The main aim of this paper is to propose an appropriate logical system that is suitable to describe the notion of IS-A link as well as is-a link. The most important point to be realized is that those relations are not set thoretical ones. They connect two `general names' to construct a proposition, so that what is needed for proper descriptions of the relations in question is a theory of general names. It will be shown that is-a is a logical unit of axiomatically determined behaviour. The axiom concerning is-a relation was established by S. Lesniewski who named his theory of general names ontology. Today `ontology' has also become a common term for AI researchers. I intend to make it clear that there is a close connection between `ontology' used by Lesniewski and by AI researchers, even though they developed quite independently. I wish to stress that ontology created by Lesniewski is a system of syllogistic equipped with singular propositions and the theory of quantification. To make this point clear, I proposed a fragment of syllogism that I called MO(minimal ontology). This paper includes comments and examples articulating the logical power of ontology.