## On the failure of standard completeness in $$\Pi$$MTL for infinite theories.(English)Zbl 1117.03032

Summary: It is well-known that Hájek’s basic fuzzy logic (BL), Łukasiewicz logic, and product logic are not strongly standard complete. On the other hand, Esteva and Godo’s monoidal t-norm-based logic (MTL) and its involutive extension IMTL are strongly standard complete. In this paper we show that $$\Pi$$MTL (an extension of MTL by the axioms characteristic of product logic) does not enjoy the strong standard completeness theorem like BL, Łukasiewicz, and product logic.

### MSC:

 03B52 Fuzzy logic; logic of vagueness 03B50 Many-valued logic
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### References:

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