Some Implicational Semilinear Gaggle Logics: (Dual) Residuated-Connected Logics

Implicational partial Galois logics and some of their semilinear extensions, such as extensions satisfying abstract dual connection properties, have been introduced together with relational semantics. However, similar residuated, residuated properties not. This paper fills the gaps by introducing those To this end, class implicational (dual) residuated-connected prelinear gaggle is defined it verified that these are semilinear. In particular, associated contribution work, we note following two: One implications can be in logics. shows important so need to investigated The other set-theoretic semantics provided for Semilinear dealt extensively algebraic context, whereas they not yet performed one.