This paper concerns modal logics of provability — Gödel-Löb systemGL and Solovay logicS — the smallest and the greatest representation of arithmetical theories in propositional logic respectively. We prove that the decision problem for admissibility of rules (with or without parameters) inGL andS is decidable. Then we get a positive solution to Friedman''s problem forGL andS. We also show that A. V. Kuznetsov''s problem of the existence of finite basis for admissible rules forGL andS has a negative solution. (...) Afterwards we give an algorithm deciding the solvability of logical equations inGL andS and constructing some solutions. (shrink)

ABSTRACT We1 study unification of formulas in modal logics and consider logics which are equivalent w.r.t. unification of formulas. A criteria is given for equivalence w.r.t. unification via existence or persistent formulas. A complete syntactic description of all formulas which are non-unifiable in wide classes of modal logics is given. Passive inference rules are considered, it is shown that in any modal logic over D4 there is a finite basis for passive rules.

Questions connected with the admissibility of rules of inference and the solvability of the substitution problem for modal and intuitionistic logic are considered in an algebraic framework. The main result is the decidability of the universal theory of the free modal algebra imageω extended in signature by adding constants for free generators. As corollaries we obtain: there exists an algorithm for the recognition of admissibility of rules with parameters in the modal system Grz, the substitution problem for Grz (...) and for the intuitionistic calculus H is decidable, intuitionistic propositional calculus H is decidable with respect to admissibility . A semantical criterion for the admissibility of rules of inference in Grz is given. (shrink)

The article is devoted to the applicability of Wittgenstein’s following the rule in the context of his philosophy of mathematics to real mathematical practice. It is noted that in «Philosophical Investigations» and «Remarks on the Foundations of Mathematics» Wittgenstein resorted to the analysis of rather elementary mathematical concepts, accompanied also by the inherent ambiguity and ambiguity of his presentation. In particular, against this background, his radical conventionalism, the substitution of logical necessity with the «form of life» of the community, as (...) well as the inadequacy of the representation of arithmetic rules by a language game are criticized. It is shown that the reconstruction of the Wittgenstein concept of understanding based on the Fregian division of meaning and referent goes beyond the conceptual framework of Wittgenstein language games. (shrink)

We give a necessary and sufficient condition for any modal logic with fmp to inherit all inference rules admissible in S4. Using this condition we describe all tabular modal logics inheriting inference rules admissible for S4.

While specifications and verifications of concurrent systems employ Linear Temporal Logic , it is increasingly likely that logical consequence in image will be used in the description of computations and parallel reasoning. Our paper considers logical consequence in the standard image with temporal operations image and image . The prime result is an algorithm recognizing consecutions admissible in image, so we prove that image is decidable w.r.t. admissible inference rules. As a consequence we obtain algorithms verifying the validity of (...) consecutions in image and solving the satisfiability problem. We start by a simple reduction of logical consecutions of image to equivalent ones in the reduced normal form . Then we apply a semantic technique based on image-Kripke structures with formula definable subsets. This yields necessary and sufficient conditions for a consecution to be not admissible in image. These conditions lead to an algorithm which recognizes consecutions admissible in image by verifying the validity of consecutions in special finite Kripke structures of size square polynomial in reduced normal forms of the consecutions. As a consequence, this also solves the satisfiability problem for image. (shrink)

We study quasi-characterizing inference rules (this notion was introduced into consideration by A. Citkin (1977). The main result of our paper is a complete description of all self-admissible quasi-characterizing inference rules. It is shown that a quasi-characterizing rule is self-admissible iff the frame of the algebra generating this rule is not rigid. We also prove that self-admissible rules are always admissible in canonical, in a sense, logics S4 or IPC regarding the type of algebra generating rules.

Purpose: To develop a realistic view that integrates the idea that knowledge is a constructive process. Problem: In the controversy between realism and constructivism, both sides have often misunderstood each other. Many realists still consider constructivism as a kind of idealism. And constructivists often assume that realists believe they have direct access to things as they really are. It seems necessary to clarify the statements of either side, to rule out some misunderstandings, and then to discuss anew the central epistemological (...) problems. Solution: A version of realism is proposed that takes into account constructivist ideas and objections. Realism as presented here is not opposed to the idea that cognition is a constructive process. According to this view, reality is something we presuppose in any attempt to attain knowledge though we can never be certain how things really are. Having knowledge amounts to the preliminary judgment that some hypotheses seem to correspond to reality better than others. In addition, it is demonstrated that a constructivist position that reduces the claim to knowledge even further does not solve the problems better but creates new ones. Finally, Mitterer's non-dualizing view of descriptions is discussed. It is argued that description necessarily presupposes something different from language. (shrink)

An algorithm recognizing admissibility of inference rules in generalized form (rules of inference with parameters or metavariables) in the intuitionistic calculus H and, in particular, also in the usual form without parameters, is presented. This algorithm is obtained by means of special intuitionistic Kripke models, which are constructed for a given inference rule. Thus, in particular, the direct solution by intuitionistic techniques of Friedman's problem is found. As a corollary an algorithm for the recognition of the solvability of (...) logical equations in H and for constructing some solutions for solvable equations is obtained. A semantic criterion for admissibility in H is constructed. (shrink)

While the notion of the common good figures frequently in both rhetoric and the inquiries of academic political theory, it is often neither closely examined nor precisely defined. This article examines Aristotle’s use of the idea, focusing primarily on two sets of key texts: first, Politics 1.1–2 and Nicomachean Ethics 1.2; and second, Nic. Ethics 8.9 and Politics 3.7. The first set of texts emphasizes the common good as flourishing and the city as its necessary condition; the second emphasizes the (...) common good as the good of all citizens as distinct from that of the rulers alone and leads to Aristotle’s notion of the generic political regime with its focus on the middle class and the rule of law. The conclusion notes both continuities and discontinuities with and challenges to contemporary politics posed by Aristotle’s view, which is neither as readily supportive of modern political programs nor as opposed to modern practices as is sometimes thought. (shrink)

Foundational theories of mental content seek to identify the conditions under which a mental representation expresses, in the mind of a particular thinker, a particular content. Normativists endorse the following general sort of foundational theory of mental content: A mental representation r expresses concept C for agent S just in case S ought to use r in conformity with some particular pattern of use associated with C. In response to Normativist theories of content, Kathrin Glüer-Pagin and Åsa Wikforss propose a (...) dilemma, alleging that Normativism either entails a vicious regress or falls prey to a charge of idleness. In this paper, I respond to this argument. I argue that Normativism can avoid the commitments that generate the regress and does not propose the sort of explanation required to charge that its explanation has been shown to be problematically idle. The regress-generating commitment to be avoided is, roughly, that tokened, contentful mental states are the product of rule-following. The explanatory task Normativists should disavow is that of explaining how it is that beliefs and other contentful mental states are produced. I argue that Normativism, properly understood as a theory of content, does not provide this kind of psychological explanation, and therefore does not entail that such explanations are to be given in terms of rule-following. If this is correct, Normativism is not the proper target of the dilemma offered by Glüer-Pagin and Wikforss. Understanding why one might construe Normativism in the way Glüer-Pagin and Wikforss must, and how, properly understood, it avoids their dilemma, can help us to appreciate the attractiveness of a genuinely normative theory of content and the importance of paying careful attention to the sort of normativity involved in norm-based theories of content. (shrink)

We investigate logical consequence in temporal logics in terms of logical consecutions. i.e., inference rules. First, we discuss the question: what does it mean for a logical consecution to be 'correct' in a propositional logic. We consider both valid and admissible consecutions in linear temporal logics and discuss the distinction between these two notions. The linear temporal logic LDTL, consisting of all formulas valid in the frame 〈L, ≤, ≥〉 of all integer numbers, is the prime object of our (...) investigation. We describe consecutions admissible LDTL in a semantic way—via consecutions valid in special temporal Kripke/Hintikka models. Then we state that any temporal inference rule has a reduced normal form which is given in terms of uniform formulas of temporal degree 1. Using these facts and enhanced semantic techniques we construct an algorithm, which recognizes consecutions admissible in LDTL. Also, we note that using the same technique it follows that the linear temporal logic L (N) of all natural numbers is also decidable w.r.t. inference rules. So, we prove that both logics LDTL and L (N) are decidable w.r.t. admissible consecutions. In particular, as a consequence, they both are decidable (Known fact), and the given deciding algorithms are explicit. (shrink)

Purpose. The article is aimed to study the anthropological, socio-philosophical and philosophical-legal dimensions of the ontological sphere of human life within the discourse of restricting human rights during pandemic threats. To do this, one should solve a number of tasks, among which are the following: 1) to explore the anthropological and praxeological understanding of fear as a primary component of human existence in a pandemic, which prevents people from changing their lives for the better and healthier, having fun and happiness; (...) 2) to put a focus on the habituation of fear as a two-dimensional adaptation to risks and threats from pandemics; 3) to reflect the anthropological features of changes in human life experience under the influence of the COVID-19 pandemic in the discourse of human rights and public health measures. Theoretical basis. Today, international guiding principles on human rights response to global natural threats have been updated. However, there are still no specific legal recommendations concerning measures on human rights protection during outbreaks of various infectious diseases. However, the influence of unexpected global challenges causes a change in the anthropological component of society and the state, so it requires immediate comprehensive research. Originality. It was substantiated a systematic approach to the implementation of modern healthcare policy towards the recognition of human life as the highest value, increasing the level of psychological preparedness for pandemic challenges and approximation of statutory provisions of human rights protection to modern challenges and threats to the health of the individual, society and state. The study of anthropological, socio-philosophical and philosophical-legal dimensions of human existence in the discourse of pandemic threats made it possible to reveal the profound influence of fear on human life, social justice and, consequently, identify the moral and legal dependence of the development level of society and the state on the level of axiological and anthropological concept of human dignity. Conclusions. Based on the study of statistical reports, international analysis and the use of personal authorial methods, the following can be stated: the methods of combating the modern pandemic have directly affected everyone on national and international level. Their influence is significant because it changes the rules of coexistence and life of people in all spheres. However, the influence on the consciousness and other intentions of the individual has mostly temporally insignificant limits. (shrink)

This paper is an attempt to actualize central ontological fundamental principles of Buddhism, in particular, the concept of universal inter-relationship. It is this idea of the all-round universal inter-dependence of everything living that may be re-comprehended in the context of aggravating global contradictions of the modern world. The archaic and at the same time fundamental Buddhist idea of universal inter-relationship can be re-comprehended with regard to establishing a global axiological program of co-existence of various socio-cultural and natural worlds and be (...) a basis for working out a global ethics, new behavior rules for man amid the aggravating ecological situation. The axiology of universal inter-relationship generates global synergetic consciousness and a program for man’scooperation with the world. (shrink)

This first of two volumes brings together invited papers of the 32nd International Wittgenstein Symposium. The relation between language and the world was undoubtedly a major issue in Wittgenstein's philosophical oeuvre. This volume provides substantial contributions on various aspects of Wittgenstein's writings such as the philosophy of mathematics, the problem of rule following, or the relation between meaning and use.

This paper attempts to synthesize the Winchian stress on constitutive rules with the Marxian stress on material relationships by developing the concept of emergently material social relations. Such relationships, it is argued, arise from the constitutive rules that constitute a group's way of life. Although such relationships thus are derivative from the conscious rule-following behavior of actors, nevertheless they have an objective existence independent of actors' specific awareness. It is argued that such material relations are an important mechanism (...) beyond the cultural rules through which our behavior is constrained, enabled, and motivated. Yet the Winchian tradition in general and contemporary structuration theory in particular have tended to peripheralize the notion of material relations, treating them largely as epiphenomenal abstractions. This, it is argued, is a mistake and the source of an important lacuna in structuration theory. In particular, because structuration theory decenters the actor, conflates the distinction between regulative and constitutive rules, and peripheralizes social relations, it lacks an adequate explanation of motivation, as symptomized by its inordinate appeal to the unconscious. The concept of emergently material social relations overcomes this problem and offers a reintegration of the Marxian and the Winchian traditions. (shrink)

: Urban bioethics seeks to broaden the traditional focus of bioethics to encompass questions about the interplay of individuals with family, group, community, and society. Urban bioethics will need to deal with cultural diversity, issues of equity, and the conflict between individual rights and the public good. Encouraging a multicultural ethical discernment, fostering an appreciation of the political, economic, sociological, and psychological issues that inform the question of urban moral choice, urban bioethics is essentially a multi-disciplinary, synthesizing enterprise. Several theoretical (...) models including social contract, rule utilitarian, communitarian, and feminist paradigms offer complementary conceptual frameworks. This paper is offered as a proposal, a road map for future study to place current bioethical analysis into a broader context. (shrink)

Urban bioethics seeks to broaden the traditional focus of bioethics to encompass questions about the interplay of individuals with family, group, community, and society. Urban bioethics will need to deal with cultural diversity, issues of equity, and the conflict between individual rights and the public good. Encouraging a multicultural ethical discernment, fostering an appreciation of the political, economic, sociological, and psychological issues that inform the question of urban moral choice, urban bioethics is essentially a multi-disciplinary, synthesizing enterprise. Several theoretical models (...) including social contract, rule utilitarian, communitarian, and feminist paradigms offer complementary conceptual frameworks. This paper is offered as a proposal, a road map for future study to place current bioethical analysis into a broader context. (shrink)

The paper studies the logic TL(NBox+-wC) – logic of discrete linear time with current time point clusters. Its language uses modalities Diamond+ (possible in future) and Diamond- (possible in past) and special temporal operations, – Box+w (weakly necessary in future) and Box-w (weakly necessary in past). We proceed by developing an algorithm recognizing theorems of TL(NBox+-wC), so we prove that TL(NBox+-wC) is decidable. The algorithm is based on reduction of formulas to inference rules and converting the rules in (...) special reduced normal form, and, then, on checking validity of such rules in models of singleexponential size in the rules. Also we consider the admissibility problem for TL(NBox+-wC) and show how to reduce the problem for admissibility to the decidability of TL(NBox+-wC) itself using definable universal modalities. (shrink)

Some are inclined to perceive the liberation of our philosophical thought from the rule of official ideology as a total break with the Marxian tradition of investigating and interpreting historical reality, as the destruction of everything that had been developed and formulated in the mainstream of this tradition. The collapse of the totalitarian system has given rise to a fashion of "criticizing Marx," specializing in exposing theoretical mistakes and miscalculations, demonstrating his scientific bankruptcy, and even searching for evil intentions in (...) his writings. Marx's doctrine is described as false from the beginning, definitively obsolete, and compromised by the experience of its practical application in the twentieth century. (shrink)

Many interpreters of Plato's Laws have seen the introduction of the ‘nocturnal council’ towards the end of that dialogue as a return to the sort of philosophic dictatorship allegedly recommended in the Republic and thus as a betrayal of the principle of the rule of law evinced in most of the Laws. This paper defends the consistency of the council with the larger programme of the Laws by showing that its function is philosophic discussion and not rule. Its influence will (...) be the influence of philosophy on its members, who already occupy political offices in the city, and not direct rule as a body. In this way, the council provides a point of entry for the transpolitical good of philosophy into the city and thus offers an essentially legal regime the means of transcending some of its characteristic limitations. It also points to larger themes in Plato's political philosophy. (shrink)

The author substantiates the principle of the researcher’s distance from the political situation in Russia and the entire post-Soviet space [Makarenko V. P., 2016, pp. 53–77] given that the main characteristics of the Russian, Soviet and post-Soviet state mind come from lie, violence and political mediocrity [Makarenko V. P., Akopyan A. G., Khaled R. K. B., 2020]. The leaders of the Russian Empire (Nicholas II) and the Soviet Union (Stalin) engaged the country in two world wars which implies that even (...) the Russian revolutions did not change the patterns of political thinking of the ruling minorities in Russia [Liven D., 2007]. The purpose of this article is to apply the author's concept of bureaucracy to explain the nature of post-Soviet wars. For this, the fundamental research of Hannah Arendt, the observations of writers, war journalists, and civilian analysts of the Soviet war in Afghanistan and the war between Russia and Chechnya in 1994–1996 are being used. The problems of reassessing the links between war and politics, the phenomenon of unknown wars in the history of the USSR and post-Soviet Russia, the reproduction of liars and the process of formation of unrecognized states in the post-Soviet space are considered. (shrink)

In Heidegger’ philosophical science writings the problematic of science occupies an important place. There are several periods in Heidegger’ articulating this problem. Among the most important are the 1930s, especially his lecture Modern Mathematical Science, which is seen by the author as one of the most considerable Heidegger’s works. Divided into two main parts it examines the relationship between the mathematical and metaphysics and Descartes’ relationship to metaphysics. In this lecture Heidegger showed himself as an excellent analytical philosopher, whose focus (...) is not on historical-philosophical reception of modern science , but on an original picture of the rise of modern science and its links with the origins of modern metaphysics as a metaphysics of subjectivity. To understand modern science means for Heidegger also a deep philosophical insight into Descartes’ Rules for the Direction of Our Native Intelligence. And with this we have but to agree. (shrink)

While the notion of the common good figures frequently in both rhetoric and the inquiries of academic political theory, it is often neither closely examined nor precisely defined. This article examines Aristotle’s use of the idea, focusing primarily on two sets of key texts: first, Politics 1.1–2 and Nicomachean Ethics 1.2; and second, Nic. Ethics 8.9 and Politics 3.7. The first set of texts emphasizes the common good as flourishing and the city as its necessary condition; the second emphasizes the (...) common good as the good of all citizens as distinct from that of the rulers alone and leads to Aristotle’s notion of the generic political regime with its focus on the middle class and the rule of law. The conclusion notes both continuities and discontinuities with and challenges to contemporary politics posed by Aristotle’s view, which is neither as readily supportive of modern political programs nor as opposed to modern practices as is sometimes thought. (shrink)

Russian idea as philosophy of longing future of Russia was formed by humanists in opposition to real state of life in the country. Beginning from Moscow kingdom in Russia there were often oppression, injustice, loutishness, bribery, cultural backwardness, lack of education. The number of civilized, highly educated, high-moral people was very narrow. But the part they played in the history was extremely great; they were always the social vanguard of our motherland. They themselves brought really human properties for their country, (...) which would be developed later and would be discovered in the lives of majority of the population of our country. What is really human or simply human in opposition to inhuman in a person? Everything is very simple. Good will in people appears when they begin to follow the commandments: don’t kill, don’t tempt, don’t steal, don’t use foul language etc. And vice versa, if a person breaks these rules, he loses his humanity. Its essence is simple; the main idea is that it is important for the highest moral principles to become the attribute of life for the majority of people in the country, just like mobile phone or computer became an integral part of people’s life today. Today Russian idea becomes global one. One cannot use other people for achieving their goals. It means that while different nations and states treat each other cautiously and suspiciously, with secret desire to gain something by deception, to acquire something fraudulently, to make a fortune by fraud, none of global problems will be solved positively. (shrink)

Russia is a country of extremes, as everyone knows. No matter what we do we are driven, as a rule, now to the extreme left and then to the extreme right. In the contemporary historiography of Soviet philosophy, such extreme turns lie at the surface. Among such extremes, I would include, in particular, the article "The Suppression of Philosophy in the USSR" [Podavlenie filosofii v SSSR], which appeared in Russian Philosophy. A Concise Encyclopedic Dictionary [Russkaia filosofiia. Malyi entsiklopedicheskii slovar'] . (...) I do not wish to say that one should not write about the suppression of Soviet philosophy. The problem is to maintain the necessary proportions. (shrink)

We find an explicit basis for all admissible rules of the modal logic S4. Our basis consists of an infinite sequence of rules which have compact and simple, readable form and depend on increasing set of variables. This gives a basis for all quasi-identities valid in the free modal algebra ℱS4 of countable rank.

Starting from the quantization of the action variable as a basic principle, I show that this leads one to the probabilistic description of physical quantities as random variables, which satisfy the uncertainty relation. Using such variables I show that the ensemble-averaged action variable in the quantum domain can be presented as a contour integral of a “quantum momentum function,” pq(z), which is assumed to be analytic. The condition that all bound states pq(z) must yield the quantized values of the action (...) variable requires the equation for pq(z) to be the Riccati differential equation, which can be converted to the Schrödinger equation for the wave function. The rule for probabilities in quantum mechanics follows from the physical meaning of pq(z) and its connection with the probability density. The discussion involves the correspondence principle and the assumption that the spacetime symmetries known in classical physics are valid in the quantum domain. (shrink)

Purpose. The purpose of the article is the analysis of the reasons and grounds of the crisis in the sphere of meaning-making, as well as searching answers to the questions about the meaning of human life in the contemporary world, which are maximally relevant in connection with the escalation of global problems, revealing the points of convergence between various theoretical positions, evaluation of their heuristic potential. Theoretical basis of the research is the historical-philosophical, comparative and system approaches, as well as (...) the analysis of philosophical insights in the field of global studies. Originality. Originality lies in the fact that this article is the first attempt to conduct comprehensive analysis in the problem of the sense of the Existence as it is presented in the first quarter of the 21st century and to relate it with the modern social situation that is characterized by a complex range of interconnected and interdependent anthropological problems of our time. Authors emphasize that the main reason in the crisis of meaning is that a man has lost touch with his roots, which is wildlife. He has created an artificial structure, civilization to satisfy his needs and finds no way to the transcendental, which is the true House of his being. Conclusions. A human must refuse from false self-conceit concerning his potential omniscience and omnipotence, cease dictating his own rules to the Existence, determine the boundaries of his freedom and try to clearly realize his place in the objective structure of being. The global situation can change for the better only if a dramatic change in the area of meaning-making happens. The decisive force, which may encourage nudging to the positive changes, can be either the free will of people who have realized the criticality of the situation or external natural and social circumstances that will make people reorganize radically. The proper prioritizing, a deep awareness of universal goals and solidarity between people could be the value basis that will become the foundation to find the meaning and create a more favorable future. (shrink)

The paper retraces the history of one of the ancient arguments, which took place in the period of the rise of metaphysics between Plato and Isocrates. The problem at issue was the balance between words and acts. Both philosophers aimed at different resolutions of the problems brought about by this conflict bewteen the words and acts . In the course of history the ways of "settling" this argument have been gradually marginalized. The metaphysics, however, had not freed itself of the (...) necessity to resolve the confilcts, which the metaphysics itself provoked by its claims on the "rule of reason". That is why even such a marginalized character as Isokrates could become an interesting and a very significant impulse for the contemporary thought, still captured by platonism and facing "isocratian objections". (shrink)

Our investigation is concerned with the finite model property with respect to admissible rules. We establish general sufficient conditions for absence of fmp w. r. t. admissibility which are applicable to modal logics containing K4: Theorem 3.1 says that no logic λ containing K4 with the co-cover property and of width > 2 has fmp w. r. t. admissibility. Surprisingly many, if not to say all, important modal logics of width > 2 are within the scope of this theorem–K4 (...) itself, S4, GL, K4.1, K4.2, S4.1, S4.2, GL.2, etc. Thus the situation is completely opposite to the case of the ordinary fmp–the absolute majority of important logics have fmp, but not with respect to admissibility. As regards logics of width ≤ 2, there exists a zone for fmp w. r. t. admissibility. It is shown that all modal logics A of width ≤ 2 extending S4 which are not sub-logics of three special tabular logics have fmp w.r.t. admissibility. (shrink)

The Golden Rule is endorsed in oneform or another by most cultures and majorreligions and is still espoused byphilosophers, business ethicists, and popularbusiness authors. Because it also resonateswith undergraduate business majors, it can bean effective teaching tool. This paperdescribes a way of teaching the Golden Rulethrough a series of business-oriented examplesintended to bring out its strengths andweaknesses. The method described alsointroduces students to some basic moralreasoning skills and acquaints them with a widerange of moral issues that arise in business. Kant's (...) Formula of Humanity is discussed in thefinal section as a principle that overcomes atleast some of the Golden Rule's defects. (shrink)

The European Union Commission’s whitepaper on Artificial Intelligence proposes shaping the emerging AI market so that it better reflects common European values. It is a master plan that builds upon the EU AI High-Level Expert Group guidelines. This article reviews the masterplan, from a culture cycle perspective, to reflect on its potential clashes with current societal, technical, and methodological constraints. We identify two main obstacles in the implementation of this plan: the lack of a coherent EU vision to drive future (...) decision-making processes at state and local levels and the lack of methods to support a sustainable diffusion of AI in our society. The lack of a coherent vision stems from not considering societal differences across the EU member states. We suggest that these differences may lead to a fractured market and an AI crisis in which different members of the EU will adopt nation-centric strategies to exploit AI, thus preventing the development of a frictionless market as envisaged by the EU. Moreover, the Commission aims at changing the AI development culture proposing a human-centred and safety-first perspective that is not supported by methodological advancements, thus taking the risks of unforeseen social and societal impacts of AI. We discuss potential societal, technical, and methodological gaps that should be filled to avoid the risks of developing AI systems at the expense of society. Our analysis results in the recommendation that the EU regulators and policymakers consider how to complement the EC programme with rules and compensatory mechanisms to avoid market fragmentation due to local and global ambitions. Moreover, regulators should go beyond the human-centred approach establishing a research agenda seeking answers to the technical and methodological open questions regarding the development and assessment of human-AI co-action aiming for a sustainable AI diffusion in the society. (shrink)

A feature of the agro-industrial sphere is the high probability of distribution of production or research sites in areas far from each other for a considerable distance. Moreover, the center for collecting information and processing it, as a rule, is concentrated in one compact place. For research institutions, this feature often acquires a state of rather urgent problem, which requires the search for new innovative approaches. The paper proposes elements of the concept of construction and technological solutions for methods of (...) operational data transfer of field research from agricultural areas to a remote database for data storage with the possibility of feedback. As an example, the procedure of qualification examination of plant varieties with the definition of the criteria of "difference, homogeneity and stability" and "suitability for propagation of the variety in Ukraine" was chosen. (shrink)

A feature of the agro-industrial sphere is the high probability of distribution of production or research sites in areas far from each other for a considerable distance. Moreover, the center for collecting information and processing it, as a rule, is concentrated in one compact place. For research institutions, this feature often acquires a state of rather urgent problem, which requires the search for new innovative approaches. The paper proposes elements of the concept of construction and technological solutions for methods of (...) operational data transfer of field research from agricultural areas to a remote database for data storage with the possibility of feedback. As an example, the procedure of qualification examination of plant varieties with the definition of the criteria of "difference, homogeneity and stability" and "suitability for propagation of the variety in Ukraine" was chosen. (shrink)

In his book Gabriele Lolli discusses the notion of proof, which is, according to him, the most important and at the same time the least studied aspect of mathematics. According to Lolli, a theorem is a conditional sentence of the form ‘if T then A’ such that A is a logical consequence of T, where A is a sentence and T is a sentence or a conjunction or set of sentences. Verifying that A is a consequence of T generally involves (...) considering infinitely many interpretations; so it is something which is impossible to do in finite terms. Proofs may serve as ‘shortcuts’ in this respect. A proof is defined by Lolli as any finite argument certifying that A is a consequence of T. A proof is a shortcut in the sense that it spares us considering infinitely many interpretations.The reason for such a very general definition of proof is Lolli's strong belief that mathematics is not a rigid system of explicit rules, but rather a set of tools; as a consequence, there is no prescription as to what a proof should or should not be. Actually, mathematics is historically situated and not timeless, and the history of mathematics is the …. (shrink)

The development of the social sciences needs to rely on precise methods. The nomological model of explanation adopted in the natural sciences is ill-suited for the social sciences. An algorithmic model of society can be a promising solution to existing problems. In its most general form, an algorithm is a generally understood prescription for what actions to perform and in what order to achieve the desired result. Any algorithm can be represented as a set of rules of the form (...) «If A, do D to get P». People are the bearers of this kind of rules that apply in different areas of their activities. The rules are subject to change based on personal and collective experience. There is a special mathematical discipline that studies the laws of evolution of such rules. This discipline is called genetic programming. Contrary to the threatening name, the algorithmic model does not imply the deprivation of a person’s right to free choice, but it needs this right as a necessary condition for the evolution of social algorithms. These algorithms allow us to give a non-causal, but law-like explanation of many well-known social phenomena, as well as to effectively model the future, which is critically important today. A retrospective look at the evolution of social algorithms shows that the current global crisis of human society is associated with the approach to the point of singularity in their evolution. This is due to the fact that there is no need for direct human participation in the implementation of social algorithms, which is reflected in a fundamental change in the sphere of employment and less need for further development of the sciences. (shrink)

This thesis provides an analysis of the existing proof systems for dynamic epistemic logic from the viewpoint of proof-theoretic semantics. After an illustration of the basic principles of proof-theoretic semantics, we review some of the most significant proposals of proof systems for dynamic epistemic logics, and we critically reject on them in the light of proof-theoretic semantic principles. The main original contributions of the present thesis are: (a) a revised version of the display-style calculus D.EAK, which we argue to be (...) more adequate from the proof-theoretic semantic viewpoint; the main feature of this revision is that a smoother proof (so-called Belnap-style) of cut-elimination holds for it, which is problematic for the original version of D.EAK. (b) The intro duction of a novel, multi-type display calculus for dynamic epistemic logic, which we refer to as Dynamic Calculus. The presence of types endows the language of the Dynamic Calculus with additional expressivity, and makes it possible to design rules with an even smoother behavior. We argue that this calculus paves the way towards a general methodology for the design of proof systems for the generality of dynamic logics, and certainly for proof systems beyond dynamic epistemic logic. We prove that the Dynamic Calculus adequately captures Baltag-Moss-Solecki's dynamic epistemic logic, and enjoys Belnap-style cut elimination. (shrink)

Open peer commentary on the article “Exploration of the Functional Properties of Interaction: Computer Models and Pointers for Theory” by Etienne B. Roesch, Matthew Spencer, Slawomir J. Nasuto, Thomas Tanay & J. Mark Bishop. Upshot: Although the authors investigate a form of distributed swarm intelligence and solve some problems with it – including sorting and summing – the major goal, which is constructing cognition, cannot be achieved by this approach alone. I propose that anticipatory mechanisms have the potential to construct (...) cognition and may very well be combined with swarm intelligence principles. (shrink)