The purpose of this paper is to explore the syntactic criteria for determining a secondary predicates as a predicate modifier or a conjunction, and to formalize the semantic aspects of the [-ke] structure as a predicate in Korean. Syntactically, the [-ke] structure is considered to be a secondary predicate when the shared arguments appear in both the [-ke] structure and the main verb structure. On the other hand, if they do not appear in both structures, the [-ke] structure is considered to be a connective element. Semantically the [-ke] structure has numerous aspects such as depictives, resultatives, objectivity, and emphasis. The depictives of the secondary predicate can be formalize as $p{wedge}q$ where p represents a propositional expression of the secondary predicate and q is a propositional expression of the main verb. Resultatives have the logical form $q{ ightarrow}{Box}p$, because the consequence has to always be true. However, objectivity has the logical form $q{ ightarrow}{diamondsuit}p$, because the consequence can be either true or false. Emphasis is represented as $q{ ightarrow}p{uparrow}$ because the secondary predicate represents the polarity of the event.