The Procedural Reasoning System (PRS) is arguably the first implementation of the Belief--Desire--Intention (BDI) approach to agent programming. PRS remains extremely influential, directly or indirectly inspiring the development of subsequent BDI agent programming languages. However, perhaps surprisingly given its centrality in the BDI paradigm, PRS lacks a formal operational semantics, making it difficult to determine its expressive power relative to other agent programming languages. This paper takes a first step towards closing this gap, by giving a formal semantics for a significant fragment of PRS. We prove key properties of the semantics relating to PRS-specific programming constructs, and show that even the fragment of PRS we consider is strictly more expressive than the plan constructs found in typical BDI languages.