<p>In recent probabilistic seismic hazard analyses (PSHA), the logic-tree framework has become a widely used approach to systematically represent epistemic uncertainties associated with the input models and parameters. While numerous studies have examined the fundamental principles behind constructing and organizing logic trees, none have provided a detailed and explicit formulation for the computation of end-branch weights and seismic hazards within the overall framework. This limitation becomes particularly important when multiple seismic sources contribute to the total hazard at a site, making the aggregation of epistemic uncertainties more complex. To address this gap, the present study introduces a clear and mathematically rigorous formulation for the calculation of end branch weights, the evaluation of hazard contributions from multiple sources, and the derivation of the combined seismic hazard at a given site. The proposed formulation aims to provide both transparency and consistency in the representation and computation of epistemic uncertainties in PSHA studies.</p>