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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...
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...
In this paper we establish a new fractional identity involving a function oftwo independent variables, and then we derive some fractionalHermite-Hadamard type integral inequalities for functions whose modulus ofthe mixed derivatives are co-ordinated s-preinvex in the second sense.
In this paper, a known result dealing with |N, pn|k summability of infinite series has been generalized to the φ-|N, pn;δ|k infinite series by using an almost increasing sequence.
In this article, we define multi-invertible, multivalued maps. These mappings are a natural generalization of r-maps (in particular, the singlevalued invertible maps). They have many interesting properties and applications. In this article, the multi-invertible maps are applied to the construction of morphisms and to the theory of coincidence.
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...
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 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 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...
This article presents the theory of focal locus applied to the hypersurfaces in the projective space which are (finitely) covered by linear spaces and such that the tangent space is constant along these spaces.
The aim of this article is to provide the local convergence analysis of two novel competing sixth convergence order methods for solving equations involving Banach space valued operators. Earlier studies have used hypotheses reaching up to the sixth derivative but only the first derivative appears in these methods. These hypotheses limit the applicability of the methods. That is why we are motivated...
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...
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