  This work is the first to propose the concept of a semantic numeration system
(SNS) as a certain class of context-based numeration methods. The development
of the SNS concept required the introduction of fundamentally new concepts such
as a cardinal abstract entity, a cardinal semantic operator, a cardinal
abstract object, a numeration space and a multicardinal number. The main
attention is paid to the key elements of semantic numeration systems - cardinal
semantic operators. A classification of semantic numeration systems is given.
