In their useful logic for a computer network Shramko and Wansing generalize initial values of Belnap’s 4-valued logic to the set 16 to be the power-set of Belnap’s 4. This generalization results in a very specific algebraic structure — the trilattice SIXTEEN 3 with three orderings: information, truth and falsity. In this paper, a slightly different way of generalization is presented. As a base for further generalization a set 3 is chosen, where initial values are a — incoming data is (...) asserted, d — incoming data is denied, and u — incoming data is neither asserted nor denied, that corresponds to the answer “don’t know”. In so doing, the power-set of 3, that is the set 8 is considered. It turns out that there are not three but four orderings naturally defined on the set 8 that form the tetralattice EIGHT 4 . Besides three ordering relations mentioned above it is an extra uncertainty ordering. Quite predictably, the logics generated by a –order (truth order) and d –order (falsity order) coincide with first-degree entailment. Finally logic with two kinds of operations ( a –connectives and d –connectives) and consequence relation defined via a –ordering is considered. An adequate axiomatization for this logic is proposed. (shrink)

We explore a possibility of generalization of classical truth values by distinguishing between their ontological and epistemic aspects and combining these aspects within a joint semantical framework. The outcome is four generalized classical truth values implemented by Cartesian product of two sets of classical truth values, where each generalized value comprises both ontological and epistemic components. This allows one to define two unary twin connectives that can be called “semi-classical negations”. Each of these negations deals only with one of the (...) above mentioned components, and they may be of use for a logical reconstruction of argumentative reasoning. (shrink)

In their useful logic for a computer network Shramko and Wansing generalize initial values of Belnap’s 4-valued logic to the set 16 to be the power-set of Belnap’s 4. This generalization results in a very specific algebraic structure — the trilattice SIXTEEN3 with three orderings: information, truth and falsity. In this paper, a slightly different way of generalization is presented. As a base for further generalization a set 3 is chosen, where initial values are a — incoming data is asserted, (...) d — incoming data is denied, and u — incoming data is neither asserted nor denied, that corresponds to the answer “don’t know”. In so doing, the power-set of 3, that is the set 8 is considered. It turns out that there are not three but four orderings naturally defined on the set 8 that form the tetralattice EIGHT4. Besides three ordering relations mentioned above it is an extra uncertainty ordering. Quite predictably, the logics generated by a–order and d–order coincide with first-degree entailment. Finally logic with two kinds of operations and consequence relation defined via a–ordering is considered. An adequate axiomatization for this logic is proposed. (shrink)

This volume offers a wide range of both reconstructions of Nikolai Vasiliev’s original logical ideas and their implementations in the modern logic and philosophy. A collection of works put together through the international workshop "Nikolai Vasiliev’s Logical Legacy and the Modern Logic," this book also covers foundations of logic in the light of Vasiliev’s contradictory ontology. Chapters range from a look at the Heuristic and Conceptual Background of Vasiliev's Imaginary Logic to Generalized Vasiliev-style Propositions. It includes works which cover Imaginary (...) and Non-Aristotelian Logics, Inconsistent Set Theory and the Expansion of Mathematical Thinking, Plurivalent Logic, and the Impact of Vasiliev's Imaginary Logic on Epistemic Logic. The Russian logician, Vasiliev, was widely recognized as one of the forerunners of modern non-classical logic. His "imaginary logic" developed in some of his work at the beginning of 20th century is often considered to be one of the first systems of paraconsistent and multi-valued logic. The novelty of his logical project has opened up prospects for modern logic as well as for non-classical science in general. This volume contains a selection of papers written by modern specialists in the field and deals with various aspects of Vasiliev's logical ideas. The logical legacy of Nikolai Vasiliev can serve as a promising source for developing an impressive range of philosophical interpretations, as it marries promising technical innovations with challenging philosophical insights. (shrink)

In this paper, I attempt to offer a general outline of my views on the origin and evolution of language. I do not pretend in any way to a completely new conception of language evolution. It seems to me that all the most important and productive hypotheses about the origin of language have already been made before, and it is only a matter of putting the pieces of the puzzle together correctly. As far as I can see it, the evolution (...) of language is directly related to the embedded and embodied emotional types, which served as the basis for the subsequent categorization of perceived objects, and thus laid the ground for the formation of first an internal language (of thought), and then an external verbal language. Consistent with this, the paper is organized as follows. In the Introduction I briefly describe the problem I am facing in this article and outline a plan for solving it. Next section comprises a survey of relevant empirical findings related primarily to the processing and understanding of abstract terms and concepts. In my view, it supports the idea of the close connection of abstract terms proceeding, and thus language comprehension, with emotional states. The third section provides relevant theoretical considerations of the relationship between emotions, cognition, and language. Consistently considering various theories of emotions and concepts of language formation, I pay attention to the connection between affective states and language as a sign system. In the fourth section, my views are presented directly. In so doing, I illustrate my approach with a telling example that shows how, in the course of evolution, embedded and embodied emotional responses and reactions could become the building blocks first for the internal language of thought, and then for the external natural language. (shrink)

There is a productive and suggestive approach in philosophical logic based on the idea of generalized truth values. This idea, which stems essentially from the pioneering works by J.M. Dunn, N. Belnap, and which has recently been developed further by Y. Shramko and H. Wansing, is closely connected to the power-setting formation on the base of some initial truth values. Having a set of generalized truth values, one can introduce fundamental logical notions, more specifically, the ones of logical operations and (...) logical entailment. This can be done in two different ways. According to the first one, advanced by M. Dunn, N. Belnap, Y. Shramko and H. Wansing, one defines on the given set of generalized truth values a specific ordering relation (or even several such relations) called the logical order(s), and then interprets logical connectives as well as the entailment relation(s) via this ordering(s). In particular, the negation connective is determined then by the inversion of the logical order. But there is also another method grounded on the notion of a quasi-field of sets, considered by Białynicki-Birula and Rasiowa. The key point of this approach consists in defining an operation of quasi-complement via the very specific function g and then interpreting entailment just through the relation of set-inclusion between generalized truth values. In this paper, we will give a constructive proof of the claim that, for any finite set V with cardinality greater or equal 2, there exists a representation of a quasi-field of sets isomorphic to de Morgan lattice. In particular, it means that we offer a special procedure, which allows to make our negation de Morgan and our logic relevant. (shrink)

The aim of the present paper is to introduce a system, where the epistemic state of an agent is represented truth-functionally. In order to obtain this system, we propose a four-valued logic, that we call the logic of rational agent, where the fact of knowing something is formalized at the level of valuations, without the explicit use of epistemic knowledge operator. On the basis of this semantics, a sound and complete system with two distinct truth-functional negations is provided. These negations (...) allow us to express the statements about knowing or not knowing something at the syntactic level. Moreover, such a system is applied to the analysis of knowability paradox. In particular, we show that the paradox is not derivable in terms of the logic of rational agent. (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)

We consider a family of logical systems for representing entailment relations of various kinds. This family has its root in the logic of first-degree entailment formulated as a binary consequence system, i.e. a proof system dealing with the expressions of the form \, where both \ and \ are single formulas. We generalize this approach by constructing consequence systems that allow manipulating with sets of formulas, either to the right or left of the turnstile. In this way, it is possible (...) to capture proof-theoretically not only the entailment relation of the standard four-valued Belnap’s logic, but also its dual version, as well as some of their interesting extensions. The proof systems we propose are, in a sense, of a hybrid Hilbert–Gentzen nature. We examine some important properties of these systems and establish their completeness with respect to the corresponding entailment relations. (shrink)

In this paper we present a solution of the axiomatization problem for the Fmla-Fmla versions of the Pietz and Rivieccio exactly true logic and the non-falsity logic dual to it. To prove the completeness of the corresponding binary consequence systems we introduce a specific proof-theoretic formalism, which allows us to deal simultaneously with two consequence relations within one logical system. These relations are hierarchically organized, so that one of them is treated as the basic for the resulting logic, and the (...) other is introduced as an extension of this basic relation. The proposed bi-consequences systems allow for a standard Henkin-style canonical model used in the completeness proof. The deductive equivalence of these bi-consequence systems to the corresponding binary consequence systems is proved. We also outline a family of the bi-consequence systems generated on the basis of the first-degree entailment logic up to the classic consequence. (shrink)

In this paper we present a solution of the axiomatization problem for the Fmla-Fmla versions of the Pietz and Rivieccio exactly true logic and the non-falsity logic dual to it. To prove the completeness of the corresponding binary consequence systems we introduce a specific proof-theoretic formalism, which allows us to deal simultaneously with two consequence relations within one logical system. These relations are hierarchically organized, so that one of them is treated as the basic for the resulting logic, and the (...) other is introduced as an extension of this basic relation. The proposed bi-consequences systems allow for a standard Henkin-style canonical model used in the completeness proof. The deductive equivalence of these bi-consequence systems to the corresponding binary consequence systems is proved. We also outline a family of the bi-consequence systems generated on the basis of the first-degree entailment logic up to the classic consequence. (shrink)

We consider an example of four valued semantics partially inspired by quantum computations and negation-like operations occurred therein. In particular we consider a representation of so called square root of negation within this four valued semantics as an operation which acts like a cycling negation. We define two variants of logical matrices performing different orders over the set of truth values. Purely formal logical result of our study consists in axiomatizing the logics of defined matrices as the systems of binary (...) consequence relation and proving correctness and completeness theorems for these deductive systems. (shrink)

Comparative study between Tibetan Bon and Buryatian Bø religion of ancient Shamanic traditions.

Introduction. One of the drivers of the Russian regions’ development is traditionally considered to be local universities and the scientific activity development, in particular. However, such a belief is usually based on speculative conclusions and is not subjected to detailed empirical testing. The purpose of the study is to assess the relationship between the development of science in universities in Russian regions and indicators of regional development according to 2017—18 data. Methods. The authors use methods of generalization, grouping, assessment of (...) indicators of central tendency and variations, as well as methods of correlation analysis. The study is based on the data from regional statistics presented on the official website of Russian Statistics Agency, as well as data from monitoring the universities effectiveness, commissioned by the Ministry of Science and Higher Education of the Russian Federation. Scientific novelty of the research. For the first time, the authors present an empirical analysis of the relationship between indicators of socioeconomic development of Russian regions and indicators of scientific activity in universities in the region. The study is characterized by using a sample of homogeneous regions. The sample excluded regions that did not have significant scientific results, as well as regions that are leaders in economic development. As a result, a “core” of 57 Russian regions with similar characteristics of both economic development and the results of scientific activity was investigated. This increased the practical significance of the conclusions and their reliability. Results. As a result of the study, it was found out that there is a statistically significant relationship between all indicators of regional development and science in universities. However, a deeper analysis made it possible to establish that this relationship is indirect. In some cases, we can talk about the opposite influence - regional development on scientific results in universities. Conclusions. It was found that the indicators used in the public administration system for assessing the effectiveness and efficiency of scientific activity are not key in terms of their impact on regional development. It was revealed that publications in leading world databases and in the Russian Science Citation Index (RSCI) are equally related to regional development. It has been determined that in a number of cases, within the considered sample, it is possible to distinguish two groups of regions with a different nature of the relationship between regional development and science in universities. (shrink)

The purpose of the study is to reveal the main actions of the major central banks during the COVID - 19 pandemic and their main impact on the world stock markets. The scientific novelty consists in identifying the key results of the impact of the pandemic in general and the restrictive measures of national governments, in particular, on the dynamics of the state of the stock markets of the world, namely, the level of decline in the main stock indexes of (...) the S &P 500, Dow Jones and NASDAQ. The measures taken by the central banks of the United States, Japan, England and other developed and developing countries of the world to provide financial assistance to commercial banks and other financial organizations related to the purchase of government bonds at a "zero" rate, targeting the yield of government bonds, reducing key rates and other measures are summarized. It is indicated that the influx of new private investors provided a great help to the stock market, for which many Central Banks introduced special programs and preferences. As a result, the main measures taken by the Central Bank of the Russian Federation to stabilize the financial situation in the country and the domestic stock market, in particular, are summarized. (shrink)

This article deals with the question of the interrelation between two papers, both called, in short, “Onomatodoxy”, dedicated to the doctrine of Name-glorification (Imiaslavie, Onomatodoxy), both of which were created in line with the Neo-Patristic movement in the Russian philosophy of the Silver Age. One of these papers is by Alexei Losev and the other by Pavel Florensky. In my opinion, there are sufficient grounds to state that Losev’s “Onomatodoxy” was written either after Florensky created his own “Onomatodoxy”, i.e., after (...) November 1922, or, at the earliest, after Florensky started to give clandestine lectures about Onomatodoxy in Moscow (where Losev lived), i.e., not earlier than spring 1921. Therefore, Losev’s article “Onomatodoxy” could have been intended for the religious-philosophical collection of articles planned for publishing by Yaschenko in 1922 in Berlin. (shrink)

Представление о шарообразном Солнце было стандартным для греческой культуры уже во времена Аристотеля, однако происхождение этого представления настолько мало освещено в источниках, что современная наука даже не попыталась взяться за решение этого вопроса. Между тем правдоподобная реконструкция вполне возможна. Греческая религия, в сущности, не препятствовала возникновению естествознания, а его основатели, Фалес и Анаксимандр, совмещая научные и философские интересы, стремились к построению всеобъемлющей космологии, в рамках которой было необходимым не только описать движение Солнца, но и объяснить, что это за тело и (...) почему с ним связаны свет и тепло. Модель Анаксимандра, описывавшая Солнце как скопление огня, пребывающего внутри колесообразного контейнера из сгустившегося воздуха и обнаруживающего себя сквозь единственное отверстие, которое кажется незначительным, но в действительности размером с Землю, оказалась несовместимой с фактами, ставшими доступными в следующем поколении в связи с расширением географического кругозора греков. В частности, было надежно установлено, что полуденное Солнце, которое в Средиземноморье неизменно видно на юге, для наблюдателей, находящихся южнее тропика Рака, в разгар лета оказывается на севере. Необходимость пересмотреть концепцию Анаксимандра с учетом новых данных вызвала идейный поиск, который привел к убеждению в том, что Солнце должно иметь форму шара. Это представление утвердилось, судя по всему, не в силу какого-либо остроумного довода, выдвинутого влиятельным мыслителем, сколько на основании согласия круга профессионалов, рассмотревших вопрос с разных сторон. Солнечный шар, однако, было трудно представить огненным, поскольку огонь сам по себе не образует компактных, очерченных тел. С этим связаны распространенные в V в. до н. э. попытки приписать свету Солнца зеркальную природу. Признание же наличия в космосе трех огромных шаров – Солнца, Луны и Земли способствовало выдвижению идеи, согласно которой земной шар, как и прочие два, является движущимся небесным телом. (shrink)

Journal Name: Apeiron Issue: Ahead of print.

Early development of animal embryos begins from spatially distributed products of gene expression, i.e., gradients. While maternal and early zygotic genes form broad and/or terminal gradients, their direct targets appear later on as relatively narrow stripes, which foreshadow presumptive germ layers or future segments. Evidently, stripe expression of the zygotic genes is among the key mechanisms of embryo patterning. In this paper, known qualitative and quantitative models for the stripe formation are considered on the example of early embryogenesis of Drosophila. (...) The current model analysis emphasizes the role of spatial information flow in development. Discussion is given on frequent network motifs, pointing to spatial stripe formation solutions. (shrink)

In 2004 Atserias, Kolaitis, and Vardi proposed $\text {OBDD}$ -based propositional proof systems that prove unsatisfiability of a CNF formula by deduction of an identically false $\text {OBDD}$ from $\text {OBDD}$ s representing clauses of the initial formula. All $\text {OBDD}$ s in such proofs have the same order of variables. We initiate the study of $\text {OBDD}$ based proof systems that additionally contain a rule that allows changing the order in $\text {OBDD}$ s. At first we consider a proof (...) system $\text {OBDD}$ that uses the conjunction rule and the rule that allows changing the order. We exponentially separate this proof system from $\text {OBDD}$ proof system that uses only the conjunction rule. We prove exponential lower bounds on the size of $\text {OBDD}$ refutations of Tseitin formulas and the pigeonhole principle. The first lower bound was previously unknown even for $\text {OBDD}$ proofs and the second one extends the result of Tveretina et al. from $\text {OBDD}$ to $\text {OBDD}$.In 2001 Aguirre and Vardi proposed an approach to the propositional satisfiability problem based on $\text {OBDD}$ s and symbolic quantifier elimination $ algorithms). We augment these algorithms with the operation of reordering of variables and call the new scheme $\text {OBDD}$ algorithms. We notice that there exists an $\text {OBDD}$ algorithm that solves satisfiable and unsatisfiable Tseitin formulas in polynomial time, but we show that there are formulas representing systems of linear equations over $\mathbb {F}_2$ that are hard for $\text {OBDD}$ algorithms. Our hard instances are satisfiable formulas representing systems of linear equations over $\mathbb {F}_2$ that correspond to checksum matrices of error correcting codes. (shrink)

This article traces some modern conceptions of memory in history (Halbwachs, Nora), indirectly comparing them with the ancient poetic tradition of so-called “catalogue poetry.” In the discussion of memory and oblivion, I argue that history encompasses multiple histories rather than constituting one single teleological and universal history. Every history is produced by a historical narrative that follows and interprets what may be called the historical proper, which comprises lists of names of people, things, or events that have to be kept (...) and transmitted within a history. The historical and the narrative within a history are relatively independent, insofar as the narrative that interprets the historical may in principle change, whereas the historical has to be preserved, which is the primary task of historical memory. Historical being, then, is being remembered within a history. (shrink)

The fact that modern artists are turning toward science and the latest technologies—robotics, information technology, biomedicine—forces us to reformulate our concept of art. One need only imagine...

This book explores the major differences between the kinds of risk encountered in different sectors of industry - production and services - and identifies the main features of accidents within different industries. Because of these differences, unique risk-mitigation measures will need to be implemented in one industry that cannot be implemented in another, leading to large managerial differences between these broad economic sectors. Based on the analysis of more than 500 disasters, accidents and incidents - around 230 cases from the (...) production sector and around 280 cases from the service sector - the authors compare the risk response actions appropriate within different sectors, and establish when and how it is possible to generalize the experience of dealing with risks in any given industry to a wider field of economic activity. This book is mainly intended for executives, strategists, senior risk managers of enterprise-wide organizations and risk management experts engaged in academic or consulting work. By setting out clearly the sector differences in risk management, the authors aim to improve the practice of general risk assessment with regard to identifying and prioritizing risks, and of risk control with regard to planning appropriate mitigation measures. (shrink)

The conserved ribosomal protein uS3 in eukaryotes has long been known as one of the essential components of the small (40S) ribosomal subunit, which is involved in the structure of the 40S mRNA entry pore, ensuring the functioning of the 40S subunit during translation initiation. Besides, uS3, being outside the ribosome, is engaged in various cellular processes related to DNA repair, NF‐kB signaling pathway and regulation of apoptosis. This review is devoted to recent data opening new horizons in understanding the (...) roles of uS3 in such processes as the assembly and maturation of 40S subunits, ensuring proper structure of 48S pre‐initiation complexes, regulation of initiation and ribosome‐based RNA quality control pathways. Besides, we summarize novel results on the participation of the protein in processes beyond translation and consider biomedical implications of previously known and recently found extra‐ribosomal functions of uS3, primarily, in oncogenesis. (shrink)

The objective of this article is to characterise elimination of finite generalised imaginaries as defined in [9] in terms of group cohomology. As an application, I consider series of Zariski geometries constructed [10, 23, 24] by Hrushovski and Zilber and indicate how their nondefinability in algebraically closed fields is connected to eliminability of certain generalised imaginaries.

We study hybrid logics in topological semantics. We prove that hybrid logics of separation axioms are complete with respect to certain classes of finite topological models. This characterisation allows us to obtain several further results. We prove that aforementioned logics are decidable and PSPACE-complete, the logics of T 1 and T 2 coincide, the logic of T 1 is complete with respect to two concrete structures: the Cantor space and the rational numbers.

A peculiarity of early medieval geometrical texts was that alongside Euclid's Elements they transmitted remnants of the corpus of Roman land surveyors and metaphysical digressions extraneous to geometry proper. Rather than dismissing these additions as irrelevant, this essay attempts to elucidate the cultural grounds for the indiscriminate mixture of the three disciplines -- geometry, surveying, and metaphysics. Inquiry into the broader context of early medieval culture suggests that neither geometry nor surveying was treated as an independent discipline. Texts on geometry (...) and surveying were studied mainly because they were thought to provide good opportunities for enlarging the scope of meditation on spiritual subjects. Accordingly, the main concern of this essay is to show how Christian symbolism influenced both the composition and the study of geometrical texts. The essay is based on a wide range of sources: treatises on geometry and surveying, pictorial representations of Creation, and philosophical literature in which geometry was used in arguments about ontological doctrines. (shrink)

The transcription factor Nrf2 is the master regulator of cellular stress response, facilitating the expression of cytoprotective genes, including those responsible for drug detoxification, immunomodulation, and iron metabolism. FDA‐approved Nrf2 activators, Tecfidera and Skyclarys for patients with multiple sclerosis and Friedreich's ataxia, respectively, are non‐specific alkylating agents exerting side effects. Nrf2 is under feedback regulation through its target gene, transcriptional repressor Bach1. Specifically, in Parkinson's disease and other neurodegenerative diseases with Bach1 dysregulation, excessive Bach1 accumulation interferes with Nrf2 activation. Bach1 (...) is a heme sensor protein, which, upon heme binding, is targeted for proteasomal degradation, relieving the repression of Nrf2 target genes. Ideally, a combination of Nrf2 stabilization and Bach1 inhibition is necessary to achieve the full therapeutic benefits of Nrf2 activation. Here, we discuss recent advances and future perspectives in developing small molecule inhibitors of Bach1, highlighting the significance of the Bach1/Nrf2 signaling pathway as a promising neurotherapeutic strategy. (shrink)

The solution of the problem of the future random events truth is considered in Vasil’ev’s logic. N. A. Vasil’ev graded the logic according to two levels—the level of facts, i.e. time fixed events, and the level of notions or rules, governing these facts. The mathematical construction previously suggested for imaginary Vasil’ev’s logic, extends to the early variant of his logic—a logic of notions. In the paper, we investigate the meaning of problematic and uncertain assertions introduced by Vasil’ev. As a result, (...) we developed a model of Vasil’ev’s logic of facts that resolves also the truth problem of future random events. The imaginary logic has also been extended to the level of notions, and the law of the excluded eighth is gotten in it. The correspondence between Vasil’ev’s terms “some” and “all” and modern quantifiers is discussed. (shrink)