Mianorm-based logics with n-contraction and n-mingle axioms

This paper investigates standard completeness for substructural fuzzy logics based on mianorms with n-contraction and n-mingle axioms. For this, first, right and left n-contractive and n-mingle logic systems based on mianorms, their corresponding algebraic structures, and their algebraic completeness results are discussed. Next, completeness with respect to algebras whose lattice reduct is [0, 1], known as standard completeness, is established for these systems via Yang's construction in the style of Jenei-Montagna. Finally, further standard completeness results are introduced for their fixpointed involutive extensions.