168 research outputs found
Interval Sheffer Stroke Basic Algebras and Yang-Baxter Equation
No full textIn this study, we give basic definitions and notions about Sheffer stroke operation and Sheffer stroke basic algebra. After presenting Sheffer stroke basic algebra on a given interval, named interval Sheffer stroke basic algebra, we give some features of an interval Sheffer stroke basic algebra. Then we investigate solutions to the set-theoretical Yang-Baxter equation in this algebraic structure by using its features. © 2020 Tahsin Oner et al., published by Sciendo 2020
Filters of strong Sheffer stroke non-associative MV-algebras
No full textIn this paper, at first we study strong Sheffer stroke NMV-algebra. For getting more results and some classification, the notions of filters and subalgebras are introduced and studied. Finally, by a congruence relation, we construct a quotient strong Sheffer stroke NMV-algebra and isomorphism theorems are proved. © 2021 Tahsin Oner et al., published by Sciendo
Correction: A disease-specific patient reported outcome instrument for spine trauma is developed, validated and available! Re: Andrzejowski et al. Measuring functional outcomes in major trauma: can we do better? (European Journal of Trauma and Emergency Surgery, (2023), 49, 3, (1605-1606), 10.1007/s00068-022-02167-8)
No full textThe article “A disease‑specific patient reported outcome instrument for spine trauma is developed, validated and available! Re: Andrzejowski et al. Measuring functional outcomes in major trauma: can we do better?”, written by Said Sadiqi, F. Cumhur Oner, was originally published electronically on the publisher’s internet portal on 15. November 2022 without open access. With the author(s)’ decision to opt for Open Choice the copyright of the article changed on 7
An algebraic analysis of categorical syllogisms by using Carroll’s diagrams
No full textIn this paper, we analyze the algebraic properties of categorical syllogisms by constructing a logical calculus system called Syllogistic Logic with Carroll Diagrams (SLCD).We prove that any categorical syllogism is valid if and only if it is provable in this system. For this purpose, we explain firstly the quantitative relation between two terms by means of bilateral diagrams and we clarify premises via bilateral diagrams. Afterwards, we input the data taken from bilateral diagrams, on the trilateral diagram. With the help of the elimination method, we obtain a conclusion that is transformed from trilateral diagram to bilateral diagram. Subsequently, we study a syllogistic conclusion mapping which gives us a conclusion obtained from premises. Finally, we allege valid forms of syllogisms using algebraic methods, and we examine their algebraic properties, and also by using syllogisms, we construct algebraic structures, such as lattices, Boolean algebras, Boolean rings, and many-valued algebras (MV-algebras). © 2019, University of Nis. All right reserved.Firat University Scientific Research Projects Management Unit2010 Mathematics Subject Classification. Primary 03B22; Secondary 03B80, 03E20, 03G27, 06A11, 18B35 Keywords. Categorical syllogisms, completeness, validity, algebraic logic Received: 02 June 2017; Revised: 10 February 2018; Accepted: 14 February 2018 Communicated by Ljubis^a D.R. Koc^inac This study is partially funded by Ege University Scientific Research Projects Directorate with the project number 15.FEN.066 Email addresses: [email protected] (Ibrahim Senturk), [email protected] (Tahsin Oner) -
INFINITE SYMMETRIC GROUPS
No full textIn this work, infinite similarities of permutation groups are investigated by means of new methods. For this purpose, we handle distinct groups on the set of natural numbers and we give the separation of the subgroups of them. Afterwards, we give the matrix representation of this groups
The Sheffer stroke operation reducts of basic algebras
No full textAbstract
In this study, a term operation Sheffer stroke is presented in a given basic algebra 𝒜 and the properties of the Sheffer stroke reduct of 𝒜 are examined. In addition, we qualify such Sheffer stroke basic algebras. Finally, we construct a bridge between Sheffer stroke basic algebras and Boolean algebras.</jats:p
An interpretation on Sheffer stroke reduction of some algebraic structures
No full text3rd International Conference of Mathematical Sciences (ICMS) -- SEP 04-08, 2019 -- Maltepe Univ, Istanbul, TURKEYsenturk, ibrahim/0000-0001-8296-2796In this paper, we obtain Sheffer stroke reduction for some algebraic structures such as BCK-algebras, MV-algebras, Wajsberg algebras and etc. by means of representing all operators in these structures with only Sheffer stroke basic algebras. We also examine some equalities and inequalities which are used in these constructions. in addition, we examine whether there is a transition from one of these structures to another by the help of this reduction
Interval Sheffer Stroke Basic Algebras and Yang-Baxter Equation
No full textIn this study, we give basic definitions and notions about Sheffer stroke operation and Sheffer stroke basic algebra. After presenting Sheffer stroke basic algebra on a given interval, named interval Sheffer stroke basic algebra, we give some features of an interval Sheffer stroke basic algebra. Then we investigate solutions to the set-theoretical Yang-Baxter equation in this algebraic structure by using its features
On Solutions to the Set-Theoretical Yang-Baxter Equation in Wajsberg-Algebras
No full textIn this work, we introduce Wajsberg algebras which are equivalent structures to MV-algebras in their implicational version, and then we define new notions and give new solutions to the set-theoretical Yang-Baxter equation by using Wajsberg algebras
The Structure of Rigid Frames of Depth 3 Only
No full text7th International Tbilisi Symposium on Logic, Language and Computation (TbiLLC 2007) -- OCT 01-05, 2007 -- Tbilisi, GACtr Language, Logic & Speech, Georgia Acad Sci, Inst Logic, Language & ComputatTurkish Scientific Technical Research Council (TUBITAK)Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK)This research was supported by Turkish Scientific Technical Research Council (TUBITAK)
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