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The interpretation of the German additive particle auch ('too, also') in quantificational contexts
Madeleine Butschety, 2022, samostojni znanstveni sestavek ali poglavje v monografski publikaciji

Opis: 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.
Ključne besede: additive particle, quantification, appositive, superset-to-subset relation, German, inclusion, presupposition, anaphora
Objavljeno v RUNG: 04.04.2024; Ogledov: 732; Prenosov: 1
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Polygroup objects in regular categories
Alessandro Linzi, 2024, izvirni znanstveni članek


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.

Ključne besede: polygroup, canonical hypergroup, multiring, Krasner hyperring, regular category, relation
Objavljeno v RUNG: 25.03.2024; Ogledov: 608; Prenosov: 3
.pdf Celotno besedilo (504,37 KB)
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Dependence relations and grade fuzzy set
Alessandro Linzi, Irina Elena Cristea, 2023, izvirni znanstveni članek

Opis: 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.
Ključne besede: dependence relation, degree of influence, grade fuzzy set, hypercompositional structure, hyperoperation
Objavljeno v RUNG: 23.01.2023; Ogledov: 1738; Prenosov: 3
.pdf Celotno besedilo (304,05 KB)
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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, izvirni znanstveni članek

Opis: 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).
Ključne besede: graph theory, hypergroup, fundamental relation, social systems, geometric space
Objavljeno v RUNG: 23.11.2022; Ogledov: 1248; Prenosov: 0
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Seyed Mousavi, Morteza Jafarpour, Hojat Babaei, Irina Elena Cristea, 2022, izvirni znanstveni članek

Ključne besede: (Krasner) hyperring, strongly regular relation, λe-closed hy- perideal.
Objavljeno v RUNG: 11.05.2022; Ogledov: 1969; Prenosov: 0
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The Reducibility Concept in General Hyperrings
Irina Elena Cristea, Milica Kankaraš, 2021, izvirni znanstveni članek

Ključne besede: general hyperring, reducibility, fundamental relation, equivalence
Objavljeno v RUNG: 25.08.2021; Ogledov: 1998; Prenosov: 45
.pdf Celotno besedilo (302,45 KB)

Symmetry in the Theory of Dependence Relations
Irina Elena Cristea, 2021, objavljeni povzetek znanstvenega prispevka na konferenci

Ključne besede: dependence relation, degree of influence, degree of impact, fuzzy set, hypercompositional algebra
Objavljeno v RUNG: 10.08.2021; Ogledov: 2052; Prenosov: 49
.pdf Celotno besedilo (216,43 KB)

Some open problems in hypercompositional algebra
Irina Elena Cristea, 2020, objavljeni povzetek znanstvenega prispevka na konferenci (vabljeno predavanje)

Ključne besede: hypergroup, hyperring, hyperfield, hypermodule, dependence relation, fundamental realtion, fuzzy reducibility
Objavljeno v RUNG: 23.06.2020; Ogledov: 3138; Prenosov: 0
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The commutative quotient structure of m-idempotent hyperrings
Azam Adineh Zadeh, Morteza Norouzi, Irina Elena Cristea, 2020, izvirni znanstveni članek

Ključne besede: Hyperring, m-idempotent hyperring, strongly regular relation
Objavljeno v RUNG: 18.03.2020; Ogledov: 2832; Prenosov: 85
.pdf Celotno besedilo (561,39 KB)

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