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Bulletin of the Section of Logic > 2019 > 48 > 2 > 99-116

Bulletin of the Section of Logic > 2019 > 48 > 2 > 137-158

Mathematica Applicanda > 2019 > 47 > 2

Mathematica Applicanda > 2019 > 47 > 2

An algebra A = ⟨A, ∨, ∧, →, 0, 1⟩ is a semi-Heyting algebra if ⟨A, ∨, ∧, 0, 1⟩ is a bounded lattice, and it satisfies the identities: x ∧ (x → y) ≈ x ∧ y, x ∧ (y → z) ≈ x ∧ [(x ∧ y) → (x ∧ z)], and x → x ≈ 1. 𝒮ℋ denotes the variety of semi-Heyting algebras. Semi-Heyting algebras were introduced by the second author as an abstraction from Heyting algebras. They share several important properties...

Bulletin of the Section of Logic > 2019 > 48 > 2 > 99-116

The goal of this paper is to propose correspondence analysis as a technique for generating the so-called erotetic (i.e. pertaining to the logic of questions) calculi which constitute the method of Socratic proofs by Andrzej Wiśniewski. As we explain in the paper, in order to successfully design an erotetic calculus one needs invertible sequent-calculus-style rules. For this reason, the proposed correspondence...

Bulletin of the Section of Logic > 2019 > 48 > 2 > 137-158

In previous work by Baaz and Iemhoff, a Gentzen calculus for intuitionistic logic with existence predicate is presented that satisfies partial cut elimination and Craig's interpolation property; it is also conjectured that interpolation fails for the implication-free fragment. In this paper an equivalent calculus is introduced that satisfies full cut elimination and allows a direct proof of interpolation...

The present note is an Erratum for the two theorems of the paper "Congruences and ideals in a distributive lattice with respect to a derivation" by M. Sambasiva Rao.

The only maximal extension of the logic of relevant entailment E is the classical logic CL. A logic L ⊆ [E,CL] called pre-maximal if and only if L is a coatom in the interval [E,CL]. We present two denumerable infinite sequences of premaximal extensions of the logic E. Note that for the relevant logic R there exist exactly three pre-maximal logics, i.e. coatoms in the interval [R,CL].

The modal logic S4.2 is S4 with the additional axiom ◊□A ⊃ □◊A. In this article, the sequent calculus GS4.2 for this logic is presented, and by imposing an appropriate restriction on the application of the cut-rule, it is shown that, every GS4.2-provable sequent S has a GS4.2-proof such that every formula occurring in it is either a subformula of some formula in S, or the formula □¬□B or ¬□B, where...

The notion of positive implicative soju ideal in BCK-algebra is introduced, and several properties are investigated. Relations between soju ideal and positive implicative soju ideal are considered, and characterizations of positive implicative soju ideal are established. Finally, extension property for positive implicative soju ideal is constructed.

Kooi and Tamminga's correspondence analysis is a technique for designing proof systems, mostly, natural deduction and sequent systems. In this paper it is used to generate sequent calculi with invertible rules, whose only branching rule is the rule of cut. The calculi pertain to classical propositional logic and any of its fragments that may be obtained from adding a set (sets) of rules characterizing...

This work is a continuation of the author's presentation of the history of mathematics in Russia as a research area within the history of science (v. Lokot (2018)). The elements of the history of mathematics began to intensively emerge in the epoch of Peter the Great and have undergone several stages of development. There are five stages that Russian scientists have gone through, shaping the elements...

This article presents the subject of the Applied Mathematics Seminar, conducted in 1948-1960 by Professor Hugon Steinhaus in Wrocław and is an important supplement to the analysis presented in the work of Szczotka (2018). This topic is illustrated by a more detailed discussion of some of the works on this subject and some of the results obtained by the participants of the Seminar. The results are...

The 47th National Conference on Mathematics Applications was held on September 4-11, 2018 in Zakopane Kościelisko. Together with the conference, the XXIV National Conference on Mathematics Applications in Biology and Medicine (4-7 September 2018) was held simultaneously with two common first days of the meeting. The plenary lecture was delivered by Urszula Ledzewicz (Southern Illinois University Edwardsville,...

On December 2--7, 2018, in Będlewo, the XLIV Conference "Mathematical Statistics" was held, organized by the Banach Center of Institute of Mathematics Polish Accademy of Science, the Committee on Statistics of the Committee of Mathematics of the Polish Academy of Sciences, and the Faculty of Mathematics and Computer Science of the Nicolaus Copernicus University in Toruń. During the 19 sessions,...

In this article we introduce a De Vylder type of approximation of the ruin probability for a two-dimensional risk process, where claims and premiums are shared with a predetermined proportion. Such a process is usually associated with the insurer - reinsurer model. Applying De Vylder’s idea to the risk process we obtain an approximation of the ruin probability for an arbitrary claim amount distribution...

Polish Nationwide Mathematical Student Conference OMatKo!!! was set up by students from all four mathematical scientific clubs at Wroclaw University of Science and Technology. The fifth edition of our conference took place from 13th to 15th of April 2018 and it has become the biggest mathematical student conference in the whole country, attracting more than 200 students. There are both Polish and...

W dniach 27 i 28 września 2018 roku na Uniwersytecie Ekonomicznym w Krakowie odbyła się konferencja {\it Nauki społeczne - matematyczne czy matematyzowalne?} poświęcona pamięci prof. dr. hab. Andrzeja Malawskiego, matematyka, filozofa i ekonomisty, wielkiego entuzjasty zastosowań matematyki w naukach społecznych, a zwłaszcza w teorii ekonomii. Andrzej Malawski ukończył dwa kierunki studiów na Uniwersytecie...

Polish Nationwide Mathematical Student Conference OMatKo!!! was set up by students from all four mathematical scientific clubs at Wroclaw University of Science and Technology. The fifth edition of our conference took place from 13th to 15th of April 2018 and it has become the biggest mathematical student conference in the whole country, attracting more than 200 students. There are both polish and...

Mathematica Applicanda > 2019 > 47 > 2

1. XLVIII National Conference on Applications of Mathematics i 9–16 September 2019, Zakopane-Kościelisko (Ł. Stettner) W dniach 9 - 16 września 2019 r. odbyła się w Zakopanem-Kościelisku w Domu Wczasowym Siwarna Czterdziesta Ósma Ogólnopolska Konferencja Naukowo-Szkoleniowa Zastosowań Matematyki. Ze względu na Jubileuszowy Zjazd Matematyków Polskich organizowany przez PTM z okazji jego stulecia oraz...

Mathematica Applicanda > 2019 > 47 > 2

In this paper we introduce and study a generalization of the split Pell quaternions - split r-Pell quaternions. We give some identities, among others Binet's formula, Catalan's, Cassini's and d'Ocagne's identity for these numbers.