The syllogism is a system of reasoning that has been both used and investigated in psychology. The syllogism has many components and defining characteristics. Four basic models of form representation (spatial, linguistic, mixed, and algorithmic) used for linear syllogisms are briefly described. Debate concerning the processes that subjects use in solving syllogisms has led to the formulation of process models. It proposed model for linear syllogisms provides a way to break down the stages of syllogistic problem solving in order to predict performance. Many factors have been shown to affect or influence subjects' performance in syllogistic reasoning. Two historical hypotheses concerning sources of error are the atmosphere, or global impression, of the syllogism--and the conversion hypothesis--which emphasizes illicit processes subjects use in solving syllogisms. Other sources of error include figure effects (syllogisms in certain figures are more difficult than others) and personal bias (one's personal beliefs and attitudes influence performance on syllogisms that are emotion laden or of a controversial nature). Formal rules with which to test the validity of categorical syllogisms are proposed as guidelines for syllogism task construction, and suggestions for experimental design are presented. Keywords: Cognitive psychology; Performance testing; Syllogisms; Reasoning.