Forward refutation for Gödel-Dummett Logics

We propose a refutation calculus to check the unprovability of a formula in Gödel-Dummett logics. From refutations we can directly extract countermodels for unprovable formulas, moreover the calculus is designed so to support a forward proof-search strategy that can be understood as a top-down construction of a model

Gödel-Dummett counter-models through matrix computation

We present a new method for deciding Gödel-Dummett logic. Starting from a formula, it proceeds in three steps. First build a conditional graph based on the decomposition tree of the formula. Then try to remove some cycles in this graph by instantiating these boolean conditions. In case this is possible, extract a countermodel from such an instance graph. Otherwise the initial formula is provable. We emphasize on cycle removal through matrix computation, boolean constraint solving and counter-model extraction. Key words: Counter-models, conditional graphs and matrices.