In this paper we propose a new approach to Categorial Grammars based on Combinatory Logic to solve some syntactic and semantic problems in the Korean language processing. We handle particularly the problems of cases, free word order structure and coordination by developing a formalism of the extended Categorial Grammar that was originally introduced by J.-P. Desclés, and I. Biskri. We call this extended Categorial Grammar “Applicative and Combinatory Categorial Grammar (ACCG)”. The ACCG formalism allows us to analyze syntactically and semantically the cases in Korean, in particular the linguistic phenomenon of double cases. In spite of the importance of the cases in the processing of the Korean language, this topic has not been well studied in view to its automatic processing and there are still many difficulties in parsing Korean texts. This article shows some robust solutions for the analysis of the free word order structure and of the coordination by introducing combinators, such as B, C*, Φ, of Combinatory Logic developed by H.-B. Curry and R. Feys.