Design of engineering systems in Polish mines in the third quarter of the 20th century

Participation of mathematicians in the implementation of economic projects in Poland, in which mathematics-based methods played an important role, happened sporadically in the past. Usually methods known from publications and verified were adapted to solving related problems. The subject of this paper is the cooperation between mathematicians and engineers in Wroc{\l}aw in the second half of the twentieth century established in the form of an analysis of the effectiveness of engineering systems used in mining. The results of this cooperation showed that at the design stage of technical systems it is necessary to take into account factors that could not have been rationally controlled before. The need to explain various aspects of future exploitation was a strong motivation for the development of mathematical modeling methods. These methods also opened research topics in the theory of stochastic processes and graph theory. The social aspects of this cooperation are also interesting.Comment: 45 pages, 11 figures, 116 reference

ABSTRACTS

AbstractThe purpose of this department is to give sufficient information about the subject matter of each publication to enable users to decide whether to read it. It is our intention to cover all books, articles, and other materials in the field.Books for abstracting and eventual review should be sent to this department. Materials should be sent to Prof. David E. Zitarelli, Department of Mathematics, Temple University, Philadelphia, PA 19122, U.S.A. (e-mail: [email protected])Readers are invited to send reprints, autoabstracts, corrections, additions, and notices of publications that have been overlooked. Be sure to include complete bibliographic information, as well as transliteration and translation for non-European languages. We need volunteers willing to cover one or more journals for this department.In order to facilitate reference and indexing, entries are given abstract numbers which appear at the end following the symbol #. A triple numbering system is used: the first number indicates the volume, the second the issue number, and the third the sequential number within that issue. For example, the abstracts for Volume 20, Number 1, are numbered: 20.1.1, 20.1.2, 20.1.3, etc.For reviews and abstracts published in Volumes 1 through 13 there are anauthor indexin Volume 13, Number 4, and asubject indexin Volume 14, Number 1.The initials in parentheses at the end of an entry indicate the abstractor. In this issue there are abstracts by Vı́ctor Albis (Bogotá), Irving Anellis (Ames, IA), Thomas L. Bartlow (Villanova, PA), David Bressoud (St. Paul, MN), Catherine Goldstein (Paris), Herbert Kasube (Peoria, IL), Albert C. Lewis (Hamilton), Laura Nurzia (Reading, GB), James V. Rauff (Decatur, IL), Paul Wolfson (West Chester), and David E. Zitarelli

Lewis meets Brouwer: constructive strict implication

C. I. Lewis invented modern modal logic as a theory of "strict implication". Over the classical propositional calculus one can as well work with the unary box connective. Intuitionistically, however, the strict implication has greater expressive power than the box and allows to make distinctions invisible in the ordinary syntax. In particular, the logic determined by the most popular semantics of intuitionistic K becomes a proper extension of the minimal normal logic of the binary connective. Even an extension of this minimal logic with the "strength" axiom, classically near-trivial, preserves the distinction between the binary and the unary setting. In fact, this distinction and the strong constructive strict implication itself has been also discovered by the functional programming community in their study of "arrows" as contrasted with "idioms". Our particular focus is on arithmetical interpretations of the intuitionistic strict implication in terms of preservativity in extensions of Heyting's Arithmetic.Comment: Our invited contribution to the collection "L.E.J. Brouwer, 50 years later

Extensions of modal logic KTB and other topics

This thesis covers four topics. They are the extensions of the modal logic KTB, the use of normal forms in modal logic, automated reasoning in the modal logic S4 and the problem of unavoidable words. Extensions of KTB: The modal logic KTB is the logic of reflexive and symmetric frames. Dually, KTB-algebras have a unary (normal) operator f that satisfies the identities f (x){u2265}x and {u231D}x{u2264}f ({u231D}f(x)). Extensions of KTB are subvarieties of the algebra KTB. Both of these form a lattice, and we investigate the structure of the bottom of the lattice of subvarieties. The unique atom is known to correspond to the modal logic whose frame is a single reflexive point. Yutaka demonstrated that this atom has a unique cover, corresponding to the frame of the two element chain. We construct covers of this element, and so demonstrate that there are a continuum of such covers. Normal Forms in Modal Logic: Fine proposed the use of normal forms as an alternative to traditional methods of determining Kripke completeness. We expand on this paper and demonstrate the application of normal forms to a number of traditional modal logics, and define new terms needed to apply normal forms in this situation. Automated reasoning in 84: History based methods for automated reasoning are well understood and accepted. Pliu{u0161}kevi{u010D}ius & Pliu{u0161}kevi{u010D}ien{u0117} propose a new, potentially revolutionary method of applying marks and indices to sequents. We show that the method is flawed, and empirically compare a different mark/index based method to the traditional methods instead. Unavoidable words: The unavoidable words problem is concerned with repetition in strings of symbols. There are two main ways to identify a word as unavoidable, one based on generalised pattern matching and one from an algorithm. Both methods are in NP, but do not appear to be in P. We define the simple unavoidable words as a subset of the standard unavoidable words that can be identified by the algorithm in P-time. We define depth separating IX x homomorphisms as an easy way to generate a subset of the unavoidable words using the pattern matching method. We then show that the two simpler problems are equivalent to each other

Reducciones totales y parciales para el análisis de validez y construcción de modelos en M3

Esta tesis estudia la demostración automática de teoremas en lógicas trivaluadas. Concretamente se presenta un demostrador denominado tas-m3 para la lógica trivaluada completa m3. Esta tesis cuenta con una orientación a las aplicaciones y es de gran importancia la forma en la que se genera el modelo para la negación de la formula de entrada. Es un método que no está basado en resolución y por tanto no adolece de las deficiencias de este método(poca interacción con el ser humano, dificultad de obtener formas normales en lógicas no clásicas, etc.). Además de la demostración de corrección y completitud del método se demuestran otros teoremas relacionados con los procesos. El trabajo se complementa con un estudio comparativo con los métodos actualmente más utilizados. También se añaden capítulos en los que se introducen los conceptos que se utilizan a lo largo del trabajo así como un capítulo dedicado a las lógicas multivaluadas. Se añade un apéndice en el que se resume el demostrador para la lógica clásica TAS-D al que se le incorporan las mejoras que el estudio del caso multivaluado ha motivado. En la exposición y defensa se utiliza una implementación del método para entornos gráficos realizada en C++

Abstract Consequence and Logics - Essays in Honor of Edelcio G. de Souza

Edelcio G. de Souza is a Brazilian logician and philosopher who has researches in the domains of abstract logic, non-classical systems, philosophy of science and the foundations of mathematics. This book is in his honor with the purpose of celebrating his 60th birthday. It contains some articles connected with the above topics and other subjects in logical investigations