Adjuncts contribute to the spatiotemporal anchoring of events and situations described by linguistic expressions, while arguments describe the participants of events and situations. We show how a deterministic parser, based on the recovery of asymmetric relations, enables the identification of adjuncts as possible antecedents to pronouns, whether they are located in the domain of the sentence or in the domain of the discourse. We suggest that Information technologies and Natural language processing more generally should rely on pronominal anaphora resolution based on asymmetric agreement in order to improve their performance.