Related papers: Relational reasoning in the region connection calc…
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 algebra is one of the main tools in the region-based theory of space. It is an extension of Boolean algebra with a relation called contact. The elements of the Boolean algebra are considered as formal representations of physical…
The question of characterizing the (finite) representable relation algebras in a ``nice" way is open. The class $\mathbf{RRA}$ is known to be not finitely axiomatizable in first-order logic. Nevertheless, it is conjectured that ``almost…
Formal Concept Analysis and its associated conceptual structures have been used to support exploratory search through conceptual navigation. Relational Concept Analysis (RCA) is an extension of Formal Concept Analysis to process relational…
Analyzing relational languages by their logical expressiveness is well understood. Something not well understood or even formalized is the vague concept of relational query patterns. What are query patterns? And how can we reason about…
The Region Connection Calculus (RCC) is a well-known calculus for representing part-whole and topological relations. It plays an important role in qualitative spatial reasoning, geographical information science, and ontology. The…
Let $\mathcal{A}$ be a separable nuclear C*-algebra, and $\mathcal{B}$ be a nonunital separable simple $\mathcal{Z}$-stable C*-algebra. Continuing the work from Gabe-Lin-Ng, we classify all essential extensions, with large complement, of…
We investigate the computational properties of the spatial algebra RCC-5 which is a restricted version of the RCC framework for spatial reasoning. The satisfiability problem for RCC-5 is known to be NP-complete but not much is known about…
This paper introduces a novel method for merging open-domain terminological knowledge. It takes advantage of the Region Connection Calculus (RCC5), a formalism used to represent regions in a topological space and to reason about their…
Given a finite tensor category $\ca$, an exact indecomposable $\ca$-module category $\Mo$, and a tensor subcategory $\Do\subseteq \ca^*_\Mo$, we describe a way to produce \textit{exact} commutative algebras in the center $Z(\ca)$, measuring…
A non-self-adjoint operator algebra is said to be residually finite dimensional (RFD) if it embeds into a product of matrix algebras. We characterize RFD operator algebras in terms of their matrix state space, and moreover show that an…
Relational concept analysis (RCA) is an extension of formal concept analysis allowing to deal with several related contexts simultaneously. It has been designed for learning description logic theories from data and used within various…
We employ the theory of canonical extensions to study residuation algebras whose associated relational structures are functional, i.e., for which the ternary relations associated to the expanded operations admit an interpretation as…
Let C be a finite dimensional algebra of global dimension at most two. A partial relation extension is any trivial extension of C by a direct summand of its relation C-C-bimodule. When C is a tilted algebra, this construction provides an…
We give a purely algebraic treatment of reduction theory for connections over the formal punctured disc. Our proofs apply to arbitrary connected linear algebraic groups over an algebraically closed field of characteristic 0. We also state…
Inspired by the perspective of Reyes' noncomutative spectral theory, we attempt to develop noncommutative algebraic geometry by introducing ringed coalgebras, which can be thought of as a noncommutative generalization of schemes over a…
We analyse the fusion of representations of the triplet algebra, the maximally extended symmetry algebra of the Virasoro algebra at c=-2. It is shown that there exists a finite number of representations which are closed under fusion. These…
Connectivity is a homotopy invariant property of separable C*-algebras which has three notable consequences: absence of nontrivial projections, quasidiagonality and a more geometric realization of KK-theory for nuclear C*-algebras using…
We define a ternary Relation Algebra (RA) of relative position relations on two-dimensional directed lines (d-lines for short). A d-line has two degrees of freedom (DFs): a rotational DF (RDF), and a translational DF (TDF). The…
Given a finite dimensional algebra $C$ (over an algebraically closed field) of global dimension at most two, we define its relation-extension algebra to be the trivial extension $C\ltimes \Ext_C^2(DC,C)$ of $C$ by the $C$-$C$-bimodule…