The goal of Aspect-Oriented Requirements Engineering is to identify possible crosscutting concerns, and to develop composition specifications, which can be used to reason about potential conflicts in the requirements. Recent work in AORE has moved from a syntactic approach to composition, which leads to fragile compositions and increased coupling between aspect and base concerns, to a semantic composition approach, based on semantics of the natural language itself. However, such compositions are at present only informally specified, and as such precise conflict detection between the requirements compositions is difficult. We present an approach for the formalisation of these semantic-based compositions which means that logical conflicts between compositions can be precisely identified and understood semantically. We show that the approach can be supported by off-the-shelf tools, meaning it is scalable and feasible for even large requirements specifications.