Murray's primary research is in the semantics and pragmatics of natural language, specifically what sorts of formal representations are needed to analyze a variety of linguistic structures across grammatically diverse languages. Topics she has worked on include evidentiality, modality, plurality, connectives, sentential mood, and speech acts.
Murray's research combines formal theories of meaning and discourse with documentation and analysis of understudied languages. She is interested in language documentation, methodology for elicitation, community-based language work, and how linguists can be allies for language revitalization and reclamation. She has worked with the Cheyenne community in Southeastern Montana since 2006 on a variety of language projects. She is also the director of the Cornell Language Documentation Lab.
Crosslinguistic semantics and pragmatics, dynamic semantics, philosophy of language, cognitive science, language documentation, methodology for semantic elicitation, Cheyenne and other Algonquian languages