The semantics of local cases in the framework of the theoryof cognitive linguistics has got an internal organization in the formof a matrix of cognitive domains, wherein each of them demonstratesthe schematization of the choice of some concrete situation. The zonesof its crossing indicate on the parts of the transition from one domainto another. Partial usages of cases belonging to transitional parts areperipheral in respect to prototypical ones. Space has got the centralplace in the matrix of cognitive domains being the basic cognitivefield for all local cases. Anyway, all the other cognitive domains aresomehow connected with space having got more or less similaritywith it. I’m trying to perform a matrix of cognitive domains for spatialcases of the Komi language analogically with the analysis of cognitivedomains of external local cases in the Estonian language (see Vainik1995).