Graph-based Decision for Gödel-Dummett Logics

We present a graph-based decision procedure for Gödel-Dummett logics and an algorithm to compute countermodels. A formula is transformed into a conditional bicolored graph in which we detect some specific cycles and alternating chains using matrix computations. From an instance graph containing no such cycle, (resp. no (n + 1)-alternating chain) we extract a countermodel in LC, (resp. LCn).

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