In the context of the cognitive study of diagrammatic representations for deductive reasoning, the availability of syntactic manipulation of diagrams has played a key role in accounting for their efficacy. Currently, however, little has been known about the interface between such syntactic or proof-theoretical aspects and the corresponding semantic or informational aspects of diagram use. The present paper investigates the cognitive processes of interpreting diagrammatic representations underlying deductive reasoning, combining the insights from both logical and cognitive studies of diagrams. A semantical analysis of two different ways of formalizing logic diagrams is provided. Based on it, a multiple stage model of cognitive processes of extracting information from logic diagrams is proposed, and evidence was found to support this model. A consequence for the way the abstract syntax and semantic of diagrammatic representations are constrained is also explored.