Involutive basic substructural core fuzzy logics: involutive mianorm-based logics (Q1697513)

This paper resents an inquiry into the weakest involutive mianorm-based logics \(\mathbf{IMIAL}\), which is a substructural fuzzy logic systems with mianorm-based semantics, and a variety of its possible extensions. These systems are based on involutively residuated mianorms (binary monotonic identity aggregation operations on the real unit interval \([0, 1]\)). The system \(\mathbf{IMIAL}\) is non-associative and non-commutative, and so are all its extensions. The standard completeness results for the defined logics are obtained using the Jenei-Montagna-style construction.