Fundamenta Informaticae - Volume 179, issue 3

Authors: Koprowski, Przemysław

Article Type: Research Article

Abstract: The group of singular elements was first introduced by Helmut Hasse and later it has been studied by numerous authors including such well known mathematicians as: Cassels, Furtwängler, Hecke, Knebusch, Takagi and of course Hasse himself; to name just a few. The aim of the present paper is to present algorithms that explicitly construct groups of singular and S-singular elements (modulo squares) in a global function field.

Keywords: global function fields, singular elements, square classes, Picard group

DOI: 10.3233/FI-2021-2022

Citation: Fundamenta Informaticae, vol. 179, no. 3, pp. 227-238, 2021

Authors: Lin, Zhe | Chakraborty, Mihir Kumar | Ma, Minghui

Article Type: Research Article

Abstract: Varieties of topological quasi-Boolean algebras in the vicinity of pre-rough algebras [28, 29] are expanded to residuated algebraic structures by introducing a new implication operation and its residual in these structures. Sequent calculi for some classes of residuated algebraic structures are established. These sequent calculi have the strong finite model property which yields the decidability of the word problem for corresponding classes of algebraic structures.

Keywords: Pre-rough algebra, residuation, word problem, finite model property, decidability

DOI: 10.3233/FI-2021-2023

Citation: Fundamenta Informaticae, vol. 179, no. 3, pp. 239-274, 2021

Authors: Martín Torres, Gabriela

Article Type: Research Article

Abstract: In the paper [13] Păun, Polkowski and Skowron introduce several indiscernibility relations among strings that are infinite index equivalence or tolerance relations, and study lower and upper rough approximations of languages defined by them. In this paper we develop a further study of some of these indiscernibility relations among strings. We characterize the classes defined by them, and the rough approximations of general and context free languages under them. We also compare some of the rough approximations these relations produce to the ones given by the congruences defining testable, reverse testable, locally testable, piecewise testable and commutative languages. Those yield …languages belonging to that families. Next, we modify some of the relations to obtain congruences, and study the families of languages the rough approximations under them give rise to. One of these modificated relations turns out to be the k -abelian congruence, that was defined by J. Karhumäki in [7], in the context of combinatorics on words. We show that it defines a pseudo-principal +-variety, a term defined in [9]. Our results in that work are then applied to determine when a given language has a best upper approximation in that family. Finally, we make some comments on the accuracy of the rough approximations obtained in each case. Show more

DOI: 10.3233/FI-2021-2024

Citation: Fundamenta Informaticae, vol. 179, no. 3, pp. 275-293, 2021

Authors: Wang, Longchun | Guo, Lankun | Li, Qingguo

Article Type: Research Article

Abstract: Formal Concept Analysis (FCA) has been proven to be an effective method of restructuring complete lattices and various algebraic domains. In this paper, the notion of contractive mappings over formal contexts is proposed, which can be viewed as a generalization of interior operators on sets into the framework of FCA. Then, by considering subset-selections consistent with contractive mappings, the notions of attribute continuous formal contexts and continuous concepts are introduced. It is shown that the set of continuous concepts of an attribute continuous formal context forms a continuous domain, and every continuous domain can be restructured in this way. Moreover, …the notion of F-morphisms is identified to produce a category equivalent to that of continuous domains with Scott continuous functions. The paper also investigates the representations of various subclasses of continuous domains including algebraic domains and stably continuous semilattices. Show more

Keywords: domain theory, Formal Concept Analysis, attribute continuous formal context, continuous formal concept, categorical equivalence

DOI: 10.3233/FI-2021-2025

Citation: Fundamenta Informaticae, vol. 179, no. 3, pp. 295-319, 2021