In this paper we describe a new quantification theory based on the Object Determination Logic (ODL). This theory extends the system of classical quantifiers as a system including the classical ones and linguistical ones, as well. It takes into account the typicality, as dimension of cognition. This theory represents the background of a computational model in semantical analysis of natural languages. This paper presents the basic elements of this quantification system (QSODL)and possibilities to implement it in a computational system.