Fuzzy relational equations in monoidal logics

We present a general framework for solving fuzzy relational equations in monoidal logics. This framework yields the general solution equations for relational systems based on large family of many-valued logics. The proofs use as a tool certain relational inequalities that we call BK-residuated bootstrap. First we extend to the realm of relational systems in monoidal logics the previous results concerning the BK-residuated bootstrap that were obtained by Kohout for relational inequalities based on fuzzy basic logic systems (BL) of Hajek (published in Proceedings of FUZZ-IEEE 2000) and also for relational systems based on left-continuous t-norms. Then we use the BK-residuated bootstrap for proving the results concerning relational equations. It should be noted that solutions for relational systems based on linear logics and intuitionistic logics are included as special cases.