Strong next-time operators for multiple-valued mu-calculus

Multiple-valued logics [2] provide an interesting alternative to classical boolean logic for modeling and reasoning about systems. By allowing additional truth values, they support the explicit modeling of uncertainty and disagreement. In order to do temporal reasoning over multiple-valued systems, we must extend a classical temporal logic to the multiple-valued case. For instance, the branchingtime temporal logic CTL is a fragment of the modal calculus [5]: it has conjunction, disjunction, negation, two next-time operators, weak (EX) and strong (AX) [4], and several additional temporal operators described as least or greatest fixpoints. For example, the property , “eventually may become true”, is the least fixpoint: