Containment logics: Algebraic Counterparts and Reduced Models

The containment companion of a logic vdash consists of the consequence relation r which satisfies all the inferences of where the variables of the conclusion are contained into those of the set of premises, in case this is not inconsistent. Following the algebraic analysis started in Bonzio and Pra Baldi (2021, Studia Logica, 109, 969-994), this paper characterizes the algebraic counterpart of a finitary containment logic r and investigates the structure of the Leibniz and Suszko reduced models. The analysis is carried within the framework of abstract algebraic logic.Mathematics Subject Classification: Primary: 03G27. Secondary: 03G25