Abstract
We define a hypersequent calculus for Gödel logic enhanced with (fuzzy) quantifiers over propositional variables. We prove soundness, completeness and cut-elimination for this calculus and provide a detailed investigation of the so-called Takeuti-Titani rule which expresses density of the ordering of truth values. Since this rule is critical from the point of view of proof search we characterize a fragment of the logic for which it can be eliminated.
This work was partially supported by the Austrian Science Fund Projects NZ29-INF and P10282-MAT, and the Max Kade Foundation.
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Baaz, M., Fermüller, C., Veith, H. (2000). An Analytic Calculus for Quantified Propositional Gödel Logic. In: Dyckhoff, R. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2000. Lecture Notes in Computer Science(), vol 1847. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10722086_12
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DOI: https://doi.org/10.1007/10722086_12
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