A variety of probabilistic models to quantify the likelihood of steam-explosion-induced (α-mode) containment failure from core melt accidents in commercial light water reactors have been proposed in the past. In many respects, these models and associated mechanistic considerations were complementary. Based on this and taking into account recent research efforts in this area, we perceived a need to consolidate a common approach. A new probabilistic framework is proposed for this purpose. Quantification of all inputs required by this framework is carried out, with the support of three companion parts of the study, for the case of a low-pressure core melt scenario in a pressurized water reactor (neglecting multiple explosions). The results support the generally prevalent expectation that steam explosions do not pose a significant threat to containment. To fully appreciate the qualitative limitations on this result all four parts must be carefully studied.