Algebraic semantics for some weak Boolean logics

This paper investigates algebraic semantics for some weak Boolean (wB) logics, which may be regarded as left-continuous t-norm based logics (or monoidal t-norm based logics (MTLs)). We investigate as infinite-valued logics each of wB-LC and wB-sKD, and each corresponding first order extension $wB-LC\forall$ and $wB-sKD\forall$. We give algebraic completeness for each of them.