Related papers: Relational lattices via duality
Discovery of (strong) association rules, or implications, is an important task in data management, and it finds application in artificial intelligence, data mining and the semantic web. We introduce a novel approach for the discovery of a…
Based on the complete-lattice approach, a new Lagrangian duality theory for set-valued optimization problems is presented. In contrast to previous approaches, set-valued versions for the known scalar formulas involving infimum and supremum…
In this paper using the connections between some subvarieties of residuated lattices, we investigated some properties of the lattice of ideals in commutative and unitary rings. We give new characterizations for commutative rings $A$ in…
In this paper, a question due to Heckenberger, Shareshian and Welker on racks in [7] is positively answered. A rack is a set together with a selfdistributive bijective binary operation. We show that the lattice of subracks of every finite…
A class of ordered relational topological spaces is described, which we call orthomodular spaces. Our construction of these spaces involves adding a topology to the class of orthomodular frames introduced by Hartonas, along the lines of…
Analytical queries often require a mixture of relational and linear algebra operations applied to the same data. This poses a challenge to analytic systems that must bridge the gap between relations and matrices. Previous work has mainly…
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…
Part B (of a project involving four Parts) is about "bases of lines", a concept introduced by C. Herrmann and the author in the late 80's. Bases of lines attempt to describe a given modular lattice in a geometric way akin to how projective…
A lattice is a partially ordered set supporting a meet (or join) operation that returns the largest lower bound (smallest upper bound) of two elements. Just like graphs, lattices are a fundamental structure that occurs across domains…
We investigate the definability (reducts) lattice of the order of integers and describe a sublattice generated by relations 'between', 'cycle', 'separation', 'neighbor', '1-codirection', 'order' and equality'. Some open questions are…
Complemented lattices and uniquely complemented lattices are very important, not only in mathematics, but also in physics, biology, and even in social sciences. They have been investigated for a long time, especially by Huntington,…
We study the problem of enumerating Tarski fixed points on finite lattices. We derive query complexity lower bounds for finding three or more Tarski fixed points of isotone maps and the subclasses of increasing and decreasing isotone maps.…
Language models and specialized table embedding models have recently demonstrated strong performance on many tasks over tabular data. Researchers and practitioners are keen to leverage these models in many new application contexts; but…
We give a complete description of Green's D relation for the multiplicative semigroup of all n-by-n tropical matrices. Our main tool is a new variant on the duality between the row and column space of a tropical matrix (studied by Cohen,…
In this paper we pursue three aims. The first one is to apply Amitsur's relations and radicals theory to the study of the lattices Id_{A} of closed two-sided ideals of C*-algebras A. We show that many new and many well-known results about…
A periodic lattice in Euclidean space is the infinite set of all integer linear combinations of basis vectors. Any lattice can be generated by infinitely many different bases. This ambiguity was only partially resolved, but standard…
The Kripke semantics of various logics arises via categorical dualities between a category of relational frames and their maps, and a category of algebras and logical homomorphisms. When the relational frames are considered as computational…
An alternative proof of the completeness of relational algebra with respect to allowed formulas of first-order logic is presented. The proof relies on the well-known embedding of relational algebra into cylindric algebra, which makes it…
Contact Boolean algebras are one of the main algebraic tools in region-based theory of space. T. Ivanova provided strong motivations for the study of merely semilattices with a contact relation. Another significant motivation for…
In relational approach to general rough sets, ideas of directed relations are supplemented with additional conditions for multiple algebraic approaches in this research paper. The relations are also specialized to representations of general…