Autor artykułu przedstawia w syntetycznym skrócie zasady kształtowania się dwóch podstawowych form wypowiedzi literacko-muzycznej w antycznym świecie cywilizacji greckiej i hellenistycznej. Pokrótce omawia sposoby przejawiania się muzyki, traktowanej jako ważny element obiegu kulturowego w ówczesnej rzeczywistości. Archetypiczne wzorce hymnu i peanu - podstawowych form literacko-muzycznych kultury greckiej - zostały omówione według charakterystycznych cech oraz poparte konkretnymi przykładami literackimi. Wskazano, że synkretyzm form literacko-muzycznych, charakterystyczny dla antycznej kultury śródziemnomorskiej, był powiązany z elementami kultu religijnego. Wymiar religijny stanowił ważne uzupełnienie praktycystycznego sposobu (...) traktowania muzyki w świecie cywilizacji antycznej, niekiedy wysuwające się na pierwszy plan. Szczególnie widoczne było to w przypadku wczesnochrześcijańskiej twórczości hymnograficznej, opartej na syntezie tradycji hellenistyczno-rzymskiej i judeochrześcijańskiej. (shrink)

We are concerned with formal models of reasoning under uncertainty. Many approaches to this problem are known in the literature e.g. Dempster-Shafer theory [29], [42], bayesian-based reasoning [21], [29], belief networks [29], many-valued logics and fuzzy logics [6], non-monotonic logics [29], neural network logics [14]. We propose rough mereology developed by the last two authors [22-25] as a foundation for approximate reasoning about complex objects. Our notion of a complex object includes, among others, proofs understood as schemes constructed in order (...) to support within our knowledge assertions/hypotheses about reality described by our knowledge incompletely. (shrink)

This book is a study in the logic of questions (sometimes called erotetic logic). The central topics in erotetic logic have been the structure of questions and the question-answer relationship. This book doesn't neglect these problems, but much of it is focussed on other issues. The main subject is the logical analysis of certain relations between questions and the contexts of their appearance. And our aim is to elaborate the conceptual apparatus of the inferential approach to the logic of questions. (...) Questions are asked for many reasons and for different purposes. Yet, before a question is asked or posed, a questioner must arrive at it. In many cases arriving at a question resembles coming to a conclusion: there are some premises involved and some inferential thought processes take place. If we agree that a conclusion need not be "conclusive", we may say that sometimes questions can play the role of conclusions. But questions can also perform the role of premises: we often pass from some "initial" question to another question. In other words, there are inferential thought processes - we shall call them erotetic inferences - in which questions play the roles of conclusions or conclusions and premises. The inferential approach to the logic of questions focusses its attention on the analysis of erotetic inferences. This book consists of eight chapters. (shrink)

Hybrid logics are extensions of standard modal logics, which significantly increase the expressive power of the latter. Since most of hybrid logics are known to be decidable, decision procedures for them is a widely investigated field of research. So far, several tableau calculi for hybrid logics have been presented in the literature. In this paper we introduce a sound, complete and terminating tableau calculus T H(@,E,D, ♦ −) for hybrid logics with the satisfaction operators, the universal modality, the difference modality (...) and the inverse modality as well as the corresponding sequent calculus S H(@,E,D, ♦ −) . They not only uniformly cover relatively wide range of various hybrid logics but they are also conceptually simple and enable effective search for a minimal model for a satisfiable formula. The main novelty is the exploitation of the unrestricted blocking mechanism introduced as an explicit, sound tableau rule. (shrink)

In 1934 Jaśkowski and Gentzen independently published their groundbreaking works on Natural Deduction. The aim of this paper is to provide some criteria for division of the diversity of existing systems on some natural subcategories and to show that despite the differences all these systems are descendants of original systems of Jaśkowski and Gentzen. Three criteria are discussed:The kind of items which are building-blocks of the proof.The format of proof.The kind of rules.The first leads to the division of ND into (...) two main classes: F-systems working on formulas and S-systems working on sequents. The second distinguishes between T-systems with tree-proofs and L-systems with linear proofs. Finally, the third leads to several minor divisions in the main categories. (shrink)

In this paper we show that some standard topological constructions may be fruitfully used in the theory of closure spaces (see [5], [4]). These possibilities are exemplified by the classical theorem on the universality of the Alexandroff's cube for T 0-closure spaces. It turns out that the closure space of all filters in the lattice of all subsets forms a generalized Alexandroff's cube that is universal for T 0-closure spaces. By this theorem we obtain the following characterization of the consequence (...) operator of the classical logic: If is a countable set and C: P() P() is a closure operator on X, then C satisfies the compactness theorem iff the closure space ,C is homeomorphically embeddable in the closure space of the consequence operator of the classical logic.We also prove that for every closure space X with a countable base such that the cardinality of X is not greater than 2 there exists a subset X of irrationals and a subset X of the Cantor's set such that X is both a continuous image of X and a continuous image of X. (shrink)

Stosunek do Innego rzutuje i będzie rzutował na konkretne wybory i losy polskiego społeczeństwa.Podejmując dyskusję znanej uwagi J.T. Grossa, łączącej podejście do imigrantówz nieprzepracowanym problemem polskich „marginesów Zagłady”, autor próbuje umieścićją w kontekście kwestii upodmiotowienia Polaków jako zbiorowości. Stawia tezę, że historycznieuwarunkowana, słaba umiejętność zbiorowego podejmowania odpowiedzialności zatrudne sprawy w podobny sposób określa oba zagadnienia. Tak wzięcie odpowiedzialnościza przeszłość, jak podjęcie jej za teraźniejsze wybory, wymaga bowiem takiej zbiorowejumiejętności. Słabość w tej sferze ogranicza samą możliwość praktykowania zalecanej przezJacques’a Derridę „gość-inności”.

The contemporary versions of the ontological argument originated from Charles Hartshorne are formalized proofs (in the metalogical sense of the word) based on unique modal theories. The simplest well-known theory of this kind arises from the system B of modal logic by adding two extra-logical axioms: (AA) “If the perfect being exists, then it necessarily exists” (Anselm’s Axiom) and (AL) “It is possible that the perfect being exists” (Leibniz’s Axiom). In the paper a similar argument is presented, however none of (...) the systems of modal logic is relevant to it. Its only premises are the axiom (AA) and, instead of (AL), the new axiom (AN): “If the perfect being doesn’t exist, it necessarily doesn’t”. The main goal of the work is to prove that (AN) is no more controversial than (AA) and — in consequence — the whole strength of the modal ontological argument lays in the set of its extra-logical premises. In order to do that, three arguments are formulated: ontological, “cosmo­logical” and metalogical. (shrink)

Quality is usually considered to be an attribute of an object, its degree of excellence or, more subjectively, fitness for use. Stemming from this point of view, the goal of most ranking systems is to find efficient ways of discovering, or rather uncovering, the quality of specific products or services. However, from a social psychological perspective it seems that the notion of quality belongs predominantly to the realm of social relationships. We argue that quality exists mainly between the users of (...) an object, not within the object itself, and its functions are predominantly social, i.e. promoting interactions, creating a shared reality, or building social relationships. Quality is constructed in social interactions and used as a token therein. In the present paper we outline the social functions of quality, and discuss the implications of this perspective for designing more useful recommendation systems. (shrink)

Pietruszczak (Bull Sect Log 38(3/4):163–171, 2009) proved that the normal logics K45 , KB4 (=KB5), KD45 are determined by suitable classes of simplified Kripke frames of the form ⟨W,A⟩ , where A⊆W. In this paper, we extend this result. Firstly, we show that a modal logic is determined by a class composed of simplified frames if and only if it is a normal extension of K45. Furthermore, a modal logic is a normal extension of K45 (resp. KD45; KB4; S5) if (...) and only if it is determined by a set consisting of finite simplified frames (resp. such frames with A≠∅; such frames with A=W or A=∅; such frames with A=W). Secondly, for all normal extensions of K45, KB4, KD45 and S5, in particular for extensions obtained by adding the so-called “verum” axiom, Segerberg’s formulas and/or their T-versions, we prove certain versions of Nagle’s Fact (J Symbol Log 46(2):319–328, 1981) (which concerned normal extensions of K5). Thirdly, we show that these extensions are determined by certain classes of finite simplified frames generated by finite subsets of the set N of natural numbers. In the case of extensions with Segerberg’s formulas and/or their T-versions these classes are generated by certain finite subsets of N. (shrink)

The article is devoted to Vilfredo Pareto’s reflections on socialism and dicusses thoroughly his important work Les syst`emes socialistes, especially its first part dealing with so called real socialist systems. This large treatise edited in 1901-1902 played an important role in the evolution of Pareto’s ideas. It brought the early version of his famous theory of social elites that was strictly connected with his refutation of historiosophical progressivism. Pareto examined many historical examples– from ancient to some tendencies in contemporary policy (...) – in order to elaborate the precise typology of the systems of real socialism. He tried to demonstrate that real socialism was an obstacle to economic and cultural development. Socialism was for him on the one hand utopian, and on the other hand – immoral. He didn’t exclude however that in the future the well organized socialist movement would come into power. (shrink)

The main result of this paper is the following theorem: a closure space X has an , , Q-regular base of the power iff X is Q-embeddable in It is a generalization of the following theorems:(i) Stone representation theorem for distributive lattices ( = 0, = , Q = ), (ii) universality of the Alexandroff's cube for T 0-topological spaces ( = , = , Q = 0), (iii) universality of the closure space of filters in the lattice of all (...) subsets for , -closure spaces (Q = 0). By this theorem we obtain some characterizations of the closure space given by the consequence operator for the classical propositional calculus over a formalized language of the zero order with the set of propositional variables of the power . In particular we prove that a countable closure space X is embeddable with finite disjunctions preserved into F iff X is a consistent closure space satisfying the compactness theorem and X contains a 0, -base consisting of -prime sets. (shrink)

Borden Parker Bowne was the founder of the School of Philosophy in Boston, taught there for more than a generation, and made a lasting impression on American philosophy. During Bowne’s career at Boston University (from 1876 until his death 1910), many of his students, who later also became professors in different areas, were inspired by his thinking and his person. His basic conviction is that it is the human person that is at the basis of Ontology and Ethics : the (...) person that preserves its identity within change thanks to memory; the person that is active in knowing and choosing; the person that acts deliberately towards values; the person that thinks – all these at least potentially. The purpose of the article is to examine Bowne’s metaphysics, i.e. the roots of his view of Personalism. What emerges is his idea of existence in general and of human existence in particular. This is done also historically, by examining some earlier views of man and reality in general, which were the background for Bowne’s specific ideas. He begins from his idea of existence as active and self-determining, and of nature as activated by the intellect and will of God, the Most-High Person. That is why the human person has the attributes of awareness and self-awareness, freedom and the ability to act, and self-control. The connection of Bowne’s Personalism with idealism also presents the problem of how do we come to discover the notion of person, which is not from simple experience of reality, but is rather developed or postulated. For Bowne the model for the notion of person is the Person of God. If we look at reality from the perspective of God-Person (Person par excellence), there is the danger of theologizing Philosophical Anthropology, and a reality of Bowne’s metaphysics, which wasn’t very popular among many philosophers. Nonetheless Bowne’s ideas were positively received by the Church in America, and were used for many years as the model for defending the Christian world-view against the attacks of naturalism. In that context, his Personalism effectively fulfilled its role, showing the human person to be a spiritual being, ultimately coming from God, the Most-High Person. (shrink)

In this paper we give probably an exhaustive analysis of the geometry of solids which was sketched by Tarski in his short paper [20, 21]. We show that in order to prove theorems stated in [20, 21] one must enrich Tarski's theory with a new postulate asserting that the universe of discourse of the geometry of solids coincides with arbitrary mereological sums of balls, i.e., with solids. We show that once having adopted such a solution Tarski's Postulate 4 can be (...) omitted, together with its versions 4' and 4". We also prove that the equivalence of postulates 4, 4' and 4" is not provable in any theory whose domain contains objects other than solids. Moreover, we show that the concentricity relation as defined by Tarski must be transitive in the largest class of structures satisfying Tarski's axioms. We build a model (in three-dimensional Euclidean space) of the theory of so called T*-structures and present the proof of the fact that this is the only (up to isomorphism) model of this theory. Moreover, we propose different categorical axiomatizations of the geometry of solids. In the final part of the paper we answer the question concerning the logical status (within the theory of T*-structures) of the definition of the concentricity relation given by Tarski. (shrink)

Zsfassung in dt. und engl. Sprache. - Dt. Zsfassung u.d.T.: Fragen und Perspektiven des Transzendentalismus.

The first part of this paper presents the fundations and some properties of the inclusive theory of quantification and analyses the relationship between inclusive and standard quantification theory. Some arguments concerning application of the inclusive theory instead of the standard theory have been discussed too. The second part of the article presents some versions of the inclusive theory of quantification formulated by: Mostowski (1951), Hailperin (1953), Quine (1954), Meyer and Lambert (1968). In the third part, a new conception of the (...) inclusive theory of predicates has been presented. This conception is based, analogically to Meyer and Lambert theory, on the idea of undersignating names the first-order language. Four consequence relations have been semantically defined, and the way, how the fundations concerning realizing in the domain of individual names condition the form of the quantification theory has been presented. The discussed consequence relations have been axiomatically characterized. The only difference between the axiomatics is the way of dealing with the formulas of the following type: ∀xα –> α [x/t] where t is the name (term) of the first-order language. (shrink)

The protagonist of Thomas Mann’s short story "The Clown" cannot became an artist because he hasn’t got enough talent. He is also unable to live among people as an ordinary citizen because his social competencies haven’t been completely developed. That is why he can be regarded as a literary figure who tries to leave the real world and to penetrate the literary world. The devil who appears in Charles Gounod’s opera "Faust" based on Johann Wolfgang Goethe’s drama "Faust" and who (...) is watching the protagonist from the stage during the opera performance seems to be the only person who can help him to find his existential space. (shrink)

In the vast literature on architectural theory and practice, the ways in which architectural knowledge is actually taught, debated, and understood are too often ignored. The essays collected in this groundbreaking volume address the current state of architecture as an academic and professional discipline. The issues considered range from the form and content of architectural education to the architect's social and environmental obligations and the emergence of a new generation of architects. Often critical of the current paradigm, these essays offer (...) a provocative challenge to accepted assumptions about the production, dissemination, and reception of architectural knowledge. Contributors: Sherry Ahrentzen, U of Wisconsin-Milwaukee; Stanford Anderson, MIT; Carol Burns, Harvard U; Russell Ellis, UC Berkeley; Thomas Fisher, U of Minnesota; Linda Groat, U of Michigan; Kay Bea Jones, Ohio State U; David Leatherbarrow, U of Pennsylvania; A. G. Krishna Menon, TVB School of Habitat Studies, India; Garth Rockcastle, U of Minnesota; Michael Stanton, American U, Beirut; Sharon E. Sutton, U of Washington; David J. T. Vanderburgh, Université Catholique de Louvain, Belgium; and Donald Watson, Rensselaer Polytechnic Institute. (shrink)

In the paper we present a technique for eliminating quantifiers of arbitrary order, in particular of first-order. Such a uniform treatment of the elimination problem has been problematic up to now, since techniques for eliminating first-order quantifiers do not scale up to higher-order contexts and those for eliminating higher-order quantifiers are usually based on a form of monotonicity w.r.t implication (set inclusion) and are not applicable to the first-order case. We make a shift to arbitrary relations “ordering” the underlying universe. (...) This allows us to incorporate background theories into higher-order quantifier elimination methods which, up to now, has not been achieved. The technique we propose subsumes many other results, including the Ackermann's lemma and various forms of fixpoint approaches when the “ordering” relations are interpreted as implication and reveals the common principle behind these approaches. (shrink)

The paper discusses properties of 4QL, a DATALOG⌉⌉-like query language, originally outlined by Maluszyński and Szalas (Maluszyński & Szalas, 2011). 4QL allows one to use rules with negation in heads and bodies of rules. It is based on a simple and intuitive semantics and provides uniform tools for “lightweight” versions of known forms of nonmonotonic reasoning. Negated literals in heads of rules may naturally lead to inconsistencies. On the other hand, rules do not have to attach meaning to some literals. (...) Therefore 4QL is founded on a four-valued semantics, employing the logic introduced in (Maluszyński et al., 2008; Vitória et al., 2009) with truth values: ‘true’, ‘false’, ‘inconsistent’ and ‘unknown’. In addition, 4QL is tractable w.r.t. data complexity and captures PTIME queries. Even though DATALOG⌉⌉ is known as a concept for the last 30 years, to our best knowledge no existing approach enjoys these properties.In the current paper we:investigate properties of well-supported models of 4QLprove the correctness of the algorithm for computing well-supported modelsshow that 4QL has PTIME data complexity and captures PTIME. (shrink)

In the article "Podstawy analizy metodologicznej kanonów Milla" [2] Jerzy Łoś proposed an operator that refered sentences to temporal moments. Let us look, for example, at a sentence ‘It is raining in Toruń’. From a logical point of view it is a propositional function, which does not have any logical value, unless we point at a temporal context from a fixed set of such contexts. If the sentence was considered today as a description of a state of affairs, it could (...) be true. If it was considered yesterday, it could be false. 1 The operator enables us to connect any sentence p with any temporal context t. Such a complex sentence we read as: a sentence p is realized at a temporal context t (a point of time, an interval of some kind, etc). (shrink)

In this paper we examine Prior’s reconstruction of Master Argument [4] in some modal-tense logic. This logic consists of a purely tense part and Diodorean definitions of modal alethic operators. Next we study this tense logic in the pure tense language. It is the logic K t 4 plus a new axiom ( P ): ‘ p Λ G p ⊃ P G p ’. This formula was used by Prior in his original analysis of Master Argument. ( P ) (...) is usually added as an extra axiom to an axiomatization of the logic of linear time. In that case the set of moments is a total order and must be left-discrete without the least moment. However, the logic of Master Argument does not require linear time. We show what properties of the set of moments are exactly forced by ( P ) in the reconstruction of Prior. We make also some philosophical remarks on the analyzed reconstruction. (shrink)

In this paper we examine Prior's reconstruction of Master Argument [4] in some modal-tense logic. This logic consists of a purely tense part and Diodorean definitions of modal alethic operators. Next we study this tense logic in the pure tense language. It is the logic $K_t 4$ plus a new axiom $:p \wedge Gp \supset PGp'$. This formula was used by Prior in his original analysis of Master Argument. is usually added as an extra axiom to an axiomatization of the (...) logic of linear time. In that case the set of moments is a total order and must be left-discrete without the least moment. However, the logic of Master Argument does not require linear time. We show what properties of the set of moments are exactly forced by in the reconstruction of Prior. We make also some philosophical remarks on the analyzed reconstruction. (shrink)

Grammar logics were introduced by Fariñas del Cerro and Penttonen in 1988 and have been widely studied. In this paper we consider regular grammar logics with converse ( REG c logics) and present sound and complete tableau calculi for the general satisfiability problem of REG c logics and the problem of checking consistency of an ABox w.r.t. a TBox in a REG c logic. Using our calculi we develop ExpTime (optimal) tableau decision procedures for the mentioned problems, to which various (...) optimization techniques can be applied. We also prove a new result that the data complexity of the instance checking problem in REG c logics is coNP-complete. (shrink)

A. Klimczuk, Book review: S. Harper, K. Hamblin, International Handbook on Ageing and Public Policy, Edward Elgar, Cheltenham, UK, Northampton, MA 2014 and R. Ervik, T.S. Lindén, The Making of Ageing Policy. Theory and Practice in Europe, Edward Elgar, Cheltenham, UK, Northampton, MA 2013., "Pol-int.org" 2017, https://www.pol-int.org/en/publications/international-handbook-ageing-and-public-policy#r5581.

Legal Philosophies of Russian Liberalism. By Andrzej Walicki. A History of Russian Philosophy, Edited by Valery A. Kuvakin.

In the paper, pre-Hilbert algebras are defined as a generalization of Hilbert algebras (namely, a Hilbert algebra is just a pre-Hilbert algebra satisfying the property of antisymmetry). Pre-Hilbert algebras have been inspired by Henkin's Positive Implicative Logic. Their properties and characterizations are investigated. Some important results and examples are given. Moreover, positive implicative pre-Hilbert algebras are introduced and studied, their connections with some algebras of logic are presented. The hierarchies existing between the classes of algebras considered here are shown.