We formulate a Hilbert-style axiomatic system and a tableau calculus for the STIT-based logic of imagination recently proposed in Wansing. Completeness of the axiom system is shown by the method of canonical models; completeness of the tableau system is also shown by using standard methods.

In this paper we consider logical inference as an activity that results in proofs and hence produces knowledge. We suggest to merge the semantical analysis of deliberatively seeing-to-it-that from stit theory and the semantics of the epistemic logic with justification from. The general idea is to understand proving that A as seeing to it that a proof of A is available. We introduce a semantics of various notions of proving as an activity and present a number of valid principles that (...) relate the various notions of proving to each other and to notions of justified knowledge, implicit knowledge, and possibility. We also point out and comment upon certain principles our semantics fails to validate. (shrink)

Notions of k-asimulation and asimulation are introduced as asymmetric counterparts to k-bisimulation and bisimulation, respectively. It is proved that a first-order formula is equivalent to a standard translation of an intuitionistic propositional formula iff it is invariant with respect to k-asimulations for some k, and then that a first-order formula is equivalent to a standard translation of an intuitionistic propositional formula iff it is invariant with respect to asimulations. Finally, it is proved that a first-order formula is equivalent to a (...) standard translation of an intuitionistic propositional formula over the class of intuitionistic Kripke models iff it is invariant with respect to asimulations between intuitionistic models. (shrink)

We show how to correct the analytic tableaux system from the paper Olkhovikov and Wansing, 259–279, 2018).

In this article we show that bi-intuitionistic predicate logic lacks the Craig Interpolation Property. We proceed by adapting the counterexample given by Mints, Olkhovikov and Urquhart for intuitionistic predicate logic with constant domains [13]. More precisely, we show that there is a valid implication $\phi \rightarrow \psi $ with no interpolant. Importantly, this result does not contradict the unfortunately named ‘Craig interpolation’ theorem established by Rauszer in [24] since that article is about the property more correctly named ‘deductive interpolation’ (...) (see Galatos, Jipsen, Kowalski and Ono’s use of this term in [5]) for global consequence. Given that the deduction theorem fails for bi-intuitionistic logic with global consequence, the two formulations of the property are not equivalent. (shrink)

Justification stit logic is a logic for reasoning about proving as a certain kind of activity, namely seeing to it that a proof is publicly available. It merges the semantical analysis of deliberatively seeing-to-it-that from stit theory and the semantics of the epistemic logic with justification from. In this paper, after recalling its language and basic semantical definitions, various ramifications and refinements of justification stit logic are presented and discussed: imposing natural restrictions upon the class of models under consideration, making (...) use of modalities that assert the existence of a proof, introducing a variant of justification stit logic based on a semantics introduced by M. Fitting, and adding variable-binding operators and extending the set of proof polynomials. (shrink)

In Part I of this paper we presented a Hilbert-style system $\Sigma _D$ axiomatizing stit logic of justification announcements interpreted over models with discrete time structure. In this part, we prove three frame definability results for $\Sigma _D$ using three different definitions of a frame plus another version of completeness result.

We consider the propositional logic equipped with Chellas stit operators for a finite set of individual agents plus the historical necessity modality. We settle the question of whether such a logic enjoys restricted interpolation property, which requires the existence of an interpolant only in cases where the consequence contains no Chellas stit operators occurring in the premise. We show that if action operators count as logical symbols, then such a logic has restricted interpolation property iff the number of agents does (...) not exceed three. On the other hand, if action operators are considered to be nonlogical symbols, then the restricted interpolation fails for any number of agents exceeding one. It follows that unrestricted Craig interpolation also fails for almost all versions of stit logic. (shrink)

The paper promotes a cultural sociological analysis of one of the most significant and hard-to-explain events in American history when the initial act of breaking and entering into the Democratic Party headquarters at the Watergate Hotel first didn't attract any substantial attention of contemporaries but later initiated a widespread political crisis. J. Alexander considers the dynamics, mechanisms and consequences of the event and its public resonance, building an explanatory model based on his cultural sociological theory. This model allows to reconstruct (...) in detail the development and maintenance of the social consensus at the different levels of cultural structures and to explain its connection to the main elements of social and political context, public rituals and performances. (shrink)

We consider a modal language over crisp frames and formulas evaluated on a finite MTL-chain (a linearly ordered commutative integral residuated lattice). We first show that the basic modal abstract logic with constants for the values of the MTL-chain is the maximal abstract logic satisfying Compactness, the Tarski Union Property and strong invariance for bisimulations. Finally, we improve this result by replacing the Tarski Union Property by a relativization property.

In addition to double‐ and single‐strand DNA breaks and isolated base modifications, ionizing radiation induces clustered DNA damage, which contains two or more lesions closely spaced within about two helical turns on opposite DNA strands. Post‐irradiation repair of single‐base lesions is routinely performed by base excision repair and a DNA strand break is involved as an intermediate. Simultaneous processing of lesions on opposite DNA strands may generate double‐strand DNA breaks and enhance nonhomologous end joining, which frequently results in the formation (...) of deletions. Recent studies support the possibility that the mechanism of base excision repair contributes to genome stability by diminishing the formation of double‐strand DNA breaks during processing of clustered lesions. BioEssays 23:745–749, 2001. © 2001 John Wiley & Sons, Inc. (shrink)

The purpose of the article is to substantiate the main theoretical and methodological provisions of museology as a humanitarian science. Its basic concepts are formulated from idealistic positions, its methodology is defined. As an object, the ideas of a person who creates a museum reality to achieve influence on the consciousness of other people are considered. The idea of a particular museum, realized in objective reality, is defined as the subject. The subject of museology is also the process of realization (...) of ideas – the functioning of museum reality and the process of its perception by visitors. The purpose of the museum is to make certain changes in the consciousness and attitude of another person – a visitor. The methodology of museology as a humanitarian science is based on the method of understanding, which provides comprehension of the ideas underlying the museum. Methods play a special role: communicative and construction. The goals of the museum determine its functions, the most important is the communicative one, it is she who realizes the main goal of the museum – to convey ideas and feelings from the museum employee to the visitor. The ways to achieve the goal may change with changing attitudes in society, while the museums themselves and their functions change. The main factor determining the role and social significance of museums is a person's interest in them, which manifests itself when the ideas embedded in their foundation correspond to the main ideological ideas prevailing in society and help people solve their vital problems. A museum should be relevant only when it plays an important role in the life of society. The next stage in the development of museology as a humanitarian science is its approbation in the course of solving scientific and practical tasks facing a museum employee. (shrink)

Our thinking is still the captive of the dichotomy “national/ international.” The reaction to nationalism takes the form of an abstract internationalism, and reaction to internationalism leads to the rebirth of nationalism. However, this dichotomy was only true (and that relatively) in 19th century Europe, or at the latest, at the beginning of the twentieth century, when subnational cultures seemed on the way to disappearing, and everything European was considered “universal” (two hypotheses that the facts prove to be untrue). As (...) H. Frey observes, “Today, the decline or decadence of the West is part of the contemporary view of the world, like the electron or the dinosaur.” The linear outline of progress, with Europe at the head, did not withstand the test of the First World War. The year 1918 marked the beginning of the end of Europeanism. Since then, we have begun to speak of “areas of civilization” (Splengler), “civilizations” (Toynbee), “cultural coalitions” (Lévi-Strauss). The existence of “areas of civilization” (regions) is commonly admitted today; it has entered journalistic language and even the structure of regional commissions and agencies of the United Nations (Europe, Near East, Southern Asia, South-east Asia, and the Far East). New communities have inserted themselves between nations and humanity. What do they represent? Are they something unique, or are they divided into a certain number of types in opposition to each other because of some characteristic? And in what way have they modified our view of universal history? (shrink)

This article will formulate an explanatory model in which all the specifics of the controversy between Rome and Constantinople in the schism of 1054 will be considered in theological and ecclesiastical-political terms. Thus, both the complexity of the historical context and the diversity of the motives of its protagonists will be taken into account. In a first step, the current state of research on the events of 1054 will be presented, before confronting it with open questions in a second step. (...) They are derived partly from the historical context, partly from the ambivalent information conveyed by Latin and Greek sources. The latter entails several source-critical problems, but thereby offers a chance to pose new questions to „old“ sources. Based on these open questions, the sources will be re-read and re-interpreted in terms of determining the course of events in 1054 and the motives of the protagonists of the 1054 schism. (shrink)

Summing up the ideas expressed in the most influential articles on the semantic halo of the Russian trochaic pentameter, scholars tend to avoid one particularly tricky question: how many units – and what kind of units – are needed to detect extra layers of meaning in a particular text? While the article of Kiril Taranovsky “О взаимоотношении стихотворного ритма и тематики” had implied that the source of these meanings (e.g. the dynamic theme of the journey) should be sought in a (...) line starting from the 3- to 4-syllable structure, incorporating a verb of motion and an anapestic anacrusis (Выхожу [verb of motion, last syllable stressed] один я на дорогу), later research objected to this principle as an oversimplification. At the same time two later contributions on the subject (Kirill Vishnevsky’s “Экспрессивный ореол пятистопного хорея” and Mikhail Gasparov’s “The semantic halo of the Russian trochaic pentameter: Thirty years of the problem”) proposed the idea of operating with whole texts as potential sources of meanings, thus calling into question a micro-level approach to the origin of the phenomenon. In my article I propose an empirical model that makes it possible to evaluate some limitations of both practices: I concentrate on some quasi-trochaic pentameters culled from the prose text of Подвиг (Glory) by Vladimir Nabokov (Sirin), and examine these quasi-verse incidents in the framework of both approaches. (shrink)

Summing up the ideas expressed in the most influential articles on the semantic halo of the Russian trochaic pentameter, scholars tend to avoid one particularly tricky question: how many units – and what kind of units – are needed to detect extra layers of meaning in a particular text? While the article of Kiril Taranovsky “О взаимоотношении стихотворного ритма и тематики” had implied that the source of these meanings (e.g. the dynamic theme of the journey) should be sought in a (...) line starting from the 3- to 4-syllable structure, incorporating a verb of motion and an anapestic anacrusis (Выхожу [verb of motion, last syllable stressed] один я на дорогу), later research objected to this principle as an oversimplification. At the same time two later contributions on the subject (Kirill Vishnevsky’s “Экспрессивный ореол пятистопного хорея” and Mikhail Gasparov’s “The semantic halo of the Russian trochaic pentameter: Thirty years of the problem”) proposed the idea of operating with whole texts as potential sources of meanings, thus calling into question a micro-level approach to the origin of the phenomenon. In my article I propose an empirical model that makes it possible to evaluate some limitations of both practices: I concentrate on some quasi-trochaic pentameters culled from the prose text of Подвиг (Glory) by Vladimir Nabokov (Sirin), and examine these quasi-verse incidents in the framework of both approaches. (shrink)

Summing up the ideas expressed in the most influential articles on the semantic halo of the Russian trochaic pentameter, scholars tend to avoid one particularly tricky question: how many units – and what kind of units – are needed to detect extra layers of meaning in a particular text? While the article of Kiril Taranovsky “О взаимоотношении стихотворного ритма и тематики” had implied that the source of these meanings (e.g. the dynamic theme of the journey) should be sought in a (...) line starting from the 3- to 4-syllable structure, incorporating a verb of motion and an anapestic anacrusis (Выхожу [verb of motion, last syllable stressed] один я на дорогу), later research objected to this principle as an oversimplification. At the same time two later contributions on the subject (Kirill Vishnevsky’s “Экспрессивный ореол пятистопного хорея” and Mikhail Gasparov’s “The semantic halo of the Russian trochaic pentameter: Thirty years of the problem”) proposed the idea of operating with whole texts as potential sources of meanings, thus calling into question a micro-level approach to the origin of the phenomenon. In my article I propose an empirical model that makes it possible to evaluate some limitations of both practices: I concentrate on some quasi-trochaic pentameters culled from the prose text of Подвиг (Glory) by Vladimir Nabokov (Sirin), and examine these quasi-verse incidents in the framework of both approaches. (shrink)

This paper considers the computational complexity of the disjunction and existential properties of intuitionistic logic. We prove that the disjunction property holds feasibly for intuitionistic propositional logic; i.e., from a proof of A v B, a proof either of A or of B can be found in polynomial time. For intuitionistic predicate logic, we prove superexponential lower bounds for the disjunction property, namely, there is a superexponential lower bound on the time required, given a proof of A v B, to (...) produce one of A and B which is true. In addition, there is superexponential lower bound on the size of terms which fulfill the existential property of intuitionistic predicate logic. There are superexponential upper bounds for these problems, so the lower bounds are essentially optimal. (shrink)

Freud's legacy deriving from his work The project for a scientific psychology (1895) could give a new impetus to the dialogue between psychoanalysis and neurosciences. A rapproachment phase is warrented. Based on the work of psychoanalysts who are themselves neuroscientists (such as Mauro Mancia, Martha Koukkou and Harold Shevrin) or have a long term dialogue with neuroscientists (Arnold Modell), three points of epistemological congruence are described: dualism is no longer a satisfactory solutioncautions for the centrality of interpretation (hermeneutics)the self-criticism of (...) neuroscientists. (shrink)

We formulate epsilon substitution method for elementary analysisEA (second order arithmetic with comprehension for arithmetical formulas with predicate parameters). Two proofs of its termination are presented. One uses embedding into ramified system of level one and cutelimination for this system. The second proof uses non-effective continuity argument.

Cut reductions are defined for a Kripke-style formulation of modal logic in terms of indexed systems of sequents. A detailed proof of the normalization (cutelimination) theorem is given. The proof is uniform for the propositional modal systems with all combinations of reflexivity, symmetry and transitivity for the accessibility relation. Some new transformations of derivations (compared to standard sequent formulations) are needed, and some additional properties are to be checked. The display formulations [1] of the systems considered can be presented as (...) encodings of Kripke-style formulations. (shrink)

The expression “the invisible hand of the market” (from the Adam Smith’s “Wealth of Nations”) sometimes acquires in modern ecomomical and everyday journalism the most unexpected overtones, like “why “the invisible hand of the market» totally disregard writer”? In the area of the scientific economic thinking “the «invisible hand” is interpreted as the objective market mechanism which coordinates the decisions of buyers and sellers. The attempts to analyze the epistemological status of “the invisible hand” are quite rare, especially in the (...) modality of the formation of the Economics as a science. Meanwhile, as it is shown in the article, there is reason to see here the first fundamental step to the origination of the scientific research program of the economic science in the strict sense. The author assumes that phenomena like “the invisible hand of the market” is comparable to what Thomas Kuhn designates as “the metaphysical parts of paradigms”, i. e. basic ontological models, which define peculiar scientific vision of the reality under research. The main difficulty for the scientific rationality in the attempts of generating scientific knowledge about society, was to represent the corresponding processes of human activity in the form of objective reality, which is required by the basic ideological attitude of the science as such. (shrink)

The article shows that prior to the debate with the Monothelites, Maximus the Confessor followed the Christian tradition going back to Gregory of Nyssa in recognizing the presence of προαίρεσις in Christ and the saints. Later during the debate, Maximus declined to apply προαίρεσις to Christ and started to speak about the deactivation of προαίρεσις in the saints in the state of deification. Maximus was the first Orthodox author who distinguished deliberate choice and natural will, and defended the presence of (...) natural will in Christ according to His humanity. At the same time, the opposition of desire and deliberate choice can be found in some Neoplatonists, such as Iamblichus, Proclus, and Philoponus. Iamblichus and Proclus rejected the presence of προαίρεσις in the gods and god-like humans, admitting only the presence of βούλησις - the desire for the Good. Thus, the evolution of the doctrine of Maximus the Confessor, regarding the application of προαίρε- σις to Christ and the saints, finds a parallel doctrine in Neoplatonism. (shrink)

A Short Introduction to Modal Logic presents both semantic and syntactic features of the subject and illustrates them by detailed analyses of the three best-known modal systems S5, S4 and T. The book concentrates on the logical aspects of ...

Dynamic topological logic provides a context for studying the confluence of the topological semantics for S4, topological dynamics, and temporal logic. The topological semantics for S4 is based on topological spaces rather than Kripke frames. In this semantics, □ is interpreted as topological interior. Thus S4 can be understood as the logic of topological spaces, and □ can be understood as a topological modality. Topological dynamics studies the asymptotic properties of continuous maps on topological spaces. Let a dynamic topological system (...) be a topological space X together with a continuous function f. f can be thought of in temporal terms, moving the points of the topological space from one moment to the next. Dynamic topological logics are the logics of dynamic topological systems, just as S4 is the logic of topological spaces. Dynamic topological logics are defined for a trimodal language with an S4-ish topological modality □ , and two temporal modalities, ○ and * , both interpreted using the continuous function f. In particular, ○ expresses f’s action on X from one moment to the next, and * expresses the asymptotic behaviour of f. (shrink)

A simple cut elimination proof for arithmetic with the epsilon symbol is used to establish the termination of a modified epsilon substitution process. This opens a possibility of extension to much stronger systems.

The completeness of the modal logic S4 for all topological spaces as well as for the real line , the n-dimensional Euclidean space and the segment etc. was proved by McKinsey and Tarski in 1944. Several simplified proofs contain gaps. A new proof presented here combines the ideas published later by G. Mints and M. Aiello, J. van Benthem, G. Bezhanishvili with a further simplification. The proof strategy is to embed a finite rooted Kripke structure for S4 into a subspace (...) of the Cantor space which in turn encodes . This provides an open and continuous map from onto the topological space corresponding to . The completeness follows as S4 is complete with respect to the class of all finite rooted Kripke structures. (shrink)