Infinitary action logic can be naturally expanded by adding exponential and subexponential modalities from linear logic. In this article we shall develop infinitary action logic with a subexponential that allows multiplexing (instead of contraction). Both non-commutative and commutative versions of this logic will be considered, presented as infinitary sequent calculi. We shall prove cut admissibility for these calculi, and estimate the complexity of the corresponding derivability problems: in both cases it will turn out to be between complete first-order arithmetic and (...) the \(\omega ^\omega \) level of the hyperarithmetical hierarchy. Here the complexity upper bound is much lower than that for the system with a subexponential that allows contraction. The complexity lower bound in turn is much higher than that for infinitary action logic. (shrink)

We consider the Lambek calculus, or noncommutative multiplicative intuitionistic linear logic, extended with iteration, or Kleene star, axiomatised by means of an$\omega $-rule, and prove that the derivability problem in this calculus is$\Pi _1^0$-hard. This solves a problem left open by Buszkowski (2007), who obtained the same complexity bound for infinitary action logic, which additionally includes additive conjunction and disjunction. As a by-product, we prove that any context-free language without the empty word can be generated by a Lambek grammar with (...) unique type assignment, without Lambek’s nonemptiness restriction imposed (cf. Safiullin, 2007). (shrink)

In the original publication, the affiliation of the author Max Kanovich was processed incorrectly. It has been updated in this correction.

We give a proof-theoretic and algorithmic complexity analysis for systems introduced by Morrill to serve as the core of the CatLog categorial grammar parser. We consider two recent versions of Morrill’s calculi, and focus on their fragments including multiplicative connectives, additive conjunction and disjunction, brackets and bracket modalities, and the! subexponential modality. For both systems, we resolve issues connected with the cut rule and provide necessary modifications, after which we prove admissibility of cut. We also prove algorithmic undecidability for both (...) calculi, and show that categorial grammars based on them can generate arbitrary recursively enumerable languages. (shrink)

We consider language models for the Lambek calculus that allow empty antecedents and enrich them with constants for the empty language and for the language containing only the empty word. No complete calculi are known with respect to these semantics, and in this paper we consider several trivalent systems that arise as fragments of these models? logics.

L.L. Maksimova and L. Esakia, V. Meskhi showed that the modal logic \ has exactly 5 pretabular extensions PM1–PM5. In this paper, we study the problem of unification for all given logics. We showed that PM2 and PM3 have finitary, and PM1, PM4, PM5 have unitary types of unification. Complete sets of unifiers in logics are described.

We give a systematic method of constructing extensions of the Kuznetsov-Gerčiu logic KG without the finite model property (fmp for short), and show that there are continuum many such. We also introduce a new technique of gluing of cyclic intuitionistic descriptive frames and give a new simple proof of Gerčiu’s result [9, 8] that all extensions of the Rieger-Nishimura logic RN have the fmp. Moreover, we show that each extension of RN has the poly-size model property, thus improving on (...) [9]. Furthermore, for each function f: omega -> omega, we construct an extension Lf of KG such that Lf has the fmp, but does not have the f-size model property. We also give a new simple proof of another result of Gerčiu [9] characterizing the only extension of KG that bounds the fmp for extensions of KG. We conclude the paper by proving that RN.KC = RN + (¬p vee ¬¬p) is the only pre-locally tabular extension of KG, introduce the internal depth of an extension L of RN, and show that L is locally tabular if and only if the internal depth of L is finite. (shrink)

ABSTRACT:Should companies’ human rights responsibilities arise, in part, from their “leverage”—their ability to influence others’ actions through their relationships? Special Representative John Ruggie rejected this proposition in the United Nations Framework for business and human rights. I argue that leverage is a source of responsibility where there is a morally significant connection between the company and a rights-holder or rights-violator, the company is able to make a contribution to ameliorating the situation, it can do so at modest cost, and the (...) threat to human rights is substantial. In such circumstances companies have a responsibility to exercise leverage even though they did nothing to contribute to the situation. Such responsibility is qualified, not categorical; graduated, not binary; context-specific; practicable; consistent with the social role of business; and not merely a negative responsibility to avoid harm but a positive responsibility to do good. (shrink)

The debates about ethics in the context of artificial intelligence have been recently focusing primarily on various types of utilitarianisms. This article suggests a categorization of the various presented utilitarianisms into static utilitarianisms and dynamic utilitarianisms. It explains the main features of both. Then, it presents the challenges the utilitarianisms in each group need to be able to deal with. Since it appears that those cannot be overcome in the context of each group alone, the article suggests a possibility of (...) using a combination of the two categories of utilitarianisms to resolve most of the challenges without the need to abandon the concept of utilitarianisms as such. Even this possibility comes with its own issues that might not be resolved within the boundaries of utilitarianisms, however. Therefore, another potential alternative based on a combination of various ethical systems is suggested and briefly explored. (shrink)

A monograph about natural law and supernatural law, with emphasis on the philosophy of natural law.

The question of why Ukraine became Christianized from Byzantium and what kind of faith she accepted - in general, Christian, Orthodox, or Catholic - is not new. We have the views that stand for any of these three assumptions. They are formed depending on the data of religious beliefs, political orientations, etc.

Diagnostics of a mental disorder completely bases on an estimation of patient’s behaviour, verbal behaviour being the most important. The behaviour, in turn, is ruled by a situation expressed as a system of signs. Perception of a situation could be seen as a function, which depends on the context resulting from the previous situations, structuring personal world. So the world is not given — it is being formed while the person is in action. We argue that distinctive features of behaviour, (...) including its abnormal variants, can be explained not in categories of characters and diseases but in terms of situations taking place in individual worlds. The situation in which a person perceives himself is not simply a site in a three-dimensional space at a certain moment, but a part of the world and an episode of his life. Like a text composed of words, individual world is composed of situations. Each of them needs certain context to cope with ambiguity. This context is induced by the world as a whole. And the world, in turn, is presented as a chain of situations. If the context cannot help to interpret a situation adequately, uncertainty can be eliminated by actions clarifying a situation, which is changed in a predictable way. Thus, purposeful activity, skills to make predictions and corrections of one’s own actions are crucial. Weakness of any of them inevitably leads to the distortion of the presentation of the world, to wrongevaluation of situations and, as a result, to inadequate actions that finally reduce the activity as being ineffective. Thus, the lack of activity becomes the key factor in the development of disorder, being simultaneously its cause and effect. In periods of insufficient activity conditions for violated (and violating) sign processing arise. Possible variants of sign malfunction are: oligosemia (reduction of the number of perceivable signs), hyposemia (decrease of significance of signs), hypersemia (increase of significance of some signs at the expense of others), ambisemia (uncertainty of sign, when situation remains unclear), cryptosemia (recognition of signs not obvious for other observers), and parasemia (perverted interpretation of signs influenced by a false context). (shrink)

У статті висвітлені процеси й події, які привели до створення "Біографічного словника діячів України". Охарактеризовано історичні умови, у яких відновила діяльність Академія наук України. Подано детальний аналіз матеріалу, який входив до видання. Висвітлено авторський колектив видання, а також описано умови, при яких змінювалися керівники та автори "біографічного видання". Розкрито об'єктивні й суб'єктивні умови припинення роботи над виданням. Виявлені основні наслідки цього "словника" для енциклопедичної науки загалом.

This paper proposes a semantic description of the linear step-like temporal multi-agent logic with the universal modality \(\mathcal{LTK}.sl_U\) based on the idea of non-reflexive non-transitive nature of time. We proved a finite model property and projective unification for this logic.

Diagnostics of a mental disorder completely bases on an estimation of patient’s behaviour, verbal behaviour being the most important. The behaviour, in turn, is ruled by a situation expressed as a system of signs. Perception of a situation could be seen as a function, which depends on the context resulting from the previous situations, structuring personal world. So the world is not given — it is being formed while the person is in action. We argue that distinctive features of behaviour, (...) including its abnormal variants, can be explained not in categories of characters and diseases but in terms of situations taking place in individual worlds. The situation in which a person perceives himself is not simply a site in a three-dimensional space at a certain moment, but a part of the world and an episode of his life. Like a text composed of words, individual world is composed of situations. Each of them needs certain context to cope with ambiguity. This context is induced by the world as a whole. And the world, in turn, is presented as a chain of situations. If the context cannot help to interpret a situation adequately, uncertainty can be eliminated by actions clarifying a situation, which is changed in a predictable way. Thus, purposeful activity, skills to make predictions and corrections of one’s own actions are crucial. Weakness of any of them inevitably leads to the distortion of the presentation of the world, to wrongevaluation of situations and, as a result, to inadequate actions that finally reduce the activity as being ineffective. Thus, the lack of activity becomes the key factor in the development of disorder, being simultaneously its cause and effect. In periods of insufficient activity conditions for violated (and violating) sign processing arise. Possible variants of sign malfunction are: oligosemia (reduction of the number of perceivable signs), hyposemia (decrease of significance of signs), hypersemia (increase of significance of some signs at the expense of others), ambisemia (uncertainty of sign, when situation remains unclear), cryptosemia (recognition of signs not obvious for other observers), and parasemia (perverted interpretation of signs influenced by a false context). (shrink)

From the earliest photographic attempts to represent tropical hybrid races to depictions of disease in new tropical medicines, Picturing Tropical Nature offers ...

Scientific knowledge systems function as effective and specialized apparatus for formulating, analyzing and solving scientific problems. In science, problems become internal parts of the knowledge systems; thus they acquire new forms and properties in comparison with common-sense problems. Definite theoretical structures connected with problems and questions appear in the theory. Among them are erotetic expressions and languages, calculi and algebras of problems. On the basis of the structure-nominative reconstruction of a theory, the unified treatment of these structures is given. Methods (...) of the theory of named sets are used in the logical analysis of problems and their systems. As a consequence a new formalized model of the problem part of theory is constructed. (shrink)

Non-classical science gives a very specific answer to the question of scientific errors and their epistemological value. But for all the specificity of this answer, it casts light on a problem that remains with us century after century, the historically constant problem of truth and error—one of the most fundamental problems of knowledge. At first sight, these two poles have always stood opposite each other, like good and evil, beauty and ugliness. But moral and aesthetic theories have long since left (...) behind this initial conception, and shown that the two polar concepts are in fact inseparable. As regards truth and error, their indivisibility has only become apparent in the context of non-classical science. Truth has ceased to be the absolute contradiction of error. Contemporary science finds it to be something relative, inseparable from its opposite pole. But the non-classical, retrospective approach, a re-evaluation of the past of science in the light of its present, and indeed even more in the light of its prognosis, its future, allows one to see that scientific truths that are adequate for the object of knowledge always reflect only one side of the objective world, a world which has an infinite number of sides. The irreversible process that leads from relative error to relative truth has an absolute character: an irreversible process of generalization, concretization and complication of a Weltanschauung that more accurately reflects the infinite complexity of life. (shrink)

In our times, when the pace of economic, scientific and technological, social and cultural change calls to mind the relativist velocities of contemporary physics, Einstein's criterion begins to be applicable to the historical process itself; movement can be recorded (and consequently the notion of velocity acquire meaning) provided an adequate reference system is available. Where science is concerned, such systems have always existed: historians have brought out the increase in adequate knowledge in the past by comparing it with present knowledge, (...) which then offered a system of absolute reference. But now, the theory of relativity, quantum mechanics, molecular biology and the radical transformation of standards of value in all cultural areas have made like absolutization of contemporary ideas impossible. Today ideas furnish no more than a point of departure for non-classical retrospection which, as Jaurès said, seeks the fire, not. the ashes, in the history of science. But: the fire of science, its dynamics, its movement, is inseparable from its value, its effect, its psychological ‘accompaniment.’ Contemporary science, with unprecedented dynamism, is distinguishable from classical science by its far more emotional coloring. It lays bare not only the logical collisions of knowledge but also the emotional collisions. Einstein called the history of science the ‘drama of ideas.’ A drama which sometimes turns into a tragedy. The tragic sense Lorentz was aware of in the crumbling of old conceptions is easily perceptible in the remark he made when he confessed he would have prefered to be dead before the structure of classical physics collapsed. For Erenfest the tormenting experience of a personal inability to understand the positive bases of non-classical physics was also tragic and, according to Einstein, was what drove him to suicide. Einstein's own dissatisfaction tor thirty years while he strove in the field theory alone to find a stable universal conception possessing more complete ‘internal perfection’ than the then existing solution, was again tragic. The real characteristic of the collisions of non-classical science, however, is their ambivalence: the tragic notes blend with the optimistic perception of irreversible general progress in knowledge. The collisions of knowledge and this optimistic perception together sound a very complex chord, major on the whole, but with minor harmonics. (shrink)

Inferencialismus idealizuje proces získání významu v komunikaci. K tomu snadno najdeme protipříklady. Zcela zde chybí nějaká, zejména pojmová analýza a také nějaké rozhodovací (meta)pravidlo pro získání významu.

The main assumption of analytical philosophy is very straightforward: the analysis of language in philosophy and in science is the only starting point which guarantees the solution to all the problems. In the so-called post-analytical philosophy this assumption becomes even more radical: substantial problems do not exist and even if they existed, their essence would vanish if one attempted to formulate them in language. The author tries to justify the view that these simple and attractive theses are not only demagogic (...) and decadent, but also destructive. (shrink)

In this volume, contributors suggest we also think beyond toleration to mutual respect, practiced before the creation of modern multiculturalism in the West.

The article examines discussion wich took place in 1911 between Polish philosophers Henryk Struve and Kazimierz Twardowski about the state of Polish philosophy and plans for its future development. The results of the discussion were extrapolated to the current situation of Ukrainian philosophy and its challenges. The conclusion is that the path of Polish philosophy of the last century can serve to modern Ukrainian philosophy as reliable guide to the future. Polish philosophy’s recipe of success transferred to modern Ukrainian philosophy (...) consists in, firstly, elimination of external domination of Russian influence due to its balancing by other foreign influences, and, secondly, purposeful development of analytical direction. (shrink)

Book review on Jan Bierhanzl, Estetika ambiguity. Praha (Karolinum) 2021, 123 str.

Physical cosmology is one of the disciplines at the forefront of modern science. Using existing physical theories and creating own ones, it describes the dynamics and evolution of the Universe, transforms and modernizes the scientific picture of the world on the largest possible scale. The article analyzes the main presuppositions and outcomes of nowadays cosmology, which are based on fundamental physical principles (theories) and astronomical observations. It has been revealed that throughout its existence as a science (about 100 years), cosmology (...) stimulated the emergence of a plenty of worldview-philosophical problems. Therefore, we need a comprehensive update of the philosophy of cosmology, which can help to realize such problems. Given the need for cooperation between cosmology and the philosophy of science, we propose to use various methodological, ontological, epistemological and other philosophical techniques to solve philosophical problems arising in cosmological research, as well as to generalize the existing knowledge about the Universe. (shrink)

Wir stellen ein präzises Modell der wissenschaftlichen Begriffs-theorie vor, in dem die Beschreibungs-, die Wirklichkeits- und die mengentheoretische Ebene verknüpft werden. Einerseits wird ein allgemeiner Rahmen für die Gesamtheit der Begriffe, andererseits die „lokale” Struktur eines Begriffs beschrieben. Wir spezialisieren diesen Rahmen auf wissenschaftliche Begriffe, wissenschaftliche Theorien, und auf die zugehörigen strukturalistischen, wissenschaftstheoretischen Konstruktionen. We introduce a precise model for the theory of concepts in philosophy of science. In this model we connect the level of description, the level of reality (...) and the level of set theoretic systems. On the one hand we describe a general frame for the collection of concepts, and on the other hand the „local” structure of a concept. We specialize this frame to scientific concepts, scientific theories, and to the appertaining structuralist constructions from philosophy of science. (shrink)