Abstract
We construct a faithful interpretation of Łukasiewicz's logic in product logic (both propositional and predicate). Using known facts it follows that the product predicate logic is not recursively axiomatizable.
We prove a completeness theorem for product logic extended by a unary connective δ of Baaz [1]. We show that Gödel's logic is a sublogic of this extended product logic.
We also prove NP-completeness of the set of propositional formulas satisfiable in product logic (resp. in Gödel's logic).
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Baaz, M., Hájek, P., Švejda, D. et al. Embedding Logics into Product Logic. Studia Logica 61, 35–47 (1998). https://doi.org/10.1023/A:1005026229560
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DOI: https://doi.org/10.1023/A:1005026229560