Related papers: Continuous Domains in Formal Concept Analysis
In this paper we establish a general framework in which the verification of support theorems for generalized convex functions acting between an algebraic structure and an ordered algebraic structure is still possible. As for the domain…
In this paper, we investigate the problem of mining numerical data in the framework of Formal Concept Analysis. The usual way is to use a scaling procedure --transforming numerical attributes into binary ones-- leading either to a loss of…
We postulate the intuitive idea of reducts of fuzzy contexts based on formal concept analysis and rough set theory. For a complete residuated lattice $L$, it is shown that reducts of $L$-contexts in formal concept analysis are…
Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…
We describe a new cognitive ability, i.e., functional conceptual substratum, used implicitly in the generation of several mathematical proofs and definitions. Furthermore, we present an initial (first-order) formalization of this mechanism…
This paper lays a practical foundation for using abstract interpretation with an abstract domain that consists of sets of quantified first-order logic formulas. This abstract domain seems infeasible at first sight due to the complexity of…
The study of Description Logics have been historically mostly focused on features that can be translated to decidable fragments of first-order logic. In this paper, we leave this restriction behind and look for useful and decidable…
We develop domain theory in constructive and predicative univalent foundations (also known as homotopy type theory). That we work predicatively means that we do not assume Voevodsky's propositional resizing axioms. Our work is constructive…
A key challenge in the legal domain is the adaptation and representation of the legal knowledge expressed through texts, in order for legal practitioners and researchers to access this information easier and faster to help with compliance…
This is the first paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In this paper, we lay the foundations for this study by introducing the…
Domain theory has its origins in Mathematics and Theoretical Computer Science. Mathematically it combines order and topology. Its central concepts have their origin in the idea of approximating ideal objects by their relatively finite or,…
This paper discusses the extension of the Prototype Verification System (PVS) sub-theory for rings, part of the PVS algebra theory, with theorems related to the division algorithm for Euclidean rings and Unique Factorization Domains that…
Concrete domains have been introduced in the context of Description Logics to allow references to qualitative and quantitative values. In particular, the class of $\omega$-admissible concrete domains, which includes Allen's interval…
This is an account of the characterization of database dependencies with Formal Concept Analysis.
Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements &…
Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This…
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by convex regions in this space. After…
Traditional category theory is typically based on set-theoretic principles and ideas, which are often non-constructive. An alternative approach to formalizing category theory is to use E-category theory, where hom sets become setoids. Our…
The present paper proposes a novel way to unify Rough Set Theory and Formal Concept Analysis. Our method stems from results and insights developed in the algebraic theory of modal logic, and is based on the idea that Pawlak's original…
We develop an axiomatic framework for fractal analysis and fractal number theory grounded in hierarchies of definability. Central to this approach is a sequence of formal systems F_n, each corresponding to a definability level S_n contained…