Towards arrow-theoretic semantics of ontologies: conceptories

In context of efforts of composing category-theoretic and logical methods in the area of knowledge representation we propose the notion of conceptory. We consider intersection/union and other constructions in conceptories as expressive alternative to category-theoretic (co)limits and show they have features similar to (pro-, in-)jections. Then we briefly discuss approaches to development of formal systems built on the base of conceptories and describe possible application of such system to the specific ontology.