# Multi-Valued Model Checking via Classical Model Checking

### Abstract

Multi-valued model-checking is an extension of classical model-checking to reasoning about systems with uncertain information, which are common during early design stages. The additional values of the logic are used to capture the degree of uncertainty. In this paper, we show that the multi-valued $\mu$-calculus model-checking problem is reducible to several classical model-checking problems. The reduction allows one to reuse existing model-checking tools and algorithms to solve multi-valued model-checking problems. This paper generalizes, extends and corrects previous work in this area, done in the context of 3-valued models, symbolic model-checking, and De Morgan algebras.