This chapter gives brief descriptions of six different contemporary theories of morphology, looking at their philosophical bases, their main concerns and leading questions, and where they stand on the balance between storage versus rules and on the status of the morpheme. The theories we consider are Distributed Morphology (DM), Construction Morphology (CxM), Paradigm Function Morphology (PFM), Natural Morphology (NM), Naïve Discriminative Learning (NDL), and the Lexical Semantic Framework (LSF).

This paper discusses the ways in which formal or model theoretic semantics has difficulty addressing questions of lexical semantics, specifically questions that arise in accounting for the pervasive polysemy of deverbal nominalizations like German Bemalung (painting) and English blending. Formal or model theoretic semantics has largely neglected issues in which analysis of complex words comes to the fore. I briefly review the history of model theoretic semantics and its relation to lexical semantics and illustrate the tendency for conceptual semantics to be quietly integrated into referential semantics, as, for example, in a recent article by Pross (2019). I conclude with a brief sketch of how Lieber’s (2004, 2016) Lexical Semantic Framework treats the polysemy of deverbal nominalizations.