We investigate concrete acquisition theories for a derived approach to linking theory development and explore to what extent two prominent linking theories in the syntactic literature--UTAH and rUTAH--can be derived from the data that English-learning children encounter. We leverage a conceptual acquisition framework that specifies key aspects of the child's acquisition task, including realistic child-directed input and a cognitively motivated mechanism for inference (the sufficiency threshold, derived from the Tolerance and Sufficiency Principles). We find that rUTAH can be derived but UTAH can't, if children derive their linking theories from their input as specified here. We discuss the implications of these results for both syntactic theory and acquisition theory.