Back to Search
Start Over
Linear Abelian Modal Logic
- Source :
- Bulletin of the Section of Logic, Vol 53, Iss 1, Pp 1-28 (2024)
- Publication Year :
- 2024
- Publisher :
- Lodz University Press, 2024.
-
Abstract
- A many-valued modal logic, called linear abelian modal logic \(\rm {\mathbf{LK(A)}}\) is introduced as an extension of the abelian modal logic \(\rm \mathbf{K(A)}\). Abelian modal logic \(\rm \mathbf{K(A)}\) is the minimal modal extension of the logic of lattice-ordered abelian groups. The logic \(\rm \mathbf{LK(A)}\) is axiomatized by extending \(\rm \mathbf{K(A)}\) with the modal axiom schemas \(\Box(\varphi\vee\psi)\rightarrow(\Box\varphi\vee\Box\psi)\) and \((\Box\varphi\wedge\Box\psi)\rightarrow\Box(\varphi\wedge\psi)\). 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.
Details
- Language :
- English
- ISSN :
- 01380680 and 2449836X
- Volume :
- 53
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Bulletin of the Section of Logic
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.292aa87155b840eca736be60a2554b12
- Document Type :
- article
- Full Text :
- https://doi.org/10.18778/0138-0680.2023.30