The general theory developed by Ben Yaacov for metric structures provides Fraïssé limits which are approximately ultrahomogeneous. We show here that this result can be strengthened in the case of relational metric structures. We give an extra condition that guarantees exact ultrahomogenous limits. The condition is quite general. We apply it to stochastic processes, the class of diversities, and its subclass of $L_1$ diversities.

Upper ontologies have traditionally arisen from the approach in which concepts that are common across a set of domains can be axiomatized at a general level. The rationale is that reuse across domains is to be supported through specialization of the general concepts from an upper ontology. Similarly, semantic integration between ontologies is to be achieved through the general concepts they specialize. The TUpper Ontology follows an alternative approach to the conventional upper ontology paradigm. Rather than think of an (...) upper ontology as a monolithic axiomatization centred on a taxonomy, the sideways approach considers an upper ontology to be a modular ontology composed of generic ontologies that cover concepts including those related to time, process, and space. TUpper is therefore composed of a set of generic ontologies, and each generic ontology axiomatizes a particular set of generic concepts. The TUpper Ontology is designed as a top-level ontology that contains modules from the ontologies within existing international standards. (shrink)

Can you find an xy-equation that, when graphed, writes itself on the plane? This idea became internet-famous when a Wikipedia article on Tupper’s self-referential formula went viral in 2012. Under scrutiny, the question has two flaws: it is meaningless (it depends on fonts) and it is trivial. We fix these flaws by formalizing the problem.