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This paper aims to explain various meanings of the ‘-ko issta’ construction based on the generative mechanism of GL (Pustejovsky 1995), type coercion and co-composition. Considering the most outstanding meaning of the ‘-ko issta’ construction is the continuation of process, the basic meaning of the aspectual auxiliary predicate ‘-ko issta’ is the continuation of process. The event structure of the aspectual auxiliary predicate ‘-ko issta’ has the event structure with the default process event and the main process event because the ‘-ko issta’ construction expresses the stage-level predication. The argument structure has one individual argument and one event argument since the aspectual auxiliary predicate ‘-ko issta’ is an event function. In its qualia structure, the Agentive role is ‘event_process_occur’ predicate and the Formal role is ‘event_process_continue.’ ‘Event_process_continue’ is realized as the final state of the event, the continuation of process. The basic meaning of the ‘-ko issta’ construction can be derived by the function application of the event argument which expresses the process, the accomplishment or the reflexive headless event with the right head. Also, if the ‘-ko issta’ construction takes the degree achievement as its event argument, it means the continuation of the process. The ‘-ko issta’ construction with the degree achievement should be interpreted as the process meaning. So the event argument has to be changed to the right-headed event by type shifting operation (Rothstein 2004), a kind of type-coercion. The motivation of this type shifting is that the degree achievement consists of the partially overlapped subevents with the close relation between them. If the event argument is the ordered achievement with plural subject, quantifier or frequency adverbial, the meaning of the ‘-ko issta’ construction should be the repetition of the whole event. In this case, the event argument must be the homogeneously simple event as the whole event by the other kind of type-coercion. If the event argument belongs to the simultaneous achievement or the reflexive headless event with the left head, the ‘-ko issta’ construction means the continuation of resultant state. It implies that the aspectual auxiliary predicate ‘-ko issta’ has polysemy. So the co-composition of GL can be applied to these cases motivated by the reflexivity of the event argument and the formal role is ‘event_resultant state_continue’ in the semantic structure of the ‘-ko issta’ construction.