On the failure of standard completeness in Pi MTL for infinite theories
It is well-known that Hajek's basic fuzzy logic (BL), Lukasiewicz 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, Lukasiewicz, and product logic. (C) 2006 Elsevier B.V. All rights reserved.
pi mtl lukasiewicz logic product logic monoidal t-norm based logic (mtl) imtl strong standard completeness gasic fuzzy logic (bl)