Semilinear substructural logics with the finite embeddability property

Abstract

Three semilinear substructural logics ${\mathbf{HpsUL}}_\omega ^*$, ${\mathbf{UL}}_\omega$ and ${\mathbf{IUL}}_\omega$ are constructed. Then the completeness of ${ \mathbf{UL}}_\omega$ and ${\mathbf{IUL}}_\omega$ with respect to classes of finite UL and IUL-algebras, respectively, is proved. Algebraically, non-integral ${\mathbf{UL}}_\omega$ and ${\mathbf{IUL}}_\omega$-algebras have the finite embeddability property, which gives a characterization for finite UL and IUL-algebras.