The logic of single-conclusion proofs () is introduced. It combines the verification property of proofs with the single valuedness of proof predicate and describes the operations on proofs induced by modus ponens rule and proof checking. It is proved that is decidable, sound and complete with respect to arithmetical proof interpretations based on single-valued proof predicates. The application to arithmetical inference rules specification and -admissibility testing is considered. We show that the provability in gives the complete admissibility test for the (...) rules which can be specified by schemes in -language. The test is supplied with the ground proof extraction algorithm which eliminates the admissible rules from a -proof by utilizing the information from the corresponding -proofs. (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)

ABSTRACT Two models of the Aristotelian syllogistic in arithmetic of natural numbers are built as realizations of an old Leibniz idea. In the interpretation, called Scholastic, terms are replaced by integers greater than 1, and s.Ap is translated as “s is a divisor of p”, sIp as “g.c.d. > 1”. In the interpretation, called Leibnizian, terms are replaced by proper divisors of a special “Universe number” u < 1, and sAp is translated as “s is divisible by p”, sIp as (...) ‘l.c.m. < u”. Both interpretations are proved to be adequate to the Aristotelian syllogistic. They are extended to syllogistic including term negation and term conjunction as well. (shrink)

Logic is usually presented as a tool of rational inquiry; however, many logicians in fact treat logic so that it does not serve us, but rather governs us – as rational beings we are subordinated to the logical laws we aspire to disclose. We denote the view that logic primarily serves us as logica serviens, while denoting the thesis that it primarily governs our reasoning as logica dominans. We argue that treating logic as logica dominans is misguided, for it leads (...) to the idea of a “genuine” logic within a “genuine” language. Instead of this, we offer a naturalistic picture, according to which the only languages that exist are the natural languages and the artificial languages logicians have built. There is, we argue, no language beyond these, especially none that would be a wholesome vehicle of reasoning like the natural languages and yet be transparently rigorous like the artificial ones. Logic is a matter of using the artificial languages as idealized models of the natural ones, whereby we pinpoint the laws of logic by means of zooming in on a reflective equilibrium. (shrink)

The triplet model treats a concept as complex structure that expresses three kinds of information. The first is about entities subsumed under a concept,their properties and relations. The second is about means and ways of representing the first information in intelligent systems. The third is about linkage between the first and second ones and methods of its constructing. The application of triplet models to generalization and development of concept models in philosophy, logic, cognitive psychology, cognitive science, linguistics, artificial intelligence has (...) been demonstrated. The componential structure of the triplet model and extended concept classification have been given. Theoretical considerations are combined with historical case-studies of concept history. For scientists and students with an interest in problems of knowledge structure and representation. Abstract and Extended Summary in English. (shrink)

The aim of this paper is to look from the point of view of admissibility of inference rules at intermediate logics having the finite model property which extend Heyting's intuitionistic propositional logic H. A semantic description for logics with the finite model property preserving all admissible inference rules for H is given. It is shown that there are continuously many logics of this kind. Three special tabular intermediate logics λ, 1 ≥ i ≥ 3, are given which describe all tabular (...) logics preserving admissibility: a tabular logic λ preserves all admissible rules for H iff 7λ has width not more than 2 and is not included in each λ. MSC: 03B55, 03B20. (shrink)

The paper has three objectives: to expound a set-theoretical triplet model of concepts; to introduce some triplet relations (symbolic, logical, and mathematical formalization; equivalence, intersection, disjointness) between object concepts, and to instantiate them by relations between certain physical object concepts.

It is proposed to analyze fuzzy concepts and relations between them in the frame of triplet concept modeling. Fuzzy concepts are introduced by means of the so-called fuzzification of dichotomous concepts. The cognitive and psychological aspects of concept possession are separated and studied.

The Cell Cycle Ontology (CCO) has the aim to provide a ‘one stop shop’ for scientists interested in the biology of the cell cycle that would like to ask questions from a molecular and/or systems pe...

It is proposed to analyze the unity of scientific knowledge in terms of its structure-nominative reconstruction. -/- .

There are no universally adopted answers to the natural questions about scientific concepts: What are they? What is their structure? What are their functions? How many kinds of them are there? Do they change? Ironically, most if not all scientific monographs or articles mention concepts, but the scientific studies of scientific concepts are rare in occurrence. It is well known that the necessary stage of any scientific study is constructing the model of objects in question. Many years logical modeling was (...) dominant in the concept studies. Last decades, concepts came to be regarded as the subject of mathematical modeling. However, different authors take different features of concepts as independent variables of their models. Our objective is to characterize informally the spectra of relevant variables for the modeling of scientific concepts. (shrink)

In his (several times reprinted) article How Wide Is the Gap Between Facts and Values? N. Rescher aspires to clarify the long-lasting discussion on the ‘is-ought’ (‘fact-value’) gap by providing a framework in which the related arguments can be perspicuously articulated. He then argues that even if the logical gap may bereal, the transition from factual premises to value conclusions is smoothly mediated by trivially true value statements. We scrutinize Rescher’s argumentation and show defects in the presented lines of reasoning. (...) In particular, we argue that his tripartite division of statements (factual, evaluative, hybrid), as well as his emphasis on the role of evaluative truisms, introduce serious problems that escape Rescher’s attention. We thus conclude that he failed to achieve his goals. (shrink)

. We demonstrate that a comprehensive nonstandard set theory can be developed in the standard $\displaystyle{\in}$ -language. As an illustration, a nonstandard ${\sf Law of Large Numbers}$ is obtained.

We study models of HST . This theory admits an adequate formulation of the isomorphism propertyIP, which postulates that any two elementarily equivalent internally presented structures of a well-orderable language are isomorphic. We prove that IP is independent of HST and consistent with HST.

Im Unterschied zum christlichen Begriff der Gerechtigkeit als einer sittlichen Tugend, wie es Thomas von Aquin zusammenfasste, als einer Einstellung, kraft deren ein Mensch festen und steten Willens jedem sein Recht zukommen lässt, erkennt Nietzsche die Herkunft der Gerechtigkeit im Ausgleich oder Kompromiss zwischen ungefähr gleich Mächtigen sowie im Zwang der weniger Mächtigen zu einem Ausgleich. Zur Untermauerung dieser Einstellung, die sich auf der Behauptung gründet, dass das Leben seinem innersten Wesen nach eine Aneignung sei bzw. dass der Wille zur (...) Macht den Lebenswillen schlechthin ausmache, griff Nietzsche auf den von Thukydides geschilderten Dialog der Athener und Melier zurück. Der Autor kommt jedoch zu dem Schluss, dass Nietzsche nicht nur ein Denker der Macht war, sondern nach einem neuen Verständnis der Gerechtigkeit trachtete, das aus der Gesamtheit seines Denkens zu deuten sei. (shrink)

Iznimni utjecaj tehnologije na ljudski život oduvijek je bio paradoksalan. Primjerice, tehnologija je jedan od činitelja koji pridonosi neizvjesnosti budućnosti uslijed unutarnje proturječnosti tehničkog sustava i društva. Naime, što je tehnologija moćnija to je svijet uznemireniji. Pojedini autori izražavaju mišljenje da je upravo tehnodiskurs u stvari diskurs čovječnosti i način njezina poboljšanja. Unatoč ovome, pojedini autori, humanisti prije svega, misle da se tehnologija može ispuniti tradicionalnim vrijednostima. U stvari, oni smatraju da današnja kultura ima samo djelatnu vrijednost odjeljenu od tradicije (...) koja je oblikovana tehničkim napretkom i ekonomskim potrebama. Kultura je snažna oblikovateljica ljudskoga ponašanja jer je temelj svjesnih i nesvjesnih uvjerenja. Ona je put »ispravnih« načina života. Ne ugrožava li razvoj tehnike i tehnologije taj put »ispravnih« načina života?The extraordinary influence of technology on the human life has always been a paradox. For example, one of the factors contributing to an increase of uncertainty of the future of technology is internal contradictions of the technical system and society. For instance, a vulnerability to accidents grows proportionally with the size of organizations. Similarly, the more powerful a technology is, the more it disturbs the world. Some people think that the technodiscourse is a discourse about humanity and the ways of advancing it. Some humanists, on the other hand, think that the technology can be saturated with traditional values. Today’s culture has just an operational value detached from tradition, molded by the technical progress and economic needs. Culture is a powerful shaper of human behavior because it is the foundation of conscious and unconscious beliefs. It is the way of ‘proper’ ways to live. Can we do something in that way? We think we can. (shrink)

We generalize, on higher projective levels, a construction of “incompatible” generic Δ1 3 real singletons given by Jensen and Johnsbråten.

We prove that a Spector‐like ultrapower extension ???? of a countable Solovay model ???? (where all sets of reals are Lebesgue measurable) is equal to the set of all sets constructible from reals in a generic extension ????[a], where a is a random real over ????. The proof involves the Solovay almost everywhere uniformization technique.

V celej Heideggerovej tvorbe predstavuje recepcia dejín filozofie dominantný rozmer jeho filozofického u?enia. Autor štúdie sa zamýš?a nad problémom, ?i Heidegger mohol úspešne zav?ši? dokon?enie svojho diela Bytie a ?as ako ho pôvodne ohlásil pri prvom vydaní . Zis?uje, že nenaplnenie pôvodných zámerov k druhej nenapísanej ?asti práce nebolo vôbec náhodným dôsledkom. H?adanie odpovede na otázku bytia v druhej polovici práce Bytie a ?as sústredením sa na filozofické u?enia Kanta, Descarta a Aristotela nemohlo prinies? o?akávané výsledky, preto sa Heidegger po (...) obrate sústredil najmä na recepciu chápania bytia v diele Hegela, Leibniza, Herakleita a Parmenida. V tejto súvislosti autor zis?uje, že ani táto vážna zmena základnej orientácie na dejiny filozofie nemohla by? úspešne zav?šená hlavným problémom Heideggerovej filozofie – premyslie? bytie bez jestvujúcna a tak prejs? od metafyziky jestvujúcna k metafyzike Bytia. (shrink)

This note is about the “calculational style” of presenting proofs introduced by Dijkstra and Scholten and adopted in some books on theoretical computer science. We define the concept of a calculation, which is a formal counterpart of the idea of a calculational proof. The definition is in terms of a new formalization DS of predicate logic. Any proof tree in the system DS can be represented as a sequence of calculations. This fact shows that any logically valid predicate formula has (...) a calculational proof. (shrink)

Ovaj tekst nastoji da nijansira dihotomiju izmedju pojmova istorije i pravde koja je uobicajena u interpretaciji Hobzovog misljenja. Hobzov kriticki stav prema istoriji objasnjava se njegovom polemikom protiv nasledja klasicne antike, koja stoji u vezi s njegovim projektom stroge nauke o moralu i politici. Medjutim, Hobzovo shvatanje pravde ne moze se zasnovati bez izvesnih faktickih, empirijskih elemenata; ono se ne svodi na neku cisto racionalnu konstrukciju. Ovi elementi otvaraju Hobzovo misljenje prema problematici stvarne istorije; za Hobza, najvazniji predstavnici takve vrste (...) istorije su Tukidid i Tacit. Konacno, istorijska dimenzija Hobzovog misljenja dopusta nam da kod njega prepoznamo i jedan siri pojam pravde, koji probija granice pravde koja proizlazi iz ugovora. (shrink)

In trying to control various aspects concerning utterance production in multi-party human–computer dialogue, argumentative considerations play an important part, particularly in choosing appropriate lexical units so that we fine-tune the degree of persuasion that each utterance has. A preliminary step in this endeavor is the ability to place an ordering relation between semantic forms (that are due to be realized as utterances, by the machine), concerning their persuasion strength, with respect to certain (explicit or implicit) conclusions. Thus, in this article, (...) we propose a mechanism for assessing utterances, in terms of their argumentative force. The framework designed conflates insights from Asher and Lascarides’ SDRT (“Segmented Discourse Representation Theory”), and from Anscombre and Ducrot’s AT (“Argumentation Theory”). These mechanisms are included in a language generation component of a multi-party dialogue system for book reservation applications (i.e., a “virtual librarian”), and thus evaluated via typical human–machine conversations. (shrink)

Для Макса Вебера «рациональная бюрократия» есть идеальный тип организации общества. Однако идеальный тип не позволяет заполнить провал между властью и обществом, который называется отчуждением. Это - миф, и когда Макс Вебер говорит о рациональности, то в основе этого лежат не требования научности, но отсылка к некоей культурной аксиологии. Этот миф можно критиковать, анализируя конкретное поведение бюрократов, обычно мало рациональное, но также ставя под вопрос и саму культуру, которая хочет быть или даже претендует быть рационалистической. В России чудовищность бюрократии является следствием (...) кризиса культуры. Pour Max Weber la « bureaucratie rationnelle » est un type idéal d’organisation de la société. Mais ce type idéal ne permet pas de combler le hiatus entre pouvoir et société, lequel s’appelle aliénation. C’est un mythe, et si Max Weber parle de rationalité, ce n’est pas en vertu d’une exigence scientifique mais par référence à une axiologie culturelle. On peut donc le critiquer en analysant le comportement concret des bureaucrates -lequel est souvent fort peu rationnel -mais également en mettant en question une culture qui se veut ou se prétend rationaliste. En Russie, la monstruosité de la bureaucratie est la conséquence d’une crise de la culture. According to Max Weber, “rational bureaucracy” is an ideal-type of social organization. But this ideal-type cannot bridge the gap between power and society, something we could call alienation. It is a myth, and if Max Weber resorts to the concept of rationality, it is not because of any scientific need, but by reference to a cultural axiology. He can therefore be criticized by analyzing the actual behavior of bureaucrats, which often is less than rational, but also by challenging a culture that wants or claims to be rationalistic. In Russia, the monstrosity of bureaucracy is the consequence of a crisis of culture. (shrink)

trata-se de discutir as relações entre a constituição da paranoia como categoria clínica e experiências estético-sociais de crise. Esta é uma maneira de se perguntar sobre as relações que categorias clínicas tecem com processos e valores advindos dos campos da política e da estética.

Let D be a division ring such that the number of conjugacy classes of the multiplicative group D ∗ is equal to the power of D ∗ . Suppose that H is the group GL or PGL, where V is a vector space of infinite dimension ϰ over D . We prove, in particular, that, uniformly in κ and D , the first-order theory of H is mutually syntactically interpretable with the theory of the two-sorted structure 〈κ,D〉 in the second-order (...) logic with quantification over arbitrary relations of power ⩽κ . A certain analogue of this results is proved for the groups ΓL and PΓL . These results imply criteria of elementary equivalence for infinite-dimensional classical groups of types H= ΓL , PΓL , GL, PGL over division rings, and solve, for these groups, a problem posed by U. Felgner. It follows from the criteria that if H≡H then κ 1 and κ 2 are second-order equivalent as sets. (shrink)

Name der Zeitschrift: Cognitive Linguistics Jahrgang: 26 Heft: 1 Seiten: 95-111.

Name der Zeitschrift: Paragrana Jahrgang: 23 Heft: 2 Seiten: 25-39.

The Russian academic theological tradition, scarcely known to the West, was the only milieu wherein the development of philosophy of religion in the pre-revolutionary Russia was under way. Philosophical investigation of the phenomenon of religion was being elaborated in the apologetic context, i.e. in critical analysis of non-theistic conceptions of the origin and essence of religion, and the figure of Friedrich Schleiermacher, with his reduction of religion firstly to cosmic feelings and later to the feeling of the ontological dependence, occupied (...) an invariable place in this analysis. The paper deals with critical comments on Schleiermacher’s Speeches on Religion and Christian Faith made by Victor Kudryavtsev-Platonov and his followers, which are being parsed in turn, as well as with historical links of the later Schleiermacher with phenomenology of religion and typological affinities of the earlier Schleiermacher with the theology of religious pluralism. (shrink)

In this article ‡ we show how the universe of HST, Hrbaček set theory admits a system of subuniverses which keep the Replacement, model Power set and Choice, and also keep as much of Saturation as it is necessary. This gives sufficient tools to develop the most complicated topics in nonstandard analysis, such as Loeb measures.

Abstract“Force dynamics” refers to a previously neglected semantic category—how entities interact with respect to force. This category includes such concepts as: the exertion of force, resistance to such exertion and the overcoming of such resistance, blockage of a force and the removal of such blockage, and so forth. Force dynamics is a generalization over the traditional linguistic notion of “causative”: it analyzes “causing” into finer primitives and sets it naturally within a framework that also includes “letting,”“hindering,”“helping,” and still further notions. (...) Force dynamics, moreover, appears to be the semantic category that uniquely characterizes the grammatical category of modals, in both their basic and epistemic usages. In addition, on the basis of force dynamic parameters, numerous lexical items fall into systematic semantic patterns, and there exhibit parallelisms between physical and psychosocial reference. Further, from research on the relation of semantic structure to general cognitive structure, it appears that the concepts of force interaction that are encoded within language closely parallel concepts that appear both in early science and in naive physics and psychology. Overall, force dynamics thus emerges as a fundamental notional system that structures conceptual material pertaining to force interaction in a common way across a linguistic range: the physical, psychological, social, inferential, discourse, and mental-model domains of reference and conception. (shrink)

In this book, Leonard Talmy proposes that a single linguistic/cognitive system, targeting, underlies two domains of linguistic reference, those termed anaphora and deixis. Talmy argues that language engages the same cognitive system to single out referents whether they are speech-internal or speech-external. Talmy explains the targeting system in this way: as a speaker communicates with a hearer, her attention is on an object to which she wishes to refer; this is her target. To get the hearer's attention (...) on it as well, she uses a trigger -- a word such as this, that, here, there, or now. The trigger initiates a three-stage process in the hearer: he seeks cues of ten distinct categories; uses these cues to determine the target; and then maps the concept of the target gleaned from the cues back onto the trigger to integrate it into the speaker's sentence, achieving comprehension. The whole interaction, Talmy explains, rests on a coordination of the speaker's and hearer's cognitive processing. The process is the same whether the referent is anaphoric or deictic. Talmy presents and analyzes the ten categories of cues, and examines sequences in targeting, including the steps by which interaction leads to joint attention. A glossary defines the new terms in the argument. (shrink)