Metaphors have been attracting much attention of many linguists since the publication of Lakoff and Johnson (1980). The study of metaphors is also an important topic for the computation since it represents a creative language use, which cannot be captured by simple rules. This paper focuses on the theoretical aspects of metaphors, which constitutes a fundamental research for computational modeling of the creative use of language. One of the important theoretical issues in the theory of metaphor is that of grounding, i.e. the reason metaphors exist or are possible. I will discuss the different ways of grounding metaphors in the theory of cognitive linguistics. In addition to co-occurrence as the grounding for metaphors, which was argued in Lakoff and Johnson (1980), Grady (1997), Lakoff and Johnson (1999) and others, I will argue that there are two other ways of grounding metaphors: grounding based on structural, image-schematic similarity and that based on evaluative similarity. It is further argued that the interaction among different groundings is not only possible but also necessary to make metaphors more refined.
Lakoff and Johnson (1980) drastically changed the way metaphors are viewed. Its insightful claim can be roughly summarized in the following two points. First, it claimed and evidenced that the metaphor is not just a figure of speech but it is about conceptual domains. Conventionally, metaphors had been thought as about words, but Lakoff and Johnson (1980) demonstrated that metaphors are rooted in the human cognitive and conceptual system. Secondly, it downplayed the importance of similarity and emphasized the importance of co-occurrence as the grounding for metaphors. Conventionally, metaphors had been thought possible because the two things are similar, but Lakoff and Johnson (1980) pointed out that similarity is a vague notion and also demonstrated that similarity is not always necessary in forming metaphors.
The second issue, which is about the grounding for metaphors, also known as grounds, experiential basis or motivation for metaphors, is what makes the metaphor possible and is a key issue to a theory of metaphor. The cognitive linguistics research following Lakoff and Johnson (1980) all placed emphasis on the co-occurrence as the grounding (Lakoff and Turner, 1989, Lakoff, 1990, Lakoff, 1993 and others). Primary metaphor theory, the most recent theory of metaphors in cognitive linguistics (Grady et al., 1996, Grady, 1997) pushed this to extremes and claimed that all important metaphors had co-occurrence as their groundings. Examples of co-occurrence basis for metaphors can be seen in (1)-(3).

(1) a. Metaphor: MORE IS UP
b. Grounding: The correlation between quantity and level in piles, fluids in containers, etc.
(2) a. Metaphor: UNDERSTANDING IS SEEING
b. Grounding: The correlation between visual perception and the conscious awareness of information.
(3) a. Metaphor: ACHIEVING A PURPOSE IS ARRIVING AT A DESTINATION
b. Grounding: The correlation between achieving a purpose and moving to a spatial location.

The present paper claims, to the contrary to the claim of the primary metaphor theory, that the grounding for metaphors does not have to be co-occurrence. Two other ways that metaphors can be grounded will be shown, namely, structural similarity and evaluative similarity, with ample examples in English and Japanese.
On the issue of the structure of domains, Lakoff (1990) stated the relationship between the structure of the source domain and that of the target domain in his paper on the Invariance Hypothesis (4a). It was later developed into Invariance Principle (Lakoff, 1993), by adding (4b).

(4) a. Metaphorical mappings preserve the cognitive topology (that is, the image-schema structure) of the source domain,
b. in a way consistent with the inherent structure of the target domain.

Notice that neither Lakoff (1990) nor Lakoff (1993) states that the structural correspondence (in his words, the cognitive topology or image-schema structure) itself can be the grounding for metaphors. The present paper will demonstrate that the structural similarity can actually ground metaphors. This will be shown using five sets of examples: metaphors using expressions of fluids in Japanese and English, metaphors of life in English, metaphors relating to force dynamics, metaphorical expressions using twins in Japanese and English and the expressions using piston in Japanese. The other way of grounding metaphors that will be discussed in this paper is evaluative similarity. It is claimed that a clearly positive or negative evaluation facilitates the use and understanding of metaphors. To achieve this, the status of evaluative meaning and the history of linguistic research on the evaluative meaning will be reviewed. Then the evaluative meaning will be defined and a test to discern the evaluative meaning will be devised. Finally, ample examples of metaphors grounded by evaluative similarity will be shown. In summary, this paper claims that there are at least three types of grounding for metaphors.

i. Co-occurrence
ii. Structural similarity
iii. Evaluative similarity

Examples of the interplay of different groundings will also be shown. This study about the grounding for metaphors is important to the theory of metaphors and should also be a vital foundation for researching and making computational model of metaphors.

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