Simplification of Many-Valued Logic Formulas Using Anti-Links

We present the theoretical foundations of the many-valued generalization of a technique for simplifying large non-clausal formulas in propositional logic, that is called removal of anti-links. Possible applications include computation of prime implicates of large non-clausal formulas as required, for example, in diagnosis. With the anti-link technique, one does not compute any normal form of a given formula; rather, one removes certain forms of redundancy from formulas in negation normal form (NNF). Its main advantage is that no clausal normal form has to be computed in order to remove redundant parts of a formula. In this paper, we deene an anti-link operation on a generic language for expressing many-valued logic formulas called signed NNF and we show that all interesting properties of two-valued anti-links generalize to the many-valued setting, although in a non-trivial way.