We introduce the functor ◦∗ which assigns to every metric space X its symmetric join ◦∗X . As a set, ◦∗X is a union of intervals connecting ordered pairs of points in X . Topologically, ◦∗X is a natural quotient of the usual join of X with itself. We define an Isom(X)–invariant metric d∗ on ◦∗X . Classical concepts known for H and negatively curved manifolds are defined in a precise way for any...

Abstract We study (strictly) join irreducible varieties in the lattice of subvarieties residuated lattices. explore connections with well-connected algebras and suitable generalizations, focusing particular on representable varieties. Moreover, we find weakened notions Halldén completeness that characterize irreducibility. strictly basic hoops use generalized rotation construction to $\mathsf{M...

We supply an upper bound on the distinguishing chromatic number of certain infinite graphs satisfying an adjacency property. Distinguishing proper n-colourings are generalized to the new notion of distinguishing homomorphisms. We prove that if a graph G satisfies the connected existentially closed property and admits a homomorphism to H, then it admits continuum-many distinguishing homomorphism...

In this paper, we study the local propagation method used in Bayesian net for belief updating from a relational database perspective. We point out and prove that the renowned local propagation method is in fact a (generalized) semi-join program used in relational database for answering database queries. This interesting connection implies and suggests that the task of belief updating can be rec...