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)

This paper attempts to provide a rationale for a 'model of the public sphere' in terms of hermeneutic ontology that begins from Heidegger's Being and Time. However, this Heideggerian hermeneutic ontology will both be weakened and extended through a dialogue with social theory, which occupies a central place in this paper. More specifically, the main aim of this paper is to suggest some ideas to bridge the gap between the ontological focus on the hermeneutic fore-structure of being-in-the-public-sphere and the focus (...) of social theory on the nexus between constructing identity and narrative, the result of which is the idea of the public sphere as an openended intercultural dialogue. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Dmitry Khanin THE POSTMODERN POSTURE Postmodernists—the sectarians ofour day—proclaim that the old kingdom of historical narrative and historical subject has perished, and is now being replaced by a new one of ahistorical discourses and ahistorical characters. According to these prophets, "history" is anyway just changes in ways of talking about history. Anyone who does not agree with the ahistoricity of the postmodern world oudook may be accused—and tried (...) on the spot—of defending the cause of the totalitarian Reason against the most liberating movement of today. This postmodernist abuse of history is paradoxical, since the very notion of history coming to its end and giving way to the ahistorical kingdom of freedom and merry debauchery is itself a very old idea, even a mythological one. The description ofhistory as marching toward its own demise relies on a whole tradition which portrays history as a drama. Aristode's conception of tragedy as a sequence of actions culminating in a dénouement has no doubt shaped this view of historical process. Christian and other religious millenarians have announced the end of history already many times. Yet another notorious instance of such eschatological daydreaming is the futurology of Karl Marx, who envisaged the kingdom of communism as occupying this same ahistorical space. A rather obsolete idea, perhaps, but it seems still to attract postmodernists, though they give it a characteristic twist, since they sincerely believe theory, discourse, écriture (i.e., theoretico-symbolical activity) are much more important than any actual historical contentprocesses and events. One of the most notable spokesmen for this approach is Arthur Danto, who insists that world history evolved in a good Hegelian manner until the theorists came to understand that history depends on their Philosophy and Literature, © 1990, 14: 239-247 240Philosophy and Literature texts much more than theorists themselves depend on historical processes and events.1 Many theoreticians working in an otherwise Marxist tradition similarly are glad to assert with FredricJameson that we must say farewell to Marx's positivistic illusion that history is driven by laws disguised as economic forces.2 In the epoch of "late capitalism," says Jameson, consumption gains the upper hand over production and becomes the mainspring of history. Of course, in light of recent doings in Europe I am tempted to ask if we owe it to postmodernists—and their ahistorical, inconsistent, and generally confounding claims about history lying in ruins—that the Berlin Wall actually is in ruins and Vaclav Havel is president of Czechoslovakia. Even more daring theorists may now declare an era of "very late capitalism." Here it will not be merely the mass media that act transformatively on society (as McLuhan claimed), but rather consumer goods themselves, like state-of-the-art washing machines or French perfumes, which create a new aura of intellectual discourse. TL· Postmodern Scene: Excremental Culture and Hyper-AesÜietics, a book by two Canadian authors, Arthur Kroker and David Cook, promotes such a sea change in the theoretical landscape and along the way presents a joyous recapitulation ofthe latest fads in postmodern thinking. The new apostolic generation ofpostmodern critics seems to enjoy the beautiful new things that can be bought for bucks, worrying at the same time that bucks may be losing some of their purchasing power. Like Hari-Krishnas dancing in the street they luckily possess a sort of happy consciousness which also recalls their puritanical great grandfathers who regarded profligacy as the greatest sin and much preferred saving to spending. In what follows I want to draw a portrait of this new postmodern posture. A few main assumptions underlie Kroker's and Cook's wake for postmodernism, which, in its peculiar genre of philosophic obituary, epitomizes and thus prepares for future oblivion views which were exceedingly popular in the preceding decade. First of all, the authors adopt Baudrillard's equation of Marx and Nietzsche: "Marx and Nietzsche shared a deep and common affinity in meditating upon historical (Christian) and materialistic (capitalist) expressions ofthewill ofpower."3 From Baudrillard's perspective Marx appears as a pathetic romantic who tried to defend the "referential illusion" by renaturalizing concrete labor even though its entirely abstract character was brilliandy revealed in Das Kapital. Baudrillard... (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 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)

Collected writings on Plato’s unwritten teachings.

While Western political scientists have a variety of opinions on democracy and how its institutions could be improved, they almost never argue about the validity of democracy as a form of government. Of course, it would be unfair here to ignore the presence of an authoritarian streak in Western thought. Thomas Hobbes comes to mind most immediately. Yet the views of those thinkers with an authoritarian bent have become marginalized in present-day discourse; or, to be more precise, it is assumed (...) that their views on the importance of a strong government are irrelevant to the present. The assumption that a strong regime might be necessary in non-Western societies is thought to be the product of these authoritarian/totalitarian societies' elite classes—that is, a justification for imposing the power of the elite upon the people. Most Western political scientists are convinced that democracy is the best of all possible forms of government. (shrink)

The recent surge of discoveries concerning the structural organization of nucleosomes, together with genetic evidence of highly specialized roles for the histones in gene regulation, have brought a renewed need for a detailed understanding of nucleosomal anatomy. Here we review recent structural advances leading to a new level of understanding of the nucleosome and chromatin fibre structure. We discuss the problems and challenges for existing models of chromatin structure and, in particular, consider how linker histones may bind within the nucleosome, (...) together with the implications of their association for the structure of the chromatin fibre. (shrink)

The article develops the idea of forming postcapitalist social relations as a social revolution of an individual, which consists in the fact that popularity becomes a key advantage, the “possession” of which is a desired goal and a significant resource of political influence. At the same time, it is shown that this process leads to forming a new dominant stratum — personalities (“people with personality”): celebrities, popular bloggers, social media influencers, micro- and nanosignature. It is substantiated that the personaliat domination (...) is a consequence of contradictory social relations between the new aristocracy represented by the representatives of the personaliat and many people who do not “possess” a popular personality - the impersonaliat (“extra people”, “lower” precariat, those who turn out to be outsiders in the world of social platforms). This contradiction is associated with the rooting of a celebrity’s culture, which encourages a lot of people to fight for popularity and focus on finding advantageous differences from others in the process of self-realization. However, this struggle in the end for the overwhelming majority turns into an increase in creative competition and subtraction. Various new forms of subtraction that appear in situations of widespread self-realization are revealed. Accordingly, arguments are given in favor of the fact that in the context of the “personality revolution”, the truly left will be rather an alternative that will call into question the ways of solving social problems formulated by popular personalities. In other words, it will be possible to oppose the total pursuit of popularity with the projects of society, in which the person is relied not as someone who rises above the others, but as an involved person who values life in harmony with others higher than his own “I”. (shrink)

Independent social life of the "Thaw” period is less examined then dissidents' resistance of the 1970s or mass public actions of Perestroika years. Analysis of the 1950-1960s protest actions allows us to trace changes in independent political projects in post-Stalin USSR. Unsolved social and economic problems, state unwillingness to listen for voices from below, repressions against dissenters stimulated the rejection of the idea to reform Soviet socialism among the part of critical intelligentsia. The disillusion in socialist ideas was not only (...) the reaction on state policy. It was also based on the redefining of the legacy of October revolution 1917 and reforms of the State socialism in Eastern Europe in the mid1950s, which were interpreted as the realization of revolutionary state governance. Dissenters of 19501960s formulated their demands to contemporary political regime using accessible classical Marxist-Leninist works and fictional biographies of revolutionaries. Usage of the legacy of the October in their texts varied from copying the revolutionary rhetoric to the testifying of Soviet political regime's compliance to the initial revolutionary theory. Many of them saw the main problem of Soviet state in the forgetting of the principle of proletarian dictatorship. The idea about party nomenclature as the main beneficiary of the October revolution was quite similar to the theory of «New Class» by M. Djilas. The book of Yugoslavian philosopher offered Marxist analysis of transformation of Yugoslavian political regime. He insisted on the inevitability of bureaucratic degradation of the revolutionary government. Acknowledgment of that inevitability did not only undermine political legitimacy of the contemporary Soviet regime but also took away the chance to justify it by appellation to its historical roots. That process stimulated the search for un-socialist alternatives for the Soviet regime such as the ideology of human rights or struggle for national sovereignty. (shrink)

This article is devoted to a critical analysis of neuropsychoanalysis, an interdisciplinary field that emerged at the end of the 20th century and set itself the task of combining neuroscience with the psychoanalytic approach. The author draws attention to the conceptual gaps of this ambitious undertaking. The main gap is argued to be the insufficient attention paid to the psychophysical problem (or mind-body problem), which ends up overlooking the fundamental difference between brain and psychic / mental reality, and attempts to (...) derive the principles of functioning of the latter from the observations of brain activity. This, in turn, leads to further problems: the problem of translation and search for a correspondence between psychoanalytic theory based on a thick observation of the subject's mental activity and the conceptual tools of neurosciences. What percentage of loss of meaning in this translation can be recognized as acceptable and what remains of psychoanalysis as a result of such a procedure? Another problem is related to the intersubjective symbolic nature of human desire, which cannot be deduced from observations of brain physiology. Finally, the author draws attention to the fact that neurosciences - and neuropsychoanalysis is no exception here - are already initially interwoven into social and cultural space, making them easy victims of contemporary- sometimes implicit - ideological attitudes. The article concludes with a call for greater reflexivity regarding neuropsychoanalysis on the part of both interested parties - psychoanalysts and neuroscientists. (shrink)

This book considers the emergence of dialectic out of the spirit of dialogue and traces the relation between the two. It moves from Plato, for whom dialectic is necessary to destroy incorrect theses and attain thinkable being, to Cusanus, to modern philosophers—Descartes, Kant, Hegel, Schleiermacher and Gadamer, for whom dialectic becomes the driving force behind the constitution of a rational philosophical system. Conceived as a logical enterprise, dialectic strives to liberate itself from dialogue, which it views as merely accidental and (...) even disruptive of thought, in order to become a systematic or scientific method. The Cartesian autonomous and universal yet utterly monological and lonely subject requires dialectic alone to reason correctly, yet dialogue, despite its unfinalizable and interruptive nature, is what constitutes the human condition. (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)

I detect a specific attitude to Byzantium (“the Byzantine Enlightenment”) in Ivan Kireevsky’ Slavophile article “On the Character of Enlightenment in Europe” (1852). I qualify this attitude as Byzantinocentrism. I take that as a focal point and, against this background, consider the image of Byzantium in Kireevsky and some thinkers of his social circle. It allows me to trace the most important lines of attitudes to Byzantium in the Russian historiosophical literature and opinion journalism of the nineteenth century. I detect (...) two opposite lines in perceiving Byzantium in Kireevsky’s early social circle: the anti- and pro-Byzantine ones. The first line goes back to an anti-Byzantine message, characteristic of the epoch of Enlightenment. It found its manifestation in G. W. F. Hegel’s Lectures on the Philosophy of History. I point to the traces of the implicit polemics with Hegel’s anti-byzantinism in Kireevsky and identify the context of these polemics in Arist Kunick. As well, I outline how these lines worked in Pyotr Chaadaev and Alexander Pushkin. Then I distinguish between how the image of Byzantium was presented, first, in Kireevsky’s earlier Slavophile article “On the Character of Enlightenment in Europe” and, second, in his last article “On the Necessity and Possibility of the new Foundations for Philosophy” (1856). In the latter article, which sees Byzantium as bipolar, I find another view on Byzantium. I suggest that this view on Byzantium as a bipolar entity goes back to Alexey Khomyakov’s Semiramis. My point is that this difference in the views on Byzantium is paradigmatic and it reflects a division that was present in the Russian Slavophile-conservative milieu of that time. I suggest that this division stands behind another division within the same milieu, which was politically oriented, the one in relation to the Greek-Bulgarian ecclesiastical question. I analyze how both monopolar (Byzantinocentric) and bipolar views on Byzantium were reflected in the Greek-Bulgarian question as it was considered by Alexey Khomyakov and Terty Filippov. I find a context for developing Kireevsky’s attitude towards Byzantium in François Guizot’s historiosophic scheme as well. (shrink)

The sources of religious tolerance but also of religious nationalism in post-soviet Russia can be found basically in the group identification of nationality and religion. In crisis situations, the historical religion of the Russian society - Orthodoxy - becomes the criterion for identifying the national identity. However, despite the fact that the majority of Russians in our times consider themselves Orthodox, many of them are not believers. The observable effect of the “external belief” results in the fact that the religion (...) tends to become a matter of personal choice and an individual value. It assumes a nationalistic function and to become an ideology. As a result, the political elite considers religion as a means of achieving different non- religious purposes. The Russian Orthodox Church, the official church, is compelled to take this fact into consider- ation and even support it. This is why religious intolerance and religious nationalism in modern Russia are often directed towards religion. (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)

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)

The authors try to show that even Wittgensteinian definition of concept is not always sufficient to analyze what really happens in science. As a result, in addition to “concept” we propose “conception” as a new promising tool for philosophy of science. We provide a brief historical analysis of this term and reveal two main interpretations of “conception” in philosophy and scientific disciplines. In accordance with the first view, conception appears as either a “twin” of the concept, or a pair entity (...) to the concept. According to the second view, conception is a kind of “strange concept” that exists among “normal” concepts. Since conception is understood differently in sciences and philosophical systems, it is not possible to give a generalized definition of conception. That is, it is impossible to formulate this definition, so to speak, inductively. Moreover, even if it was possible, such a definition would not necessarily have to be automatically accepted by philosophy of science. That is why the introduction of a concept of conception was carried out through the analysis of a global process associated with the return of metaphysics to science. We define conception as a semantic construction denoting the unknown (and, possibly, fundamentally unknowable) and ensuring the possibility of working with this unknown (unknowable). By virtue of the way conception was introduced (conception is not a “generalization” of the interpretations available in specific sciences) many conceptions that are considered as conception in specific sciences turn out to not to be conceptions within this definition. Thus, the article interprets conception as a new possible tool of philosophy of science, which is aimed at understanding how specific sciences develop. (shrink)

The ‘New Apuleius’ is a set of Latin summaries of Plato's works first published in 2016 by Justin Stover, who attributed it to Apuleius. The present article attempts to assess two key aspects of Stover's argument, viz. his reconstruction of the manuscript transmission of the new text and his use of computer-assisted stylometric techniques. The authors suggest that both strands of his argument are inconclusive. First, it is argued that the transposition of gatherings in the archetype of the Apuleian philosophica (...) as envisaged by Stover is highly unrealistic. Second, replications of Stover's stylometric experiments show that their results are highly dependent on the particular algorithm settings and on the composition of the corpus. It is further shown that Stover's choice of highly specialized stylometric techniques is suboptimal, because popular generalist methods for statistical data analysis are demonstrably more successful in correctly identifying authors of Latin text fragments and do not support the case for Apuleius’ authorship of the new text. The authors conclude that there are no solid grounds to conclude that the ‘New Apuleius’ was indeed written by Apuleius. (shrink)

The article is devoted to understanding a healthy lifestyle in old age, significant limitations and differences that arise with age and redefine many basic ideas about health. The article begins by identifying basic ideas about healthy aging, which are questioned and clarified through an analytical analysis of dense interviews (the author’s terminology for qualitative interviews, the closest analogue of which in the Russian-speaking environment is in-depth interviews) with old people. Field work took place in the Republic of Khakassia in three (...) cities: Abakan, Chernogorsk and Abaza. A total of 12 interviews were conducted with older people receiving long-term care services. Based on the received narratives, five conditions accompanying aging were identified: living in illness; accepting limitations; loneliness; support and withdrawal from others; emotional depression. Through a critical understanding of the life world of aging, four signs of a healthy lifestyle in old age are identified: attention to the old man, the need for the old man, the value of aging and the presence of a goal in life for the old man. Modern social policy in Russia is based on only one component of “attention to the elderly” (although other components are also declared by law), through the organization of long-term care, the development and implementation of rehabilitation means, and the creation of an accessible environment. But the most important elements remain the formation of the need for the old man among significant loved ones (relatives and others), joint agreement, the formation of goal-setting in the old man in life and the promotion of the value of aging as such. The article proposes an agenda for further research to more accurately shape domestic policies in the field of aging. (shrink)

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.

The article examines the representations of the "diaspora” in texts published on "migrant” digital communication platforms. With the help of discourse analysis The messages posted in open access in thematic groups in VKontakte, Odnoklassniki, and Telegram channels were studied. The purpose of the study was to find out what meanings and functions the users of these sites give the word "diasporas”. The "Diaspora” was considered as a nodal point, uniting the narratives of people visiting "migrant” sites into a single framework. (...) It was assumed that the "diaspora” does not have a clear, fixed content and various actors are trying to turn it from an "element” into a "moment”, securing a certain meaning for it. More than a thousand messages found on "migrant” sites were analyzed. The study showed that the "diaspora” within the considered digital platforms is most often mentioned in the reposts of press releases of state and public organizations, where it is presented as an object of social action, an intermediary between migrants and the state. In these texts, the "diaspora” is represented in the same semantic row with various state authorities and their representatives. At the same time, the "diaspora” is defined as a participant in events organized by the state bureaucracy of the host country or the donor country, the purpose of which is the manifestation of ethnicity. In user comments, these values are disputed: people either doubt its existence or its ability to effectively solve their problems. (shrink)

The article critically addresses Boris Groys’ interpretation of photographs by Alexandre Kojève. In 2012, Groys organized the exhibition After History: Alexandre Kojève as a Photographer, which intended to demonstrate the “posthistorical” dimension in Kojève’s artistic output. The article questions the adequacy of that perspective, given the somewhat tendentious curatorial presentation of the photos as showing an empty, dehumanized world. Considering the aesthetic and ontological aspects of the analysis of visual images that were central to Kojève’s brief account of his 1920 (...) visit to the Borghese Gallery in Rome and to his 1936 article on Kandinsky, Groys’ reading of Kojève’s photographic stance is subject to revision. The notion of aura, as proposed by Walter Benjamin, is operative in a comparative treatment of the photos by Kojève and Eugène Atget. (shrink)

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 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)

We apply the theory of partial algebras, following the approach developed by Van Alten, to the study of the computational complexity of universal theories of monotonic and normal modal algebras. We show how the theory of partial algebras can be deployed to obtain co-NP and EXPTIME upper bounds for the universal theories of, respectively, monotonic and normal modal algebras. We also obtain the corresponding lower bounds, which means that the universal theory of monotonic modal algebras is co-NP-complete and the universal (...) theory of normal modal algebras is EXPTIME-complete. It also follows that the quasi-equational theory of monotonic modal algebras is co-NP-complete. While the EXPTIME upper bound for the universal theory of normal modal algebras can be obtained in a more straightforward way, as discussed in the paper, due to its close connection to the equational theory of normal modal algebras with the universal modality operator, the technique based on the theory of partial algebras is applicable to the study of universal theories of algebras corresponding to a wide range of logics with intensional operators, where no such connection is available. (shrink)