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)

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)

Розкрито сутність поняття «рейтинг». Доведено значущість рейтингової оцінки для суб’єктів фінансового ринку, зокрема для страхових компаній, потенційних страхувальників, інвесторів та кредиторів.

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)

"Williams's masterful translation satisfies (at last!) a long-standing need. There are lots of good translations of Augustine's great work, but until now we have been forced to choose between those that strive to replicate in English something of the majesty and beauty of Augustine's Latin style and those that opt instead to convey the careful precision of his philosophical terminology and argumentation. Finally, Williams has succeeded in capturing both sides of Augustine's mind in a richly evocative, impeccably reliable, elegantly readable (...) presentation of one of the most impressive achievements in Western thought--Augustine's Confessions." --Scott MacDonald, Professor of Philosophy and Norma K. Regan Professor in Christian Studies, Cornell University. (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.

This book offers a critical introduction to the work of American philosopher D. G. Leahy (1937-2014). Leahy's fundamental thinking can be characterized as an absolute creativity in which all creating is 'live' -- a happening occurring now that manifests a supersaturated polyontological actuality that is essentially created by the logic that characterizes it. Leahy leaves behind the categorial presuppositions of modern thought, eclipsing both Cartesian and Hegelian subjectivities and introducing instead an essentially new form of thinking founded in a nondual (...) logic of creation. The new thinking delineates the absolute unicity of existence as a creative interactivity beyond all traditional dichotomies (such as one vs. many, unity vs. plurality, identity vs. change): a fully "digitized" actuality that is nothing but newness, which inherently implies nothing but change. Through this new form of thinking, change itself is revealed to be the very essence of reality and mind. Any reader looking for a quantum leap beyond the thrall of modern and postmodern fixations is invited to hear and apprehend this new thinking that refuses to be conditioned by paradigms, categories, species, genera, walls, bridges, boundaries, or abstractions: an essentially free thinking that embodies creative novelty itself. (shrink)

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.

R.I.G Hughes offers the first detailed and accessible analysis of the Hilbert-space models used in quantum theory and explains why they are so successful.

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)

In this first paperback edition, a new introduction by Tom Burke establishes the ongoing importance of Sleeper's analysis of the integrity of Dewey's work and ...

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)

This book is not a study of Plato's philosophy, but a contribution to the literary interpretation of the dialogues, through analysis of their formal structure, ...

Linking the process of rational decision making to emotions, an award-winning scientist who has done extensive research with brain-damaged patients notes the dependence of thought processes on feelings and the body's survival-oriented regulators. 50,000 first printing.