Kybernetika 34 no. 1, 121-134, 1998

Considering uncertainty and dependence in Boolean, quantum and fuzzy logics

Mirko Navara and Pavel Pták


A degree of probabilistic dependence is introduced in the classical logic using the Frank family of $t$-norms known from fuzzy logics. In the quantum logic a degree of quantum dependence is added corresponding to the level of noncompatibility. Further, in the case of the fuzzy logic with $P$-states, (resp. $T$-states) the consideration turned out to be fully analogous to (resp. considerably different from) the classical situation.