Pronouns are a typical realization of Presuming reference in text, but Presuming reference has a range of realizations (Martin, 1992). In order to resolve anaphora in discourse, all instances of Presuming reference first need to be identified. One obstruction to extending resolution of anaphora to realizations beyond pronouns is the influential concept of bridging (Clark, 1977), a type of inference which posits a distinction between direct reference, including pronouns, and indirect reference. This paper outlines objections to bridging, and recommends that semantic relations, including repetition, superordination and composition (e.g. meronymy), better explain referential ties than bridging. This reinterpretation positions anaphora in the system of Presuming reference under the semantic category of repetition. Adopting a centering approach (Strube and Hahn, 1999) within a systemic-functional framework of discourse semantics, the resolution of Presuming reference is enabled by semantic relations. Consequently, anaphora, as realizations of Presuming reference, can be resolved through a range of sense relations. Examples of text analysis are provided with quantitative results. Suggestions for incorporating computational tools such as Word-net demonstrate the applicability of the model to computational implementation.