This paper provides the foundations of a uni-fied cognitive decision-making framework (QulBIT)which is derived from quantum theory. The mainadvantage of this framework is that it can caterfor paradoxical and irrational human decision mak-ing. Although quantum approaches for cognitionhave demonstrated advantages over classical prob-abilistic approaches and bounded rationality mod-els, they still lack explanatory power. To addressthis, we introduce a novel explanatory analysis ofthe decision-maker’s belief space. This is achievedby exploiting quantum interference effects as a wayof both quantifying and explaining the decision-maker’s uncertainty. We detail the main modulesof the unified framework, the explanatory analy-sis method, and illustrate their application in situ-ations violating the Sure Thing Principle.