This paper provides a system capable of analyzing the combinatorics of a wide range of conventionally implicated and expressive constructions in natural language via an extension of Potts's (2005) L_CI logic for supplementary conventional implicatures. In particular, the system is capable of analyzing objects of mixed conventionally implicated/expressive and at-issue type, and objects with conventionally implicated or expressive meanings which provide the main content of their utterances. The logic is applied to a range of constructions and lexical items in several languages. doi:10.3765/sp.3.8 BibTeX info