Formal concept analysis has grown from a new branch of the mathematical field of lattice theory to a widely recognized tool in Computer Science and elsewhere. In order to fully benefit from this theory, we believe that it can be enriched with notions such as approximation by computation or representability. The latter are commonly studied in denotational semantics and domain theory and captured most prominently by the notion of algebraicity, e.g. of lattices. In this paper, we explore the notion of algebraicity in formal concept analysis from a category-theoretical perspective. To this end, we build on the the notion of approximable concept with a suitable category and show that the latter is equivalent to the category of algebraic lattices. At the same time, the paper provides a relatively comprehensive account of the representation theory of algebraic lattices in the framework of Stone duality, relating well-known structures such as Scott information systems with further formalisms from logic, topology, domains and lattice theory.
Computational and Categorical Frameworks of Finite Ternary $Γ$-Semirings: Foundations, Algorithms, and Industrial Modeling Applications
Government College (A), Rajahmundry, A.P., India（政府学院（A），拉贾姆恩德拉，安得拉邦，印度）；Department of Mathematics, Acharya Nagarjuna University, Guntur, A.P., India（阿查里亚·纳加朱纳大学数学系，贡土尔，安得拉邦，印度）；Government College For Women(A), Guntur, Andhra Pradesh, India（女子政府学院（A），贡土尔，安得拉邦，印度）
An Algebraic Extension of Intuitionistic Linear Logic: The $L_!^S$-Calculus and Its Categorical Model
Université de Lorraine, CNRS, Inria, LORIA（洛林大学、法国国家科学研究中心、法国国家信息与自动化研究所、洛林研究与信息学院）；Universidad Nacional de Quilmes, DCyT（基尔梅斯国立大学、计算机与信息技术系）；Universidad de Buenos Aires, DC, FCEyN（布宜诺斯艾利斯大学、计算系、经济与理学院）；Universidad de Buenos Aires-CONICET, ICC（布宜诺斯艾利斯大学-阿根廷国家科学研究委员会、计算中心）；Universidad de la República–MEC, PEDECIBA（共和国大学-教育部、PEDECIBA）；Universidad de la República, IMERL, FIng（共和国大学、IMERL、工程学院）
