Do semantic modal maps have a role in a constructionalization approach to modals?

My aim in this paper is to show that, in modified form, semantic connectivity maps of the kind developed in van der Auwera & Plungian (1998) and van der Auwera (2013) can be useful for showing the development over time of relationships among polysemous constructions. Since these maps pertain primarily to meaning and are intended as contributions to cross-linguistic generalizations rather than to language-specific grammars, their purpose might seem orthogonal to construction grammar, in which form–meaning pairs are the basic units of grammar. I propose that the semantic maps can usefully be rethought as being of two kinds: schema-construction maps that represent relationships between abstract, conceptual schemas linked to underspecified form, and micro-construction maps that represent relationships between specific constructions. These two kinds of maps capture both form and meaning since they represent form–meaning pairings, but at different levels of abstraction. They can also capture direction of changes, as tendencies at the schema level and specific trajectories at the micro-level. My case study is the development of the marginal modals better, rather, sooner (see Denison & Cort 2010, van der Auwera & De Wit 2010). I show that better is significantly different in distribution and meaning from rather and sooner, and that, although they form a family of micro-constructions, they do not form a tight-knit group. This can be captured well by modified semantic maps.