Categorical properties of intuitionistic fuzzy groups

The category theory deals with mathematical structures and relationships between them. Categories now appear in most branches of mathematics and in some areas of theoretical computer science and mathematical physics, and acting as a unifying notion. In this paper, we study the relationship between the category of groups and the category of intuitionistic fuzzy groups. We prove that the category of groups is a subcategory of category of intuitionistic fuzzy groups and that it is not an Abelian category. We establish a function β : Hom(A, B) → [0; 1] × [0; 1] on the set of all intuitionistic fuzzy homomorphisms between intuitionistic fuzzy groups A and B of groups G and H, respectively. We prove that β is a covariant functor from the category of groups to the category of intuitionistic fuzzy groups. Further, we show that the category of intuitionistic fuzzy groups is a top category by establishing a contravariant functor from the category of intuitionistic fuzzy groups to the lattices of all intuitionistic fuzzy groups.

The Category Of Quantitativeness In Modern Linguistics

The article under discussion depicts the issues of the category of quantitativeness in modern linguistics. The author of the article examines separate parts of speech representing quantitative semantics and describes general categorical properties of quantification as a grouping of lexico-grammatical units of the natural language. Particular attention is paid to numerals and their pragmatic possibilities.

On a Covariant Functor v in the Category R - of Compact Tychonov Spaces and their Continuous Mappings into Itself

This note defines a covariant functor V: ТуchТусh acting on the category of Tychonov spaces and continuous mappings into itself. Studying the topological and categorical properties of this functor V, it is shown that the functor V is a normal functor in the category R - of compact spaces and continuous mappings into itself, which is a subcategory of Тусh . It is proved that the functor V: ТуchТусh is an open functor, in the considered category R - of compact spaces and continuous mappings into yourself.

Particular Semantic and Syntactic Properties of Polyfunctional Lexeme LI

The object of the article is a non-descriptive lexeme. Its use is investigated in various semantic-syntactic and communicativepragmatic contexts. The relevance of the work is due to the need for amore holistic description of a number of primitive linguistic units (a, and, either, or, etc.), the categorical properties of which are not fully and systematically identified within the framework of traditional methods of analysis. The novelty of the work lies in the consideration of all uses within the framework of the functioning of the lexeme-particular of the same name. This approach is due to the principles of nonparadigmatic linguistics — a modern trend in the study of primitive lexemes. The theoretical significance of the work lies in the introduction into scientific circulation of the principles of the analysis of a particular li based on its ancient categorical properties associated with the semantics of conjecture. It has been established that in all the considered contexts we are dealing with the same particular lexeme, which retains its original categorical properties in them. They are manifested in the questioningness of li (direct or indirect), as well as in various hypothetical meanings that are realized in sentences-statements at a deep syntactic level. Asimilar description technique is applicable to the analysis of the properties of other particular units of the Russian language.

Towards a Unitary Case for Russellian Panpsychism

One of the most pressing challenges that occupy the Russellian panpsychist’s agenda is to come up with a way to reconcile the traditional argument from categorical properties (Seager Journal of Consciousness Studies, 13(10–11), 129–145, 2006; Alter & Nagasawa, 2015) with H. H. Mørch’s dispositionalism-friendly argument from the experience of causation (2014, Topoi, 39, 1073–1088, 2018, 2020) — on the way to a unitary, all-encompassing case for the view. In this regard, Mørch claims that, via the commitment to the Identity theory of properties, one can consistently hold both panpsychist arguments without contradiction (2020: 281) — I shall refer to such proposal as Reconciliation. In my paper, I shall argue that this is not the case. To this extent, I will first consider H. Taylor’s argument that the Identity theorists have the exact same resources as the dispositionalists (as, after careful enquiry, their views on the metaphysics of properties turn out to coincide (Philosophical Studies, 175, 1423–1440, 2018: 1438)), and thus contend that Reconciliation fails to obtain. Then, I will suggest that one can avoid the problem and reconcile the arguments by adopting a different version of the powerful qualities view, namely the Compound view — and thus advance a reformulated version of the claim, i.e. Reconciliation*. Finally, even though pursuing my proposed solution might expose Russellian panpsychism to the risk of epiphenomenalism, I shall conclude that such specific form of epiphenomenalism is a rather benign one, and thus that, via Reconciliation*, the constitution of a unitary case for panpsychism as a positive proposal (and not as a mere alternative to dualism and physicalism) can be achieved.

Through war miles to the truths of Russian speech (to the 100th anniversary of the birth of V. P. Zhukov)

The article briefly highlights the life path and scientific heritage of Vlas Platonovich Zhukov (1921– 1991), Doctor of Philology, Professor, Honoured Scientist of the RSFSR, one of the leading phraseologists in Russia. The constructive pillars of the scholar’s concept consisted in two oppositions: 1) a phraseological unit and a word 2) a word and a component of a phraseological unit. In line with this direction and using the method of phraseological application, a whole complex of fundamental problems can be solved: the originality of the phraseological meaning in comparison with the lexical meaning, the sign properties of the components, the typology of accompanying words, the differentiation of synonymy and variance of phraseological units, the role of evaluativity in the formation of the semantics of a phraseological unit and its categorical properties, etc. The author’s main theoretical provisions were successfully implemented in his textbooks, teaching aids and dictionaries.

The categorical relationships between neighborhood spaces, ┬-neighborhood spaces and stratified L-neighborhood spaces

In this paper, for a complete residuated lattice L, we present the categorical properties of ?-neighborhood spaces and their categorical relationships to neighborhood spaces and stratified L-neighborhood spaces. The main results are: (1) the category of ?-neighborhood spaces is a topological category; (2) neighborhood spaces can be embedded in ?-neighborhood spaces as a reflective subcategory, and when L is a meet-continuous complete residuated lattice, ?-neighborhood spaces can be embedded in stratified L-neighborhood spaces as a reflective subcategory; (3) when L is a continuous complete residuated lattice, neighborhood spaces (resp., ?-neighborhood spaces) can be embedded in ?-neighborhood spaces (resp., stratified L-neighborhood spaces) as a simultaneously reflective and coreflective subcategory.