An interpolant in predicate Gödel logic

Por • 12 mar, 2018 • Sección: Crítica

Matthias Baaz, Mai Gehrke, Sam van Gool

Abstract: A logic satisfies the interpolation property provided that whenever a formula Delta is a consequence of another formula Gamma, then this is witnessed by a formula Theta which only refers to the language common to Gamma and Delta. That is, the relational (and functional) symbols occurring in Theta occur in both Gamma and Delta, Gamma has Theta as a consequence, and Theta has Delta as a consequence. Both classical and intuitionistic predicate logic have the interpolation property, but it is a long open problem which intermediate predicate logics enjoy it. In 2013 Mints, Olkhovikov, and Urquhart showed that constant domain intuitionistic logic does not have the interpolation property, while leaving open whether predicate Godel logic does. In this short note, we show that their counterexample for constant domain intuitionistic logic does admit an interpolant in predicate Godel logic. While this has no impact on settling the question for predicate Godel logic, it lends some credence to a common belief that it does satisfy interpolation. Also, our method is based on an analysis of the semantic tools of Olkhovikov and it is our hope that this might eventually be useful in settling this question.

arXiv:1803.03003v1 [math.LO]

Logic (math.LO)

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