When we want to translate Japanse sentences into English, we have some difficulties in understanding why some concepts that are literally related to space can be used to refer to time in quite different ways. In this paper, the author mainly considers why some vertical or horizontal spatial expressions can be used to refer to time and how metaphorical concepts can be constructed appropriately in a certain situation in the framework of the cognitive pragmatics (i.e. Relevance Theory). He argues that the Relevance-theoretic Ad hoc concept construction approach to metaphor is superior to other cognitive approaches, because if we adopt Ad hoc concept construction account, we need no special principles or processes in order to explain loan concept metaphor, TIME IS SPACE metaphor and some grammaticalization processes. Metaphor is a natural outcome of some very general abilities and processes used in verbal communication. Other cognitive approaches such as Lakovian conceptual metaphor account ignore the problems with interpretation processes. They only describe the results of interpretation. In short, Relevance Theory can account for the interpretation processes of various meaning changes in a principled way.