Conditions for logical contextuality and nonlocality

Contextuality and nonlocality are nonclassical properties exhibited by quantum statistics whose implications profoundly impact both the foundations applications of theory. In this paper we provide some insights into logical contextuality inequality-free proofs. The former can be understood as possibility version contextuality, while latter refers to proofs that not based on violations noncontextuality (or Bell) inequality. By ``possibilistic'' mean a description in terms possibilities for outcomes, which Boolean variables assuming value one when corresponding probability is strictly larger than zero otherwise. present work aims build bridge between these two concepts from what call possibilistic paradoxes, sets conditions occurrence implies nonlocality. As main result, demonstrate existence paradoxes necessary sufficient condition very important class scenarios. Finally, discuss interesting consequences arising completeness paradoxes.