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The interpretation of the German additive particle auch ('too, also') in quantificational contexts
Madeleine Butschety, 2022, independent scientific component part or a chapter in a monograph

Abstract: This article discusses an unexpected interpretation that arises for the German additive particle auch (‘too, also’) in quantificational contexts. It will be proposed that what auch conveys in such contexts is a superset-to-subset relation between two of its arguments. This rather unusual meaning and its alternation with the classical additive meaning will be argued to be tied to specific syntactic constructions in which the particle occurs. The main purpose of this article is to present novel data and make a tentative suggestion on how the correspondence between syntactic structure and semantic interpretation could be explained.
Keywords: additive particle, quantification, appositive, superset-to-subset relation, German, inclusion, presupposition, anaphora
Published in RUNG: 04.04.2024; Views: 457; Downloads: 1
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Polygroup objects in regular categories
Alessandro Linzi, 2024, original scientific article


We express the fundamental properties of commutative polygroups (also known as canonical hypergroups) in category-theoretic terms, over the category $ \mathbf{Set} $ formed by sets and functions. For this, we employ regularity as well as the monoidal structure induced on the category $ {\mathbf{Rel}} $ of sets and relations by cartesian products. We highlight how our approach can be generalised to any regular category. In addition, we consider the theory of partial multirings and find fully faithful functors between certain slice or coslice categories of the category of partial multirings and other categories formed by well-known mathematical structures and their morphisms.

Keywords: polygroup, canonical hypergroup, multiring, Krasner hyperring, regular category, relation
Published in RUNG: 25.03.2024; Views: 393; Downloads: 3
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Dependence relations and grade fuzzy set
Alessandro Linzi, Irina Elena Cristea, 2023, original scientific article

Abstract: With the aim of developing the recent theory of dependence relations, we elaborate a procedure to measure the strength of the influence of an element on another with respect to a given dependence relation on a finite set. We call this measure the degree of influence. Its definition is based on a partial hyperoperation and a directed graph which we associate with any dependence relation. We compute the degree of influence in various examples and prove some general properties. Among these properties, we find symmetries that have the potential to be applied in the realization of effective algorithms for the computations.
Keywords: dependence relation, degree of influence, grade fuzzy set, hypercompositional structure, hyperoperation
Published in RUNG: 23.01.2023; Views: 1483; Downloads: 3
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Semihypergroup-Based Graph for Modeling International Spread of COVID-n in Social Systems
Narjes Firouzkouhi, Reza Ameri, Abbas Amini, Hashem Bordbar, 2022, original scientific article

Abstract: Graph theoretic techniques have been widely applied to model many types of links in social systems. Also, algebraic hypercompositional structure theory has demonstrated its systematic application in some problems. Influenced by these mathematical notions, a novel semihypergroup based graph (SBG) of G = hH, Ei is constructed through the fundamental relation gn on H, where semihypergroup H is appointed as the set of vertices and E is addressed as the set of edges on SBG. Indeed, two arbitrary vertices x and y are adjacent if xgny. The connectivity of graph G is characterized by xg y, whereby the connected components SBG of G would be exactly the elements of the fundamental group H/g . Based on SBG, some fundamental characteristics of the graph such as complete, regular, Eulerian, isomorphism, and Cartesian products are discussed along with illustrative examples to clarify the relevance between semihypergroup H and its corresponding graph. Furthermore, the notions of geometric space, block, polygonal, and connected components are introduced in terms of the developed SBG. To formulate the links among individuals/countries in the wake of the COVID (coronavirus disease) pandemic, a theoretical SBG methodology is presented to analyze and simplify such social systems. Finally, the developed SBG is used to model the trend diffusion of the viral disease COVID-n in social systems (i.e., countries and individuals).
Keywords: graph theory, hypergroup, fundamental relation, social systems, geometric space
Published in RUNG: 23.11.2022; Views: 1092; Downloads: 0
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Seyed Mousavi, Morteza Jafarpour, Hojat Babaei, Irina Elena Cristea, 2022, original scientific article

Keywords: (Krasner) hyperring, strongly regular relation, λe-closed hy- perideal.
Published in RUNG: 11.05.2022; Views: 1799; Downloads: 0
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The Reducibility Concept in General Hyperrings
Irina Elena Cristea, Milica Kankaraš, 2021, original scientific article

Keywords: general hyperring, reducibility, fundamental relation, equivalence
Published in RUNG: 25.08.2021; Views: 1794; Downloads: 45
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Symmetry in the Theory of Dependence Relations
Irina Elena Cristea, 2021, published scientific conference contribution abstract

Keywords: dependence relation, degree of influence, degree of impact, fuzzy set, hypercompositional algebra
Published in RUNG: 10.08.2021; Views: 1869; Downloads: 49
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Some open problems in hypercompositional algebra
Irina Elena Cristea, 2020, published scientific conference contribution abstract (invited lecture)

Keywords: hypergroup, hyperring, hyperfield, hypermodule, dependence relation, fundamental realtion, fuzzy reducibility
Published in RUNG: 23.06.2020; Views: 2885; Downloads: 0
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The commutative quotient structure of m-idempotent hyperrings
Azam Adineh Zadeh, Morteza Norouzi, Irina Elena Cristea, 2020, original scientific article

Keywords: Hyperring, m-idempotent hyperring, strongly regular relation
Published in RUNG: 18.03.2020; Views: 2655; Downloads: 85
.pdf Full text (561,39 KB)

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