In this report, three theories of transitive inference are compared as they apply to the solution of linear syllogisms: a spatial theory, a linguistic theory, and a new mixed linguistic-spatial theory. Each theory is expressed in terms of an information-processing (flow chart) model and a mathematical model that quantifies the information-processing model. The results of four experiments testing the mathematical models for their ability to account for latency data are reported, and it is shown that they overwhelmingly support the mixed theory. This support holds over varied modes of problem presentation, adjectives, sessions, and subjects. The duration of each component process in the mixed theory is estimated, and its contribution to total solution time is assessed. Then the mixed theory is shown to account for most patterns of individual-difference data. Finally, the theory is shown to be consistent with a variety of data obtained in previous investigations of transitive inference. (Fourteen tables are appended.) (Author/MAI)