Residuated skew lattices with modal operator

Abstract

In this paper, we define modal operators in residuated skew lattices and prove some fundamental properties of monotone modal operators on residuated skew lattices (RSL). We prove that the composition of two modal operators is a modal operator if and only if they commute. We investigate strong modal operators in RSL and get a characterization of them. Deductive systems under a modal operator are investigated.

Keywords

• (normal) residuated skew lattice
• modal operator
• strong modal operator
• primary 03g10
• secondary 06a75, 06b20, 03b75