A recent meta-analysis (Khemlani & Johnson-Laird, 2012) showed that the conclusions drawn by humans in psychological experiments about syllogistic reasoning deviate from the conclusions drawn by classical logic. Moreover, none of the current cognitive theories predictions fit the empirical data. In this paper we show how human syllogistic reasoning can be modeled under a new cognitive theory, the Weak Completion Semantics. An analysis by computational logics clarifies seven principles necessary to draw the inferences. This work contributes to a computational foundation of cognitive reasoning processes.