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.

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.

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.

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)

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.

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 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)

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)

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.

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)

For centuries, humans have contemplated the minds of gods. Research on religious cognition is spread across sub-disciplines, making it difficult to gain a complete understanding of how people reason about gods' minds. We integrate approaches from cognitive, developmental, and social psychology and neuroscience to illuminate the origins of religious cognition. First, we show that although adults explicitly discriminate supernatural minds from human minds, their implicit responses reveal far less discrimination. Next, we demonstrate that children's religious cognition often matches adults' implicit (...) responses, revealing anthropomorphic notions of God's mind. Together, data from children and adults suggest the intuitive nature of perceiving God's mind as human-like. We then propose three complementary explanations for why anthropomorphism persists in adulthood, suggesting that anthropomorphism may be an instance of the anchoring and adjustment heuristic; a reflection of early testimony; and/or an evolutionary byproduct. (shrink)

This paper considers the responsibilities of the FDA with regard to disseminating information about the benefits and harms of e-cigarettes. Tobacco harm reduction advocates claim that the FDA has been overcautious and has violated ethical obligations by failing to clearly communicate to the public that e-cigarettes are far less harmful than cigarettes. We argue, by contrast, that the FDA’s obligations in this arena are more complex than they may appear at first blush. Though the FDA is accountable for informing the (...) public about the health risks and benefits of products it regulates, it also has other roles that inform when and how it should disseminate information. In addition to being a knowledge purveyor, it is also a knowledge producer, an advisor to the public, and a practical agent shaping the material conditions in which people make health-related choices. In our view, those other roles call for caution in the way the FDA interprets and communicates the available evidence. (shrink)

People perceive that if their memories and moral beliefs changed, they would change. We investigated why individuals respond this way. In Study 1, participants judged that identity would change more after changes to memories and widely shared moral beliefs versus preferences and controversial moral beliefs. The extent to which participants judged that changes would affect their relationships predicted identity change and mediated the relationship between type of moral belief and perceived identity change. We discuss the role that social relationships play (...) in judgments of identity and highlight implications for psychology and philosophy. (shrink)

Adults report that moral characteristics—particularly widely shared moral beliefs—are central to identity. This perception appears driven by the view that changes to widely shared moral beliefs would alter friendships and that this change in social relationships would, in turn, alter an individual's personal identity. Because reasoning about identity changes substantially during adolescence, the current work tested pre- and post-adolescents to reveal the role that such changes could play in moral cognition. Experiment 1 showed that 8- to 10-year-olds, like adults, judged (...) that people would change more after changes to their widely shared moral beliefs (e.g., whether hitting is wrong) than after changes to controversial moral beliefs (e.g., whether telling prosocial lies is wrong). Following up on this basic effect, a second experiment examined whether participants regard all changes to widely shared moral beliefs as equally impactful. Adults, but not children, reported that individuals would change more if their good moral beliefs (e.g., it is not okay to hit) transformed into bad moral beliefs (e.g., it is okay to hit) than if the opposite change occurred. This difference in adults was mediated by perceptions of how much changes to each type of belief would alter friendships. We discuss implications for moral judgment and social cognitive development. (shrink)

People perceive that if their memories and moral beliefs changed, they would change. We investigated why individuals respond this way. In Study 1, participants judged that identity would change more after changes to memories and widely shared moral beliefs (e.g., about murder) versus preferences and controversial moral beliefs (e.g., about abortion). The extent to which participants judged that changes would affect their relationships predicted identity change (Study 2) and mediated the relationship between type of moral belief and perceived identity change (...) (Study 3). We discuss the role that social relationships play in judgments of identity and highlight implications for psychology and philosophy. (shrink)

We appreciate that all our commentators accepted the central framework we argued for, namely that the FDA has multiple roles and attendant responsibilities, and we are excited to see this framework...

The Ontology for Biomedical Investigations (OBI) is an ontology that provides terms with precisely defined meanings to describe all aspects of how investigations in the biological and medical domains are conducted. OBI re-uses ontologies that provide a representation of biomedical knowledge from the Open Biological and Biomedical Ontologies (OBO) project and adds the ability to describe how this knowledge was derived. We here describe the state of OBI and several applications that are using it, such as adding semantic expressivity to (...) existing databases, building data entry forms, and enabling interoperability between knowledge resources. OBI covers all phases of the investigation process, such as planning, execution and reporting. It represents information and material entities that participate in these processes, as well as roles and functions. Prior to OBI, it was not possible to use a single internally consistent resource that could be applied to multiple types of experiments for these applications. OBI has made this possible by creating terms for entities involved in biological and medical investigations and by importing parts of other biomedical ontologies such as GO, Chemical Entities of Biological Interest (ChEBI) and Phenotype Attribute and Trait Ontology (PATO) without altering their meaning. OBI is being used in a wide range of projects covering genomics, multi-omics, immunology, and catalogs of services. OBI has also spawned other ontologies (Information Artifact Ontology) and methods for importing parts of ontologies (Minimum information to reference an external ontology term (MIREOT)). The OBI project is an open cross-disciplinary collaborative effort, encompassing multiple research communities from around the globe. To date, OBI has created 2366 classes and 40 relations along with textual and formal definitions. The OBI Consortium maintains a web resource providing details on the people, policies, and issues being addressed in association with OBI. (shrink)

In this paper we shall prove that certain subvarieties of the variety of Salgebras (Heyting algebras with successor) has amalgamation. This result together with an appropriate version of Theorem 1 of [L. L. Maksimova, Craig’s theorem in superintuitionistic logics and amalgamable varieties of pseudo-boolean algebras, Algebra i Logika, 16(6):643-681, 1977] allows us to show interpolation in the calculus IPC S (n), associated with these varieties.We use that every algebra in any of the varieties of S-algebras studied in this work has (...) a canonical extension, to show completeness of the calculus IPC S (n) with respect to appropriate Kripke models. (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)

On the 3rd of April, 2023, the Doctor of Philosophy, Larisa Viktorovna Anzhiganova celebrated her anniversary. She is the first and currently the only woman in the region with a degree of the Doctor of Philosophy. Her research interests are related to the study of ethnocultural problems of Khakassia, in particular, the philosophy of ethnos, ethnic culture, interethnic relations, gender studies. Her scientific activity was conducted within the walls of the N. F. Katanov Khakass State University (since 1980), Khakass (...) Research Institute for Language, Literature, and History (1994–1998). It is of particular interest due to the relevance of the topic of the doctoral dissertation “The evolution of the worldview of an ethnic group (by the example of the Khakass people)” (1999, Moscow) and other works that cover the value problems of the ethnic group, including women’s family values. The researcher pays significant attention to the issues of the Khakass’ ethnocultural foundations. An important stage in the development of scientific and organizational activities of L.V. Anzhiganova was the holding of the Interregional Сonference “Ethnic Capital: Resources and Institutional Forms”, which promises to become regular. The philosopher’s ideas played an important role in the formation of the ethnic culture of the Khakass people. (shrink)

Dans deux études à paraître, José Luis Garcia Ramón et moi avons proposé de nouvelles interprétations de quelques épiclèses de la déesse thessalienne Ennodia : Ennodia est Κορουταρρα, « celle qui fait grandir », et plus précisément « celle qui dote de nourriture / de croissance », Στροπικά, déesse « aux éclairs », porteuse de lumière, et encore Μυκαικα, « déesse des tombeaux ». Cette interprétation nouvelle de l’épiclèse Μυκαικα apporte un témoignage supplémentaire sur le caractère de déesse protectrice des (...) tombeaux qu’il faut reconnaître à Ennodia. Ce caractère d’Ennodia peut être confirmé encore par la réinterprétation d’une autre inscription thessalienne, la dédicace IG IX 2, 592, de Larisa. L’on peut en effet reconnaître dans ce texte fragmentaire une consécration à Ennodia d’un enclos funéraire et l’on peut y restituer de plus une autre épiclèse de la déesse, épiclèse qu’a fait connaître une dédicace d’Azôros récemment publiée par P. Chrysostomou, pour Ἐννοδία Ἰλιάδι.In two studies currently awaiting publication, José Luis Garcia Ramón and I have proposed new interpretations of some epithets of the Thessalian goddess Ennodia: Ennodia is Κορουταρρα, ‘the one who makes grow’ and, more precisely, ‘the one who provides food’, Στροπικά ‘the goddess who carries lightning’, and Μυκαικα, ‘goddess of the tombs’. This new interpretation of this last epiclesis gives us new evidence on the character of Ennodia as protectress of the tombs. This character of Ennodia can now be confirmed by the reinterpretation of another votive inscription, IG IX 2, 592, from Larisa. It is possible to recognize in this fragmentary inscription the consecration of a funerary enclosure to Ennodia; here we can make the restitution of another epiclesis of Ennodia, an epiclesis which is now seen in a votive inscription coming from Azoros in northern Thessaly and recently published, with the formula Ἐννοδία Ἰλιάδι. (shrink)

When someone says she believes that God exists, is she expressing the same kind of mental state as when she says she thinks that a lake bigger than Lake Michigan exists⎯i.e., does she refer to the same kind of cognitive attitude in both cases? Using evidence from linguistic corpora (Study 1) and behavioral experiments (Studies 2-4), the current work provides evidence that individuals typically use the word “believe” more in conjunction with statements about religious credences and “think” more in conjunction (...) with factual statements, pointing to two different understandings of claims made with these two terms. These patterns do not appear to reflect low-level differences based on the amount of consensus surrounding a particular claim, the extent to which the truth of a particular claim is known to the participant, or linguistic differences between religious and factual statements. We discuss implications of these findings for religious cognition (e.g., as supporting the theory that religious credences are qualitatively distinct from factual beliefs) as well as cognitive processes more broadly. Finally, we relate the present findings to prior theoretical work on differences between factual belief and religious credence. (shrink)

The purpose of the study is to develop and describe the author's model of teaching foreign language listening using authentic video content. As a result, the author presents a six-stage model, which includes content-goal-setting, two activity-technological, two control-evaluative and revising-target stages, concretized through the system of communicative tasks. The novelty of the study lies in the identification of the linguo-methodological potential of authentic video content for teaching foreign language listening and modeling this process on the basis of the corresponding principles (...) – main and specific. (shrink)