LINEAR ABELIAN MODAL LOGIC

A many-valued modal logic, called linear abelian modal logicLK(A) is intro-duced as an extension of the abelian modal logicK(A). Abelian modal logicK(A) is the minimal modal extension of the logic of lattice-ordered abeliangroups. The logicLK(A) is axiomatized by extendingK(A) with the modalaxiom schemas square(phi boolean OR psi)->(square phi boolean OR square psi) and (square phi boolean AND square psi)->square(phi boolean AND psi). Complete-ness theorem with respect to algebraic semantics and a hypersequent calculusadmitting cut-elimination are established. Finally, the correspondence betweenhypersequent calculi and axiomatization is investigated