An analytic calculus for quantified propositional Godel logic

摘要

We define a hypersequent calculus for Godel 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.