Kline's conceptualization of teaching. For example, the problem of communicating complex cumulative culture is an adaptive problem; teaching methods that manage transmission so that acquisition of some cultural variants increases the probability of acquiring others, provide a partial solution.

Among the types of strings which are technically ungrammatical but fully intelligible, dialect variants form a special class. They can be viewed as generated by alternate transformations within the grammar; the means by which they are interpreted is therefore identical with the means by which interpretations are assigned to well-formed strings. Such language-specific rules thus differ from the universal procedures by which other types of ungrammatical strings are apparently derived.

The tableaux-constructions have a number of properties which advantageously distinguish them from equivalent axiomatic systems . The proofs in the form of tableaux-constructions have a full accordance with semantic interpretation and subformula property in the sense of Gentzen’s Hauptsatz. Method of tatleaux-construction gives a good substitute of Gentzen’s methods and thus opens a good perspective for the investigations of theoretical as well as applied aspects of logical calculi. It should be noted that application of tableau method in modal, tense, relevant (...) and other non-classical logics is connected with serious difficulties. Tableaux variants are constructed only for a few normal modal systems. As to relevant and paraconsistent logic, the absence of its tableau variants may be considered as a question of special interest. We shall formulate the tableaux for propositional modal system S4.1, S4.2, S4.3, S4.4 and relevant R∗ and E ∗ using Beth’s tableaux construction with indexed formulas. (shrink)

The relationship between formal logic and informal reasoning has always been a hot topic. In this paper, we propose another possible way to bring it up inspired by connexive logic. Our approach is based on the following presupposition: whatever method of formalizing informal reasoning you choose, there will always be some classically acceptable deductive principles that will have to be abandoned, and some desired schemes of argument that clearly are not classically valid. That way, we start with a new version (...) of connexive logic which validates Boethius’ Theses and quashes their converse from right to left. We provide a sound and complete axiomatization of this logic. We also study the implication-negation fragment of this logic supplied with Boolean negation as a second negation. (shrink)

In this paper, we introduce anaffective variant of the Simon paradigm. Three experiments are reported in which nouns and adjectives with a positive, negative, or neutral affective meaning were used as stimuli. Depending on the grammatical category of the presented word (i.e. noun or adjective), participants had to respond as fast as possible by saying a predetermined positive or negative word. In Experiments 1 and 2, the words POSITIVE and NEGATIVE were required as responses, in Experiment 3, FLOWER and CANCER (...) were used as response words. Despite the fact that participants were explicitly instructed to ignore the affective meaning of the presented words, reaction times were faster when the affective connotation of the presented word and the correct response was the same than when it differed. The results lendfurther support tothe hypothesis that stimulus valence can be processed automatically. We also argue that the affective Simon paradigm can be used as a flexible tool for the study of affective-processing and discuss how other variants of the Simon paradigm can be developed to stimulate research on other aspects of information-processing. (shrink)

Infinite time Turing machines represent a model of computability that extends the operations of Turing machines to transfinite ordinal time by defining the content of each cell at limit steps to be the lim sup of the sequences of previous contents of that cell. In this paper, we study a computational model obtained by replacing the lim sup rule with an ‘eventually constant’ rule: at each limit step, the value of each cell is defined if and only if the content (...) of that cell has stabilized before that limit step and is then equal to this constant value. We call these machines weak infinite time Turing machines. We study different variants of wITTMs adding multiple tapes, heads, or bidimensional tapes. We show that some of these models are equivalent to each other concerning their computational strength. We show that wITTMs decide exactly the arithmetic relations on natural numbers. (shrink)

El autor Luis Rodríguez Manzanera propone el concepto de macrocriminalidad al referirse a una etapa histórica que involucra el desarrollo de manifestaciones delictivas, que se mantienen por una justificación sociopolítica y que implica a toda una sociedad. Esta definición fue propicia incorporarla para el análisis de Noticia de un secuestro (1996), debido a que, en esta novela periodística, se narran sucesos vinculados con acciones subversivas que respaldan el tráfico ilícito de drogas, junto con atentados que provocó Pablo Escobar, organizador del (...) Cartel de Medellín (Colombia), a las entidades gubernamentales. Algunos indicadores que se apropian a esta conceptualización son la violencia, la locura y el narcoterrorismo. (shrink)

In recent years, dependency grammars have established themselves as valuable tools in theoretical and computational linguistics. To many linguists, dependency grammars and the more standard constituency-based formalisms are notational variants. We argue that, beyond considerations of formal equivalence, cognition may also serve as a background for a genuine comparison between these different views of syntax. In this paper, we review and evaluate some of the most common arguments and evidence employed to advocate for the cognitive or neural reality of dependency (...) grammars in linguistics, psycholinguistics, or neurolinguistics. We then raise the possibility that the abilities to represent and track, alternatively or in parallel, constituency and dependency structures co-exist in human cognition and are constitutive of syntactic competence. (shrink)

In this paper, we define a first-order logic CFʹ with strong negation and bounded static quantifiers, which is a variant of Thomason's logic CF. For the logic CFʹ, the usual Kripke formal semantics is defined based on situations, and a sound and complete axiomatic system is established based on the axiomatic systems of constructive logics with strong negation and Thomason's completeness proof techniques. With the use of bounded quantifiers, CFʹ allows the domain of quantification to be empty and allows for (...) nondenoting constants. CFʹ is intended as a fragment of a logic for situation theory. Thus the connection between CFʹ and infon logic is discussed. (shrink)

This article examines the evolution of Lev P. Karsavin, the connection between the philosopher’s historical perspective and his ontological constructions, his postulation of the personhood principle of being’s organization, and the common mindsets of the philosophy of all-unity. The author of this article distinguishes between reflections on the future found in Karsavin’s pre-emigration work and the image of the future he creates within the framework of the Eurasianist paradigm. This article presents three variants of representation of the future: the universal, (...) the national-cultural, and the state. The author analyzes the image of the future associated with the coming-to-be of the All-One Humanity, its transformation into a truly symphonic person, and show how this image turns into a concept of the future that affirms the self-development of national culture. The prospect of developing Russia-Eurasia as an ideocratic and statist state that acts as a form of manifestation of the national culture represents the final stage of this evolution. (shrink)

Genetic research into ageing, longevity and late-onset disease is becoming increasingly common. Yet, there is a paucity of knowledge related to clinical actionability and the return of pathogenic variants to otherwise healthy elderly individuals. Whether or not genetic research in the elderly should be managed differently from standard practices adapted for younger populations has not yet been defined. In this article, we provide an overview of ethical and practical challenges in preparing for a genetic study of over 14 000 healthy (...) Australians aged 70 years or older enrolled in the ASPirin in Reducing Events in the Elderly Healthy Ageing Biobank. At the time of consent, all participants in this study were free of life-threatening illness, cardiovascular disease or cognitive impairment. ASPREE is thus a cohort of healthy elderly individuals with seemingly minimal burden of genetic disease recruited without ascertainment bias. The cohort presents a unique opportunity to address the penetrance of known pathogenic variants in a population without disease symptoms; however, it also raises a number of ethical concerns regarding the interpretation and disclosure of variants with known clinical actionability. Some of the challenges include how to manage the interpretation, disclosure and actioning of pathogenic variants found in otherwise healthy elderly adults without disease symptoms, whether or not to disclose findings for the benefit of family members rather than elderly consented donors themselves, how to manage the return of genetic findings to the elderly individuals who are now in severe cognitive decline or terminal illness, how to ensure quality of information and clinical service upon disclosure of results to this demographic and how to prepare for the insurance implications of disclosing genetic information under Australian law. We discuss these and other dilemmas and propose a defensible plan of management. Trial registration number ISRCTN83772183. (shrink)

This is the first part of a two-part article on semantic compositionality, that is, the principle that the meaning of a complex expression is determined by the meanings of its parts and the way they are put together. Here we provide a brief historical background, a formal framework for syntax and semantics, precise definitions, and a survey of variants of compositionality. Stronger and weaker forms are distinguished, as well as generalized forms that cover extra-linguistic context dependence as well as linguistic (...) context dependence. In the second article, we survey arguments for and arguments against the claim that natural languages are compositional, and consider some problem cases. It will be referred to as Part II. (shrink)

IN Hilbert's theory of the foundations of any given branch of mathematics the main problem is to establish the consistency (of a suitable formalisation) of this branch. Since the (intuitionist) criticisms of classical logic, which Hilbert's theory was intended to meet, never even alluded to inconsistencies (in classical arithmetic), and since the investigations of Hilbert's school have always established much more than mere consistency, it is natural to formulate another general problem in the foundations of mathematics: to translate statements of (...) theorems and proofs in the branch considered into those of some preferred system, where the translation must satisfy certain appropriate conditions (interpretation). The problem is relative to the choice of preferred system, as is Hilbert's consistency problem since he required the consistency to be established by particular methods (finitist ones). A finitist interpretation of classical number theory, which has been published in full detail elsewhere, is here described by means of typical examples. Partial results on analysis (theory of arbitrary functions whose arguments and values are the non-negative integers) are here presented for the first time. One of these results is restricted to functions whose values are bounded; its interest derives from the fact that real numbers may be represented by such functions. It is hoped that diverse general observations and comments, which would bore the specialist, may be of help to the general reader. The specialist may find some points of interest in the last two sections of the main text and in the notes following it. (shrink)

The occurrence of a new strain of SARS-CoV-2 cannot be ruled out. Therefore, this study seeks to investigate the possible effects of a hypothetical imperfect anti-COVID-19 vaccine on the control of not only the first variant of SARS-CoV-2 but also the second variant of SARS-CoV-2. We further examine the rates and a, escape of quarantined infectious individuals from isolation centers. The control R c and basic reproduction numbers R 0 are computed which gives assess to obtain asymptotic stability of disease-free (...) equilibrium point globally and the existence of a unique persistent equilibrium solution. Numerical results reveal that people infected with the second strain who are vaccinated with an imperfect vaccine are under control but the prevalence of the second variant enhances the prevalence of the first variant. Thus, discovering a vaccine that is effective for the prevention of variant 2 is necessary for the control of COVID-19. Numerical results also reveal that increase in the rate at which individuals infected with the first variant escape the isolation center gives rise to the population infected with the first variant and lowers the peak of the population infected with the second variant. This is probably because individuals infected with the second variant appear to be more careful with their lives and get vaccinated more than individuals infected with the first variant. (shrink)

This paper presents detailed formalizations of ontological arguments in a simple modal natural deduction calculus. The first formal proof closely follows the hints in Scott’s manuscript about Gödel’s argument and fills in the gaps, thus verifying its correctness. The second formal proof improves the first one, by relying on the weaker modal logic KB instead of S5 and by avoiding the equality relation. The second proof is also technically shorter than the first one, because it eliminates unnecessary detours and uses (...) Axiom 1 for the positivity of properties only once. The third and fourth proofs formalize, respectively, Anderson’s and Bjørdal’s variants of the ontological argument, which are known to be immune to modal collapse. (shrink)

Kreisel’s conjecture is the statement: if, for all$n\in \mathbb {N}$,$\mathop {\text {PA}} \nolimits \vdash _{k \text { steps}} \varphi (\overline {n})$, then$\mathop {\text {PA}} \nolimits \vdash \forall x.\varphi (x)$. For a theory of arithmeticT, given a recursive functionh,$T \vdash _{\leq h} \varphi $holds if there is a proof of$\varphi $inTwhose code is at most$h(\#\varphi )$. This notion depends on the underlying coding.${P}^h_T(x)$is a predicate for$\vdash _{\leq h}$inT. It is shown that there exist a sentence$\varphi $and a total recursive functionhsuch that$T\vdash (...) _{\leq h}\mathop {\text {Pr}} \nolimits _T(\ulcorner \mathop {\text {Pr}} \nolimits _T(\ulcorner \varphi \urcorner )\rightarrow \varphi \urcorner )$, but, where$\mathop {\text {Pr}} \nolimits _T$stands for the standard provability predicate inT. This statement is related to a conjecture by Montagna. Also variants and weakenings of Kreisel’s conjecture are studied. By the use of reflexion principles, one can obtain a theory$T^h_\Gamma $that extendsTsuch that a version of Kreisel’s conjecture holds: given a recursive functionhand$\varphi (x)$a$\Gamma $-formula (where$\Gamma $is an arbitrarily fixed class of formulas) such that, for all$n\in \mathbb {N}$,$T\vdash _{\leq h} \varphi (\overline {n})$, then$T^h_\Gamma \vdash \forall x.\varphi (x)$. Derivability conditions are studied for a theory to satisfy the following implication: if, then$T\vdash \forall x.\varphi (x)$. This corresponds to an arithmetization of Kreisel’s conjecture. It is shown that, for certain theories, there exists a functionhsuch that$\vdash _{k \text { steps}}\ \subseteq\ \vdash _{\leq h}$. (shrink)

First we give an overview about variants of visibility and related problems. Then we prove that some guarding and covering problems are NP-hard for ortho-polygons with holes, using a so-called vertex cover technique.

Brain‐derived neurotrophic factor (BDNF) is the most‐abundant neurotrophin in the brain. In mammals, it is synthesized as a precursor called proBDNF, which is proteolytically cleaved to generate mature BDNF. The BDNF gene is located on chromosome 11p13, and a functional single nucleotide polymorphism (SNP) of this gene has been shown to produce a valine (Val)‐to‐methionine (Met) substitution in the proBDNF protein at codon 66 (Val66Met). Several papers suggest that this SNP is related to decreased hippocampal volume and hippocampus‐mediated memory performance (...) in humans. Recently, Chen et al.1 generated a variant BDNF mouse (BDNFMet/Met) that reproduces the phenotypic hallmarks in humans with a variant Met allele. In the behavioral analysis, BDNFMet/Met mice show increased anxiety‐related behaviors. This mini‐review examines the impact of Met substitution of proBDNF on anxiety‐related behaviors. BioEssays 29: 116–119, 2007. © 2007 Wiley Periodicals, Inc. (shrink)

Designed to meet the needs of both student and scholar, this edition of _Leviathan_ offers a brilliant introduction by Edwin Curley, modernized spelling and punctuation of the text, and the inclusion, along with historical and interpretive notes, of the most significant variants between the English version of 1651 and the Latin version of 1668. A glossary of seventeenth-century English terms, and indexes of persons, subjects, and scriptural passages help make this the most thoughtfully conceived edition of _Leviathan_ available.

A number of significant contributions in the last four decades show that non-normal modal logics can be fruitfully employed in several applied fields. Well-known domains are epistemic logic, deontic logic, and systems capturing different aspects of action and agency such as the modal logic of agency, concurrent propositional dynamic logic, game logic, and coalition logic. Semantics for such logics are traditionally based on neighbourhood models. However, other model-theoretic semantics can be used for this purpose. Here, we systematically study multi-relational structures, (...) whose investigation is still relatively underdeveloped. After a brief introduction to two different versions of multi-relational semantics – which we call strong and weak multi-relational semantics – we proceed to study several modal schemata. Special attention is paid to the schemata CON and D. Finally we offer completeness proofs for several systems using both strong and weak semantic tools: The proofs thus cover both classical system.. (shrink)

This paper introduces the notion of cW10-creative set, which strengthens that of semicreative set in a similar way as complete creativity strengthens creativity. Two results are proven, both of which imply that not all semicreative sets are cW10-creative. First, it is shown that semicreative Dedekind cuts cannot be cW10-creative; the existence of semicreative Dedekind cuts was shown by Soare. Secondly, it is shown that if A ⊕ B, the join of A and B, is cW10-creative, then either A or B (...) is cW10-creative, and the same is not true with ‘cW10-creative’ replaced by ‘semicreative’. Moreover, sets A, B which provide a counterexample for can be constructed within any given nonrecursive r.e. T-degrees a, b. MSC: 03D30. (shrink)