All extensions of the modal Grzegorczyk logic Grz possessing projective Beth's property PB2 are described. It is proved that there are exactly 13 logics over Grz with PB2. All of them are finitely axiomatizable and have the finite model property. It is shown that PB2 is strongly decidable over Grz, i.e. there is an algorithm which, for any finite system Rul of additional axiom schemes and rules of inference, decides if the calculus Grz+Rul has the projective Beth property.

Introduction. The article is focused on analyzing the utopian direction of Russian cosmism and its influence on the Soviet cosmonautics and the development of society in the USSR. This philosophical theory was created in the period that made it possible to incorporate the applied aspects of utopia into scientific and technological progress and thereby embody a number of steps towards the outer space exploration. The authors have developed criteria and parameters for assessing the utopian component of the Russian cosmism theories, (...) which made it possible to bring this construct to a higher level of abstraction and thereby create a working model for conducting such studies in the context of other utopias of models. The purpose of the article is to show the influence of the Russian cosmism utopia on the cosmonautics development in the USSR, develop empirical criteria for evaluating the phenomenon. Achieving the goal required solving the following tasks: 1) considering and analyzing the subject matter of the cosmism utopia; 2) developing parameters for assessing the impact of utopia on the development of the social system; 3) applying the developed parameters to assess the impact of utopian ideas on the development of the Soviet cosmonautics system. Methods. Developing the theoretical model for assessing social utopias, as well as considering and analyzing the cosmism utopia, required the use of structural-functional and systems analysis. The research was conducted within the framework of a synergistic paradigm. Scientific novelty of the research. The article conceptualizes the concept of utopia. It is shown that most of the definitions of utopia as a socio-political ideal focus on the limitations of its existence: utopia cannot be embodied, often has an unscientific character, does not correlate with the real state of the system, i.e. definitions of utopia are often reduced to the negative format. The authors believe that the influence of utopia on society, as a rule, is positive. It is noted that, along with limitations, utopianism has certain unique essential features that qualitatively affect the social projects implementation. Utopia in the systemic understanding acts as a complex of ideas influencing the development of the system, being both internal (since it is created artificially and consciously by the very elements of the system) and an external factor of influence. Unlike Plato’s eidos, the projection of which is reality, utopia is created inductively, but after its creation it again “descends” to the level of reality, since it begins to influence the social model in which it was created. Results. The article discusses the prognostic and modeling functions of the social utopias of Russian cosmists. It has been proved that one of the essential functions of the Russian cosmism utopias is the formation of an ideal type, towards which, in a historical perspective, the real social system begins to strive. It is convincingly demonstrated that utopia acts as a cognitive support and inevitably forms the canvas along which society begins to move, defining the utopian model as an attractor, although such a goal is not always formulated when creating a utopia. This relationship makes it possible to assess the degree of influence of utopian ideas on the formation of reality in each specific case, which, in turn, provides an opportunity to answer the question of how and to what extent the utopian ideal type participates in determining the characteristics and parameters of a real social system. Conclusions. It was found that the social utopia of cosmists as a cognitive concept is an important effective factor influencing the development of the space industry in the USSR. The parameters adopted in the study allow us to describe the measure of its influence as both an internal and an external factor on the development of the society in which it is implemented. The validity of perceiving the utopia of cosmists as a construct with a certain life cycle, the main part of which is the period of functioning, is stated. During this time period, utopian theory can have a significant impact on the actual development of society from various angles. (shrink)

We study modal logics in the setting of varieties of modal algebras. Any variety of modal algebras generated by a finite algebra — such, a variety is called tabular — has only finitely many subvarieties, i.e. is of finite height. The converse does not hold in general. It is shown that the converse does hold in the lattice of varieties of K4-algebras. Hence the lower part of this lattice consists of tabular varieties only. We proceed to show that there is (...) a continuum of pretabular varieties of K4-algebras — those are the non-tabular varieties all of whose proper subvarieties are tabular — in contrast with Maksimova's result that there are only five pretabular varieties of S4-algebras. (shrink)

ABSTRACT The two main directions pursued in the present paper are the following. The first direction was started by Pigozzi in 1969. In [Mak 91] and [Mak 79] Maksimova proved that a normal modal logic has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property. In this paper we extend Maksimova's theorem to normal multi-modal logics with arbitrarily many, not necessarily unary modalities, and to not necessarily normal multi-modal logics with modalities of ranks (...) smaller than 2. To extend the characterization beyond multi-modal logics, we look at arbitrary algebraizable logics. We will introduce an algebraic property equivalent with the Craig interpolation property in algebraizable logics, and prove that the superamalgamation property implies the Craig interpolation property. The problem of extending the characterization result to non-normal non-unary modal logics also will be discussed. In the second direction pursued herein: for non-normal modal logic with one unary modality Lemmon [Lem 66] gave a possible worlds semantics. Here we give a more general possible worlds semantics for not necessarily normal multi-modal logics with arbitrarily many not necessarily unary modalities. Strongly related to the above is the theorem, proved, e.g., in Jóns son-Tarski [JT 52] and Henkin-Monk-Tarski [HMT 71], that every normal Boolean algebra with operators can be represented as a subalgebra of the complex algebra of some relational structure. We extend this result to not necessarily normal BAO's as follows. We define partial relational structures and show that every not necessarily normal BAO is embeddable into the complex algebra of a partial relational structure. This gives a possible worlds semantics for not necessarily normal multi-modal logics. (shrink)

For intermediate logics, there is obtained in the paper an algebraic equivalent of the disjunction propertyDP. It is proved that the logic of finite binary trees is not maximal among intermediate logics withDP. Introduced is a logicND, which has the only maximal extension withDP, namely, the logicML of finite problems.

This is a survey of results on interpolation in propositional normal modal logics. Interpolation properties of these logics are closely connected with amalgamation properties of varieties of modal algebras. Therefore, the results on interpolation are also reformulated in terms of amalgamation.

A family of prepositional logics is considered to be intermediate between the intuitionistic and classical ones. The generalized interpolation property is defined and proved is the following.Theorem on interpolation. For every intermediate logic L the following statements are equivalent:(i) Craig's interpolation theorem holds in L, (ii) L possesses the generalized interpolation property, (iii) Robinson's consistency statement is true in L.

It is proved that there are exactly 16 superintuitionistic propositional logics with the projective Beth property. These logics are finitely axiomatizable and have the finite model property. Simultaneously, all varieties of Heyting algebras with strong epimorphisms surjectivity are found.

Algebraic approach to study of classical and non-classical logical calculi was developed and systematically presented by Helena Rasiowa in [48], [47]. It is very fruitful in investigation of non-classical logics because it makes possible to study large families of logics in an uniform way. In such research one can replace logics with suitable classes of algebras and apply powerful machinery of universal algebra. In this paper we present an overview of results on interpolation and definability in modal and positive logics,and (...) also in extensions of Johansson's minimal logic. All these logics are strongly complete under algebraic semantics. It allows to combine syntactic methods with studying varieties of algebras and to flnd algebraic equivalents for interpolation and related properties. Moreover, we give exhaustive solution to interpolation and some related problems for many families of propositional logics and calculi. (shrink)

In this paper we find an algebraic equivalent of the Hallden property in modal logics, namely, we prove that the Hallden-completeness in any normal modal logic is equivalent to the so-called super-embedding property of a suitable class of modal algebras. The joint embedding property of a class of algebras is equivalent to the Pseudo-Relevance Property. We consider connections of the above-mentioned properties with interpolation and amalgamation. Also an algebraic equivalent of of the principle of variable separation in superintuitionistic logics will (...) be found. (shrink)

Narratives of artificial intelligence frame public perceptions and expectations, and have a performative role, potentially leading to increased attention and resource allocation, acceptance of AI, or resistance to the technology. However, research on AI narratives frequently produces generalized and decontextualized accounts. This paper argues for closer examination of the specific processes that shape AI narratives in particular contexts. To explore this, nine AI-related exhibitions held in German museums from 2022 to 2023 were analyzed. The study draws on interviews with curatorial (...) teams and exhibition materials to investigate what narratives of AI museums are formed and how those relate to the dominant AI narratives described in previous research. It is shown that curators are critical of dominant AI narratives and aim to deconstruct common myths and present more nuanced portrayals of AI. Yet, they also face challenges in balancing this critical stance with the need for creating engaging, accessible exhibitions. The analysis reveals that while some curatorial strategies successfully counter AI stereotypes, others fail or inadvertently reproduce mainstream imaginaries. Curators discover that avoiding problematic understandings of AI in the way they had initially intended is challenging or even impossible. In other cases, when elements of mainstream AI discourse resurface in museum exhibits despite the critical stance of the curators, they remain unexamined, or are regarded as insignificant and inconsequential. (shrink)

We consider the problem of recognizing important properties of logical calculi and find complexity bounds for some decidable properties. For a given logical system L, a property P of logical calculi is called decidable over L if there is an algorithm which for any finite set Ax of new axiom schemes decides whether the calculus L + Ax has the property P or not. In [11] the complexity of tabularity, pre-tabularity, and interpolation problems over the intuitionistic logic Int and over (...) modal logic S4 was studied, also we found the complexity of amalgamation problems in varieties of Heyting algebras and closure algebras. In the present paper we deal with positive calculi. We prove NP-completeness of tabularity, DP-hardness of pretabularity and PSPACE-completeness of interpolation problem over Int + . In addition to above-mentioned properties, we consider Beth's definability properties. Also we improve some complexity bounds for properties of superintuitionistic calculi. (shrink)

Three variants of Beth's definability theorem are considered. Let L be any normal extension of the provability logic G. It is proved that the first variant B1 holds in L iff L possesses Craig's interpolation property. If L is consistent, then the statement B2 holds in L iff L = G + {0}. Finally, the variant B3 holds in any normal extension of G.

In a previous paper [ 21 ] all extensions of Johansson’s minimal logic J with the weak interpolation property WIP were described. It was proved that WIP is decidable over J. It turned out that the weak interpolation problem in extensions of J is reducible to the same problem over a logic Gl, which arises from J by adding tertium non datur. In this paper we consider extensions of the logic Gl. We prove that only finitely many logics over Gl (...) have the Craig interpolation property CIP, the restricted interpolation property IPR or the projective Beth property PBP. The full list of Gl-logics with the mentioned properties is found, and their description is given. We note that IPR and PBP are equivalent over Gl. It is proved that CIP, IPR and PBP are decidable over the logic Gl. (shrink)

The provability logic GL was in the field of interest of A.V. Kuznetsov, who had also formulated its intuitionistic analog—the intuitionisticprovability logic—and investigated these two logics and their extensions.In the present paper, different versions of interpolation and of the Bethproperty in normal extensions of the provability logic GL are considered. Itis proved that in a large class of extensions of GL almost all versions of interpolation and of the Beth propertyare equivalent. It follows that in finite slice logics over GL (...) the three versionsCIP, IPD and IPR of the interpolation property are equivalent. Also theyare equivalent to the Beth properties B1, PB1 and PB2. (shrink)

Lotman’s contribution to semiotic theory, anthroposemiotics, the study of artistic texts and defining the relationship between language and culture represent some of the most powerful work produced within the Tartu–Moscow School of Semiotics. The importance of translation is one of the central principles that unites all of Lotman’s work. In the following paper, we will consider Lotman’s definition of translatability in the context of (1) the definition of semiospheric internal and external boundaries and the importance of crossing these boundaries, (2) (...) the role of no fewer than two languages as a minimal unit of semiotic meaning-generation, (3) culture text-level generation of collective memory, and (4) the ever-present tension in the communication act. In our concluding section, we will offer an extended model of the communication act, based on the fundamental principles given in Jakobson, Sebeok and Lotman, in order to specify important moments of the translation process. (shrink)

This book is a specialized monograph on interpolation and definability, a notion central in pure logic and with significant meaning and applicability in all areas where logic is applied, especially computer science, artificial intelligence, logic programming, philosophy of science and natural language. Suitable for researchers and graduate students in mathematics, computer science and philosophy, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism, J. M. Dunn and G. Hardegree's Algebraic Methods in (...) Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning, P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2, and David J. Pym and Eike Ritter's Reductive Logic and Proof Search: Proof theory, semantics and control. (shrink)

This edited volume focuses on the work of Professor Larisa Maksimova, providing a comprehensive account of her outstanding contributions to different branches of non-classical logic. The book covers themes ranging from rigorous implication, relevance and algebraic logic, to interpolation, definability and recognizability in superintuitionistic and modal logics. It features both her scientific autobiography and original contributions from experts in the field of non-classical logics. Professor Larisa Maksimova's influential work involved combining methods of algebraic and relational semantics. Readers will (...) be able to trace both influences on her work, and the ways in which her work has influenced other logicians. In the historical part of this book, it is possible to trace important milestones in Maksimova’s career. Early on, she developed an algebraic semantics for relevance logics and relational semantics for the logic of entailment. Later, Maksimova discovered that among the continuum of superintuitionisitc logics there are exactly three pretabular logics. She went on to obtain results on the decidability of tabularity and local tabularity problems for superintuitionistic logics and for extensions of S4. Further investigations by Maksimova were aimed at the study of fundamental properties of logical systems in big classes of logics, and on decidability and recognizability of such properties. To this end she determined a powerful combination of algebraic and semantic methods, which essentially determine the modern state of investigations in the area, as can be seen in the later chapters of this book authored by leading experts in non-classical logics. These original contributions bring the reader up to date on the very latest work in this field. (shrink)

We provide a sucient frame-theoretic condition for a super bi-intuitionistic logic to have Maksimova's variable separation property. We conclude that bi-intuitionistic logic enjoys the property. Furthermore, we offer an algebraic characterization of the super-bi-intuitionistic logics with Maksimova's property.

Durkheim écrit ce livre avec un but double : d'abord il voulait expliquer ce qui crée une société, ce qui la tient ensemble ; ensuite il voulait éclaircir l'influence qu'a la société sur la pensée logique. Pour Durkheim, la religion est la clé utilisée pour déverrouiller ces deux problématiques.Dans ce livre, Durkheim argumente que les représentations religieuses sont en fait des représentations collectives : l'essence du religieux ne peut être que le sacré. Il est une caractéristique qui se trouve universellement (...) dans toutes les religions. Le sacré, être collectif et impersonnel, représente ainsi la société elle-même. Ensuite il argumente que la société a un impact majeur dans la genèse de la pensée logique. C'est la société qui fournit à l'individu les catégories (le temps, l'espace, le nombre etc.) et les concepts nécessaires pour la pensée logique. (shrink)

É bem conhecida a oposição estabelecida por Kant entre experiência possível e dialética, na medida em que esta última é caracterizada como a “lógica da ilusão”. Ao mesmo tempo, o modo de pensar metafísico, que ocorre dialeticamente, em sentido kantiano, é uma tendência inevitável da razão, expressa na exigência formal de completude das categorias. Como o pensar, enquanto exercício livre da razão, é em si mesmo mais amplo do que a atividade de conhecer, própria do entendimento, o pensar contém o (...) conhecimento, embora este se qualifique pelas regras e pelos limites determinantes da objetividade. A pergunta que tentaremos formular é se essa relação continente-conteúdo não poderia configurar também uma dependência da experiência em relação ao raciocínio dialético, que estaria de algum modo indicada na função reguladora das idéias da razão. Nesse caso, a oposição formal entre conhecer e pensar seria inseparável da inclusão estrutural (dependência) da experiência no âmbito da razão. Na raiz do problema estaria talvez a tensão (dialética) entre a aspiração subjetiva de totalidade e as exigências objetivas de limitação e segmentação da experiência e a forma da experiência teria de ser finalmente concebida a partir de um fundo de inteligibilidade problemática. Dialectics and experienceThe separation of possible experience as objective knowledge and dialetics as a non-objective or non-theoretical knowledge is one of the most important aspects of kantian critical philosophy. But Kant also says that the activity of reason, as a pure thinking, has more amplitude than understanding knowledge. So we could say that theoric knowledge would depend on rational ( and non-theoretical) knowledge, as something contained in it. If we accept that, the consequence would be a relation of dependence between the form of objective knowledge and the background of a problematic – even doubtful – inteligible knowledge. (shrink)

gl. 1. Ėkofilosofii︠a︡ kak zhiznesokhrani︠a︡i︠u︡shchiĭ kulʹturnyĭ proekt -- gl. 2. Obrazy kulʹtury mira v istoriko-personologicheskom izmerenii -- gl. 3. Borʹba za mir v sovremennom mire : opyt, kont︠s︡ept︠s︡ii, modeli resheniĭ.

Em artigo inédito, Franklin Leopoldo e Silva desenvolve os sentidos da memória na produção da identidade, destacando as relações significativas do presente com o passado e o futuro na construção da história. Desse ponto, o autor acentua o papel das instituições nesse processo – um processo de exercício de poder, no qual se tem, na verdade, a institucionalização do poder – e, dentre elas, em particular a instituição universitária.