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Fregean Algebraic Tableaux : Automating Inferences in Fuzzy Propositional Logic

We develop a tableau procedure for finding theorems and consequence relations of RPL△ (i.e., Lא extended with constants and a determinacy operator). RPL△ includes a large number of proposed truthfunctions for fuzzy logic. Our procedure simplifies tableaux for infinitevalued systems by incorporating an insight of Frege’s. We take formulas of the language to be names for their truth-values, which permits them to be manipulated in the tableaux as if they were algebraic variables. Hence, we call our system FAT, for Fregean Algebraic Tableaux. We have additionally developed an automated procedure for proving theorems using FAT, which we will briefly describe.