A recent meta-analysis (Khemlani & Johnson-Laird, 2012)about psychological experiments of syllogistic reasoningdemonstrates that the conclusions drawn by human reasonersstrongly deviate from conclusions of classical logic. Moreover,none of the current cognitive theories predictions fit reliablythe empirical data. In this paper, we show how humansyllogistic reasoning can be modeled under a new cognitivetheory, the Weak Completion Semantics. Our analysis basedon computational logics identifies seven principles necessaryto draw the inferences. Hence, this work contributes to acomputational foundation of cognitive reasoning processes.