Existing accounts of syllogistic reasoning oppose rule-based and model-based methods. Stenning and Oberlander (1995) show that the latter are isomorphic to well-known graphical methods, when these are correctly interpreted. We here extend these results by showing that equivalent sentential implementations exist, thus revealing that all these theories are members of a family of abstract individual identification algorithms variously implemented in diagrams or sentences. This abstract logical analysis suggests a novel individual identification task for observing syllogistic reasoning processes. Comparison of the results of this task with the Standard Task confirms that the tasks are psychologically closely related, throwing light on sources of error, on subjects' sensitivity to metalogical properties, and on term-ordering phenomena. Since it avoids posing the subtask of formulating a quantified conclusion, the new task allows comparison of explanations of problem difficulty in terms of the number of models (e.g., Johnson-Laird & Bara, 1984) with alternatives in terms of the difficulty of choosing a quantifier for the conclusion. Logical concepts of source and conditional premisses provide a comprehensive account of term order data, including figural effects, at a level abstract with regard to imagistic or sentential representations. These results argue that much richer empirical evidence will be required to discriminate phenomenologically distinct reasoning processes than has hitherto been supposed.