The standard completeness of interval-valued monoidal t-norm based logic

In this paper we prove the strong standard completeness of interval-valued monoidal t-norm based logic (IVMTL) and some of its extensions. For other extensions we show that they are not strong standard complete. We also give a local deduction theorem for IVMTL and other extensions of interval-valued monoidal logic. Similar results are obtained for interval-valued fuzzy logics expanded with Baaz’s Delta.