The goal of Aspect-Oriented Requirements Engineering (AORE) is to identify possible crosscutting concerns, and to develop composition specifications around those concerns. These compositions can be used to reason about potential conflicts in the requirements and to relate requirements to architecture in semantically meaningful ways. 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 formal reasoning about the requirements and the subsequent derivations are difficult. We present a formal approach to these semantic-based compositions which facilitates this reasoning. We show that the approach especially lends itself to identifying conflicts between requirements and mapping compositions to a derived architecture.