Linear Abelian Modal Logic - Mohammadi, Hamzeh (Bulletin of the Section of Logic, 2023)
A many-valued modal logic, called linear abelian modal logic \(LK(A) \) is introduced as an extension of the abelian modal logic \(K(A)\). Abelian modal logic \(K(A)\) is the minimal modal extension of the logic of lattice-ordered abelian groups. The logic \(LK(A)\) is axiomatized by extending \(K(A)\) with the modal axiom schemas \((φψ)→(φψ)\) and \((φψ)→(φψ)\). Completeness theorem with respect to algebraic semantics and a hypersequent calculus admitting cut-elimination are established. Finally, the correspondence between hypersequent calculi and axiomatization is investigated.