In a fluent, clear, and lively style this translation by two of Maslov's junior colleagues brings the work of the late Soviet scientist S. Yu. Maslov to a wider audience. Maslov was considered by his peers to be a man of genius who was making fundamental contributions in the fields of automatic theorem proving and computational logic. He published little, and those few papers were regarded as notoriously difficult. This book, however, was written for a broad audience of readers and (...) describes elegant examples of applications in such fields as computer science, artificial intelligence, operations research, economic modeling, and biological modeling, among others. The book also brings to light the work by the American mathematician E. L. Post, which inspired Maslov's own work in the development of a general theory and which has been long neglected by mathematicial logicians and systems theorists in the United States. The book's first chapter introduces the Rules of the Game. Part I, Mathematics of Calculi, covers E. L. Post's canonical systems, deductive systems and algorithms, and probabilistic calculi and deductive information. Part II, Horizonal Modeling, takes up a "toy" economy, the calculi of technological possibilities, and the development of rules. Part III, Vertical Modeling, deals with the topics of "to fight and to search" and the consequences of the asymmetry of cognitive mechanisms. Vladimir Lifschitz is affiliated with the Department of Computer Science at Stanford University, and Michael Gelfond with the Department of Electrical Engineering and Computer Science at the University of Texas, El Paso. Theory of Deductive Systems and Its Applicationsis included in the Foundation of Computing Series, edited by Michael Garey. (shrink)

Qu'est-ce que la musique? Selon Jankélévitch, il y a dans la musique une double complication, génératrice de problèmes métaphysiques et de problèmes moraux. Car la musique est à la fois expressive et inexpressive, sérieuse et frivole, profonde et superficielle ; elle a un sens et n'en a pas. Il y a une ironique disproportion entre la puissance incantatoire de la musique et l'inévidence foncière du beau musical.

Religious art within postmodernism is discussed. Postmodern art, I argue, projects the myth of a miraculously generating chaos which cannot be maintained as absolute and therefore postmodern art cannot be genuinely religious. The myth is adopted for ideological, not philosophical reasons and calls for alternatives to make religious art possible.

L'alternative.--L'economie.--Métaphysique de l'ennui.

Qu'est-ce que l'ironie? Quelles en sont les formes? Quels en sont les pièges aussi? Autant de délicates questions auxquelles l'auteur répond, non sans ironie lui-même, avec l'aide d'une infinité d'exemples qui montrent son immense culture, musicale aussi bien que philosophique. Sommairement, qu'est-ce que l'ironie, sinon la conscience, mais une bonne conscience joyeuse, ce en quoi elle se distingue de l'hypocrisie? Pas d'humour sans amour, ni d'ironie sans joie. L'ironie, en somme, sauve ce qui peut être sauvé. Elle est mortelle aux (...) illusions ; partout elle tisse les toiles d'araignée où se prendront les pédants, les vaniteux et les grotesques. " Ironie, vraie liberté! ", s'écrie Proudhon au fond de sa cellule de Sainte-Pélagie. L'ironie remet tout en question ; par ses interrogations indiscrètes elle ruine toute définition, dérange à tout moment la pontifiante pédanterie prête à s'installer dans une déduction satisfaite. Grâce à l'ironie, la pensée respire plus légèrement quand elle s'est reconnue, dansante et grinçante, dans le miroir de la réflexion. (shrink)

If a formal theory T is able to reason about its own syntax, then the diagonalizable algebra of T is defined as its Lindenbaum sentence algebra endowed with a unary operator □ which sends a sentence φ to the sentence □φ asserting the provability of φ in T. We prove that the first order theories of diagonalizable algebras of a wide class of theories are undecidable and establish some related results.

The subject of this study is the participants in artificial sociality (humans and artificial intelligence (AI) tools) and communication between them. The first section analyses (using Luhmann’s methodology) communication as the basis of sociality. The second section shows how AI tools became social technologies in the framework of artificial sociality. The third section describes experimental communication between authors and AI tools (the case of ChatGPT). For the first time in the Baltic countries, the authors examined sociological, humanitarian, natural and technological (...) aspects of the functioning AI tools, which participate in creation of a new social reality for human society – artificial sociality. (shrink)

This article discusses the connection between the ideas of Fyodor M. Dostoevsky and Vladimir S. Solovyov on the need for cultural and moral transformation of those who would claim to participate in...

My dear Aleksandr!I have finally found some quiet time for a slow and attentive read of your article “The Beginning of the Black Notebooks.”1 I very much liked the article, especially for your trul...

The paper contains some observations on e-complete, precomplete, and uniformly finitely precomplete r. e. equivalence relations. Among these are a construction of a uniformly finitely precomplete r. e. equivalence which is neither e- nor precomplete, an extension of Lachlan's theorem that all precomplete r. e. equivalences are isomorphic, and a characterization of sets of fixed points of endomorphisms of uniformly finitely precomplete r. e. equivalences.

Changes in the productive forces and, consequently, in the economic structure of socialist society as a whole are being prepared by the current relationships of production. We refer particularly to the influence of socioeconomic processes under the conditions of the revolution in science and technology on the development of the individual as a factor in the productive forces and as subject in production relationships.

We prove that the diagonalizable algebras of PA and ZF are not isomorphic.

In this paper we prove that the preordering $\lesssim $ of provable implication over any recursively enumerable theory $T$ containing a modicum of arithmetic is uniformly dense. This means that we can find a recursive extensional density function $F$ for $\lesssim $. A recursive function $F$ is a density function if it computes, for $A$ and $B$ with $A\lnsim B$, an element $C$ such that $A\lnsim C\lnsim B$. The function is extensional if it preserves $T$-provable equivalence. Secondly, we prove a (...) general result that implies that, for extensions of elementary arithmetic, the ordering $\lesssim $ restricted to $\Sigma_{n}$-sentences is uniformly dense. In the last section we provide historical notes and background material. (shrink)

Not only Greek philosophers listened to prophets. René Descartes also long pondered over the familiar words of Ausonius: "What path shall I choose for myself in life?" And-what an amusing play on words-the idea of methodos entered philosophy with Descartes. The very path of his metaphysical thought was the last possible one within the confines of Aristotelian metaphysics, when, having posited certain principles of discourse, in the end they themselves are conclusively reached and the entire system becomes a manifest certainty. (...) Descartes provides a glimpse of the possibility of a new type of metaphysical reflection in which the correctness of the chosen principles is grounded in the completeness and noncontradictoriness of the system built on their basis but not confined to them. (shrink)