A model is a set of theoretical propositions that tells you how something is organized and works. For metaphor in language use, researchers in linguistics, psychology, and interaction need models that conceptualizes how metaphors are produced and comprehended in utterances in discourse events. This modelling typically starts with comprehension.

The generally dominant model for all utterance comprehension in discourse is Van Dijk & Kintsch’s Construction-Integration model. This conceptualizes utterances as linearly and hierarchically ordered sets of meaning units that are represented in four distinct, interacting, and evolving mental representations of utterances and their roles in the growing overall representation of the discourse event. The distinction between language use and discourse and their multiple interactions is crucial for a solid model of metaphor.

DMT has elaborated the CI model for utterance comprehension in discourse in terms of (a) four dimensions of all metaphor in language use in discourse, which correspond with the four mental models. This has yielded the beginning of an inventory of metaphor properties that produce a multi-dimensional taxonomy. The contrast between deliberate and non-deliberate metaphor use is the main value of one of the four dimensions.

DMT is also working on (b) the role of these metaphors in the discourse event by assuming that there are genre-driven constraints for the function of language in the text in the code in the context of the discourse event. This also affects the structure, function, and effect of the metaphorical elements in the utterances. Again, deliberate versus non-deliberate metaphor use is one of the metaphor properties that is influenced by this interaction.

DMT holds that metaphor in both language use and discourse generates a problem of incoherence if it is taken as a metaphor. This occurs when the intended sense of the metaphor-related expression comes from a different conceptual domain than the rest of the utterance. Then this incoherence requires resolution by analogy (or cross-domain mapping), which includes figurative comparison in order to comprehend the utterance in the discourse. Metaphor does not generate a problem of incoherence if it is not taken as a metaphor, that is, when its intended sense is not based in some source domain, for then it is resolved by lexical disambiguation.

Given the findings of contemporary metaphor research, DMT posits that structurally most metaphor is ambiguous between the possibilities of taking it as a metaphor or not, because most metaphor is based in metaphorically motivated polysemy. This leads the possibility of ambivalent metaphor use and to the paradox of metaphor, since most metaphor does not need to be taken metaphorically for comprehension. DMT also holds that the priority of taking one route (deliberate metaphor) or the other (non-deliberate metaphor) in comprehending a metaphorical expression is affected by distinct aspects of discourse aspects that have to do with the genre-specific properties of the text in the code in the context of the discourse event.