Semantically Inactive Multiplicatives and Words as Types

The literature on categorial type logic includes proposals for semantically inactive additives, quantifiers, and modalities Morrill (1994[17]), Hepple (1990[2]), Moortgat (1997[9]), but to our knowledge there has been no proposal for semantically inactive multiplicatives. In this paper we formulate such a proposal (thus filling a gap in the typology of categorial connectives) in the context of the displacement calculus Morrill et al. (2011[16]), and we give a formulation of words as types whereby for every expression w there is a corresponding type W(w). We show how this machinary can treat the syntax and semantics of collocations involving apparently contentless words such as expletives, particle verbs, and (discontinuous) idioms. In addition, we give an account in these terms of the only known examples treated by Hybrid Type Logical Grammar (HTLG henceforth; Kubota and Levine 2012[4]) beyond the scope of unaugmented displacement calculus: gapping of particle verbs and discontinuous idioms.