Related papers: Boolean Substructures in Formal Concept Analysis
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…
Taking an algebraic perspective on the basic structures of Rough Concept Analysis as the starting point, in this paper we introduce some varieties of lattices expanded with normal modal operators which can be regarded as the natural rough…
For a partially ordered set P, we denote by Co(P) the lattice of order-convex subsets of P. We find three new lattice identities, (S), (U), and (B), such that the following result holds. Theorem. Let L be a lattice. Then L embeds into some…
The notion of an internal preneighbourhood space on a finitely complete category with finite coproducts and a proper $(\mathsf{E}, \mathsf{M})$ system such that for each object $X$ the set of $\mathsf{M}$-subobjects of $X$ is a complete…
Notions of ordinal submodularity/supermodularity have been introduced and studied in the literature. We consider several classes of ordinally submodular functions defined on finite Boolean lattices and give characterizations of the set of…
We determine all composition-closed equational classes of Boolean functions. These classes provide a natural generalization of clones and iterative algebras: they are closed under composition, permutation and identification…
We devise exact conditions under which a join semilattice with a weak contact relation can be semilattice embedded into a Boolean algebra with an overlap contact relation, equivalently, into a distributive lattice with additive contact…
We analyse various structural and order-theoretical aspects of abstract separation systems and partial lattices, as well as the relationship between the different submodularity conditions one can impose on them.
The notion of a complete Boolean algebra, although completely legitimate in constructive mathematics, fails to capture some natural structures such as the lattice of subsets of a given set. Sambin's notion of an overlap algebra, although…
We start from two closure operators defined on the elements of a special kind of partially ordered sets, called causal nets. Causal nets are used to model histories of concurrent processes, recording occurrences of local states and of…
The Blackboard Architecture provides a mechanism for storing data and logic and using it to make decisions that impact the application environment that the Blackboard Architecture network models. While rule-fact-action networks can…
Sachs showed that a Boolean algebra is determined by its lattice of subalgebras. We establish the corresponding result for orthomodular lattices. We show that an orthomodular lattice L is determined by its lattice of subalgebras Sub(L), as…
We think about what the subscheme of the formal scheme is. Differently form the ordinary scheme, the formal scheme has different notions of ``subscheme''. We lay a foundation for these notions and compare them. We also relate them to…
Boolean spaces with internal semigroups generalize profinite semigroups and are pertinent for the recognition of not-necessarily regular languages. Via recognition, the study of existential quantification in logic on words amounts to the…
We investigate computability in the lattice of equivalence relations on the natural numbers. We mostly investigate whether the subsets of appropriately defined subrecursive equivalence relations -for example the set of all polynomial-time…
Dualization of a monotone Boolean function on a finite lattice can be represented by transforming the set of its minimal 1 to the set of its maximal 0 values. In this paper we consider finite lattices given by ordered sets of their meet and…
A Concept Tree is a structure for storing knowledge where the trees are stored in a database called a Concept Base. It sits between the highly distributed neural architectures and the distributed information systems, with the intention of…
Natural language contexts display logical regularities with respect to substitutions of related concepts: these are captured in a functional order-theoretic property called monotonicity. For a certain class of NLI problems where the…
The purpose of this short communication is to make some observations on the connections between various existing formulas of counting the number of sublattices of a fixed index in an $n$-dimensional lattice and their connection with the…
Necessary and sufficient conditions allowing a previously unknown space to be explored through scanning operators are reexamined with respect to measure theory. Generalized conceptions of distances and dimensionality evaluation are…