Problems of substitution and admissibility in the modal system Grz and in intuitionistic propositional calculus

AbstractQuestions connected with the admissibility of rules of inference and the solvability of the substitution problem for modal and intuitionistic logic are considered in an algebraic framework. The main result is the decidability of the universal theory of the free modal algebra Fω(Grz) extended in signature by adding constants for free generators. As corollaries we obtain: (a) there exists an algorithm for the recognition of admissibility of rules with parameters (hence also without them) in the modal system Grz, (b) the substitution problem for Grz and for the intuitionistic calculus H is decidable, (c) intuitionistic propositional calculus H is decidable with respect to admissibility (a positive solution of Friedman's problem). A semantical criterion for the admissibility of rules of inference in Grz is given

Simultaneous Fluorination and Oxidation of Iridium by Metal Tetrafluorobromates

AbstractIridium is one of the most important platinum group metals and is used in several alloys and in the automotive industry for the purposes of making catalysts. Therefore, its recycling is a very actual challenge for researchers working in the field of urban mining. Reactions of various tetrafluorobromates MBrF4 (M = K, Rb, Cs) and M’(BrF4)2 (M’ = Ba) with Ir metal have been investigated. Compositions of the obtained products have been determined, corresponding reaction schemes have been suggested, and proper conditions for the reactions have been established

Inference Rules in Nelson’s Logics, Admissibility and Weak Admissibility

© 2015, Springer Basel. Our paper aims to investigate inference rules for Nelson’s logics and to discuss possible ways to determine admissibility of inference rules in such logics. We will use the technique offered originally for intuitionistic logic and paraconsistent minimal Johannson’s logic. However, the adaptation is not an easy and evident task since Nelson’s logics do not enjoy replacement of equivalences rule. Therefore we consider and compare standard admissibility and weak admissibility. Our paper founds algorithms for recognizing weak admissibility and admissibility itself – for restricted cases, to show the problems arising in the course of study

Branching time logics BTL, U,S , N,N −1(Z)α with operations until and since based on bundles of integer numbers, logical consecutions, deciding algorithms

This paper is intended as an attempt to describe logical consequence in branching time logics. We study temporal branching time logics which use the standard operations Until and Next and dual operations Since and Previous (LTL, as standard, uses only Until and Next). Temporal logics are generated by semantics based on Kripke/Hinttikka structures with linear frames of integer numbers with a single node (glued zeros). For , the permissible branching of the node is limited by α (where 1≤α≤ω). We prove that any logic is decidable w.r.t. admissible consecutions (inference rules), i.e. we find an algorithm recognizing consecutions admissible in . As a consequence, it implies that itself is decidable and solves the satisfiability problem

Until-since temporal logic based on parallel time with common past. Deciding algorithms

We present a framework for constructing algorithms recognizing admissible inference rules (consecutions) in temporal logics with Until and Since based on Kripke/Hintikka structures modeling parallel time with common past. Logics with various branching factor after common past are considered. The offered technique looks rather flexible, for instance, with similar approach we showed [33] that temporal logic based on sheafs of integer numbers with common origin is decidable by admissibility. In this paper we extend obtained algorithms to logics . We prove that any logic is decidable w.r.t. admissible consecutions (inference rules), as a consequence, we solve satisfiability problem and show that any itself is decidable

The structure of rigid frames of restricted depth

[No abstract available

Temperature dependence of molecular coefficients and activation energy of nematic mixture 2F-3333 [Температурные Зависимости Молекулярных Коэффициентов И Энергия Активации Нематической Смеси 2F-3333]

The paper presents the frequency spectra of the dielectric permittivity obtained by dielectric spectroscopy for the nematic mixture 2f-3333 having a complex molecular structure. On the basis of the obtained results, the activation energy of relaxation processes and the values of the molecular coefficients determining these processes are calculated. © 2018 Ivanovo State University Publishing.В работе представлены частотные спектры диэлектрической проницаемости нематической смеси 2f-3333 со сложной молекулярной структурой, полученные с помощью метода диэлектрической спектро- скопии. На основе полученных результатов рассчитана энергия активации релаксационных процессов, а также рассчитаны величины молекулярных коэффициентов, определяющих эти процессы

Adaptation of junior orienteers to loads, developing local-regional and special muscular endurance

Purpose: complex assessment of junior sport orientation athletes in conditions of concentrated training of local-regional muscular endurance and stroke loads (final part of preparation for competitions). Materials: in the research sport orientation athletes (n=34, age 13-16 years) participated. The athletes were divided into tested group (n=17) and group of comparison (n=17). In every group there were 17 boys and girls. The tested group consisted of volunteers, who practiced sport orientation. Comparison group included average distance and steeplechase runners. Results: In system of junior orienteers’ training we found: gender distinctions in carbohydrates and fats consumption (in the ranges of aerobic and anaerobic thresholds; substantial physiological changes in static-kinetic balance (tests with open and closed eyes. Dynamic coefficient of balance in main stance was better in sport orienteers, comparing with runners. Conclusions: it is recommended to fulfill exercises in conditions of stretching, combined with motor actions of speed-power orientation and relaxation

ELECTRICAL DOUBLE LAYERS AND THEIR EFFECT ON THE LOW-FREQUENCY DIELECTRIC PERMITTIVITY OF 4-n-PENTYL-4 '-CYANOBIPHENYL (5CB)

On the basis of the dielectric spectroscopy experimental results of 4-n-pentyl-4'-cyanobiphenyl (5CB), an empirical model describing the formation of double electrical layers (DEL) for the cells with the homeotropic and planar orientation is constructed. The model allows to determine the parameters of DEL, such as thickness and capacity, taking into account physical parameters of liquid crystal. It is also shows the empirical dependence of the parasitic capacitance, which is due to the presence of conduction ions, on the thickness of these layers

Description of Modal Logics Inheriting Admissible Rules for S4

We give a necessary and su#cient condition for any modal logic with fmp to inherit all inference rules admissible in S4. Using this condition we describe all tabular modal logics inheriting inference rules admissible for S4