Value Oriented Science for A Sustainable Society The essay deals with the relationship between ethics, science and the character of society associated with challenges such as: What is the contemporary role of science in society and how does it fulfil it? Is value oriented "engaged" science possible? What does the responsibility of science mean? What is the reason for and the state of integrative, interdisciplinary, cross-disciplinary and/or post-disciplinary approaches in the science? What is the role and meaning of evaluation in (...) scientific production and/or its usefulness? What is the value, cost and effectiveness of science? Is scientometrics an adequate answer? What is the role of ethics and science in the context of sustainable development/living/society? In the final section of the essay several examples drawing on the international as well as the national level are introduced. The ambition of the author, a professional environmental geographer, is not to submit an extensive excursion into most fashionable aspects of the topic within the global philosophical context. The author describes his own personal experience and position and tries to discover what the emerging challenges and threats in this field may be, first of all in the current Slovak context. (shrink)

Violence in the world, explosive population growth, uneven and unfair distribution of wealth, destruction of the environment and/or the ineffectiveness of supranational political and economic tools and institutions and other problems are more and more achieving global character. The growth of number, frequency and intensity of global problems and threats is a reality. In the same time it represents a big challenge: How to find a generally acceptable, adequate global solution? The majority of political and intellectual leaders around the world (...) acknowledge concept of sustainable development/sustainable living as the most important tool for protecting the biosphere and for securing reasonable development for the future. The development and implementation of the sustainable living concept is driven by the effort to reach – as much as possible – the ideals of humanism and the harmony between man and nature, based on the respect of life. Values compatible with a sustainable way of living are a set of values, the implementation of which promote the shift towards sustainable future. These values are not completely new. Just the opposite. They create the core of the common heritage of humankind, since the oldest religious cultures. The submitted study tries to map the recent developments of values compatible with the sustainable way of living problematic from both Czech, Slovak and thinkers from abroad perspectives in the wider framework of relevant international activities. (shrink)

The Enlightenment has often been written about as a sequence of disembodied 'great ideas'. The aim of this book is to put the beliefs of the Enlightenment firmly into their social context, by revealing the national soils in which they were rooted and the specific purposes for which they were used. It brings out the regional divergences of the Enlightenment experience, shaped by different local intellectual and economic priorities. At the same time it also shows how central concerns were shared (...) everywhere, and how the writings of certain key areas came to be influential elsewhere. The thirteen essays, each written by a historian specialising in the particular country, examine national contexts from Sweden to Italy, from Russia to North America. As well as focusing attention on the interplay of thought and action, ideology and society, the book offers important insights into the place of the intelligentsia in the modern world. (shrink)

Essential Buddhism, the fundamental teachings of the historical Buddha and the core of all major branches of Buddhism, is psychology, not religion or philosophy. Essential Buddhism is described from a psychological perspective and interrelated with Western psychology in general, and cognitive science, behaviour modification, psychoanalysis, and transpersonal psychology, in specific. Integrating Buddhist psychology and Western psychology yields a more comprehensive psychology and more powerful therapies.

The class \ of t rue p airing a lgebras is defined to be the class of relation algebras expanded with concrete set theoretical projection functions. The main results of the present paper is that neither the equational theory of \ nor the first order theory of \ are decidable. Moreover, we show that the set of all equations valid in \ is exactly on the \ level. We consider the class \ of the relation algebra reducts of \ ’s, (...) as well. We prove that the equational theory of \ is much simpler, namely, it is recursively enumerable. We also give motivation for our results and some connections to related work. (shrink)

In this paper we define computationally well-behaved versions of classical first-order logic and prove that the validity problem is decidable.

Henkin and Tarski proved that an atomic cylindric algebra in which every atom is a rectangle must be representable . This theorem and its analogues for quasi-polyadic algebras with and without equality are formulated in Henkin, Monk and Tarski [13]. We introduce a natural and more general notion of rectangular density that can be applied to arbitrary cylindric and quasi-polyadic algebras, not just atomic ones. We then show that every rectangularly dense cylindric algebra is representable, and we extend this result (...) to other classes of algebras of logic, for example quasi-polyadic algebras and substitution-cylindrification algebras with and without equality, relation algebras, and special Boolean monoids. The results of op. cit. mentioned above are special cases of our general theorems. We point out an error in the proof of the Henkin-Monk-Tarski representation theorem for atomic, equality-free, quasi-polyadic algebras with rectangular atoms. The error consists in the implicit assumption of a property that does not, in general, hold. We then give a correct proof of their theorem. Henkin and Tarski also introduced the notion of a rich cylindric algebra and proved in op. cit. that every rich cylindric algebra of finite dimension satisfying certain special identities is representable. We introduce a modification of the notion of a rich algebra that, in our opinion, renders it more natural. In particular, under this modification richness becomes a density notion. Moreover, our notion of richness applies not only to algebras with equality, such as cylindric algebras, but also to algebras without equality. We show that a finite dimensional algebra is rich iff it is rectangularly dense and quasi-atomic; moreover, each of these conditions is also equivalent to a very natural condition of point density . As a consequence, every finite dimensional rich algebra of logic is representable. We do not have to assume the validity of any special identities to establish this representability. Not only does this give an improvement of the Henkin-Tarski representation theorem for rich cylindric algebras, it solves positively an open problem in op. cit. concerning the representability of finite dimensional rich quasi-polyadic algebras without equality. (shrink)

We show that the equational theory of representable lattice-ordered residuated semigroups is not finitely axiomatizable. We apply this result to the problem of completeness of substructural logics.

We show that the equational theory of representable lower semilattice-ordered residuated semigroups is finitely based. We survey related results.

In this paper we show that relativized versions of relation set algebras and cylindric set algebras have undecidable equational theories if we include coordinatewise versions of the counting operations into the similarity type. We apply these results to the guarded fragment of first-order logic.

The class $$\mathsf{TPA}$$ TPA of t rue p airing a lgebras is defined to be the class of relation algebras expanded with concrete set theoretical projection functions. The main results of the present paper is that neither the equational theory of $$\mathsf{TPA}$$ TPA nor the first order theory of $$\mathsf{TPA}$$ TPA are decidable. Moreover, we show that the set of all equations valid in $$\mathsf{TPA}$$ TPA is exactly on the $$\Pi ^1_1$$ Π 1 1 level. We consider the class $$\mathsf{TPA}^-$$ (...) TPA - of the relation algebra reducts of $$\mathsf{TPA}$$ TPA ’s, as well. We prove that the equational theory of $$\mathsf{TPA}^-$$ TPA - is much simpler, namely, it is recursively enumerable. We also give motivation for our results and some connections to related work. (shrink)

We look at lower semilattice-ordered residuated semigroups and, in particular, the representable ones, i.e., those that are isomorphic to algebras of binary relations. We will evaluate expressions in representable algebras and give finite axiomatizations for several notions of validity. These results will be applied in the context of substructural logics.

In this paper we show that relativized versions of relation set algebras and cylindric set algebras have undecidable equational theories if we include coordinatewise versions of the counting operations into the similarity type. We apply these results to the guarded fragment of first-order logic.

The problem of whether Lambek Calculus is complete with respect to (w.r.t.) relational semantics, has been raised several times, cf. van Benthem (1989a) and van Benthem (1991). In this paper, we show that the answer is in the affirmative. More precisely, we will prove that that version of the Lambek Calculus which does not use the empty sequence is strongly complete w.r.t. those relational Kripke-models where the set of possible worlds,W, is a transitive binary relation, while that version of the (...) Lambek Calculus where we admit the empty sequence as the antecedent of a sequent is strongly complete w.r.t. those relational models whereW=U×U for some setU. We will also look into extendability of this completeness result to various fragments of Girard's Linear Logic as suggested in van Benthem (1991), p. 235, and investigate the connection between the Lambek Calculus and language models. (shrink)

SummaryAmong the several remarkable properties of mercury is that it dissolves many of the metals (but not iron), forming amalgams. It was the recognition of the ready formation of gold and silver amalgams that led to the extraction of precious metals by the amalgamation method. In this article I trace some of the historical aspects associated with the development of the European amalgamation process, first devised by Ignaz von Born in the 1780s. In particular, I describe an international gathering of (...) experts in mining and metallurgy which was held at Skleno in Slovakia in 1786, and the founding there of a society for mining sciences called ‘Die Societät der Bergbaukunde’. (shrink)

We consider the problem of the product finite model property for binary products of modal logics. First we give a new proof for the product finite model property of the logic of products of Kripke frames, a result due to Shehtman. Then we modify the proof to obtain the same result for logics of products of Kripke frames satisfying any combination of seriality, reflexivity and symmetry. We do not consider the transitivity condition in isolation because it leads to infinity axioms (...) when taking products. (shrink)

The aim of this paper is to give a new proof for the decidability and finite model property of first-order logic with two variables (without function symbols), using a combinatorial theorem due to Herwig. The results are proved in the framework of polyadic equality set algebras of dimension two (Pse 2 ). The new proof also shows the known results that the universal theory of Pse 2 is decidable and that every finite Pse 2 can be represented on a finite (...) base. Since the class Cs 2 of cylindric set algebras of dimension 2 forms a reduct of Pse 2 , these results extend to Cs 2 as well. (shrink)

The aim of this paper is to give a new proof for the decidability and finite model property of first-order logic with two variables, using a combinatorial theorem due to Herwig. The results are proved in the framework of polyadic equality set algebras of dimension two. The new proof also shows the known results that the universal theory of Pse$_2$ is decidable and that every finite Pse$_2$ can be represented on a finite base. Since the class Cs$_2$ of cylindric set (...) algebras of dimension 2 forms a reduct of Pse$_2$, these results extend to Cs$_2$ as well. (shrink)

We prove that algebras of binary relations whose similarity type includes intersection, union, and one of the residuals of relation composition form a nonfinitely axiomatizable quasivariety and that the equational theory is not finitely based. We apply this result to the problem of the completeness of the positive fragment of relevance logic with respect to binary relations.

Demonic composition, demonic refinement and demonic union are alternatives to the usual ‘angelic’ composition, angelic refinement (inclusion) and angelic (usual) union defined on binary relations. We first motivate both the angelic and the demonic via an analysis of the behaviour of non-deterministic programs, with the angelic associated with partial correctness and demonic with total correctness, both cases emerging from a richer algebraic model of non-deterministic programs incorporating both aspects. Zareckiĭ has shown that the isomorphism class of algebras of binary relations (...) under angelic composition and inclusion is finitely axiomatized as the class of ordered semigroups. The proof can be used to establish that the same axiomatization applies to binary relations under demonic composition and refinement, and a further modification of the proof can be used to incorporate a zero element representing the empty relation in the angelic case and the full relation in the demonic case. For the signature of angelic composition and union, it is known that no finite axiomatization exists, and we show the analogous result for demonic composition and demonic union by showing that the same axiomatization holds for both. We show that the isomorphism class of algebras of binary relations with the ‘mixed’ signature of demonic composition and angelic inclusion has no finite axiomatization. As a contrast, we show that the isomorphism class of partial algebras of binary relations with the partial operation of constellation product and inclusion (also a ‘mixed’ signature) is finitely axiomatizable. (shrink)

We show that the variety of weakly representable relation algebras is neither canonical nor closed under Monk completions.

Recenze knihy:Mikuláš Koperník, O obězích nebeských sfér. První kniha. Přel. Zdeněk Horský. Ed. Vojtěch Hladký. Pavel Mervart, Praha – Červený Kostelec 2016, 248 stran.