Linear Abelian Modal Logic
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 \(\...
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| Format: | Article |
| Language: | English |
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Lodz University Press
2024-03-01
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| Series: | Bulletin of the Section of Logic |
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| Online Access: | https://czasopisma.uni.lodz.pl/bulletin/article/view/13976 |
| _version_ | 1797214540224528384 |
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| author | Hamzeh Mohammadi |
| author_facet | Hamzeh Mohammadi |
| author_sort | Hamzeh Mohammadi |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T11:15:48Z |
| format | Article |
| id | doaj.art-292aa87155b840eca736be60a2554b12 |
| institution | Directory Open Access Journal |
| issn | 0138-0680 2449-836X |
| language | English |
| last_indexed | 2024-04-24T11:15:48Z |
| publishDate | 2024-03-01 |
| publisher | Lodz University Press |
| record_format | Article |
| series | Bulletin of the Section of Logic |
| spelling | doaj.art-292aa87155b840eca736be60a2554b122024-04-11T07:51:47ZengLodz University PressBulletin of the Section of Logic0138-06802449-836X2024-03-0153112810.18778/0138-0680.2023.3013877Linear Abelian Modal LogicHamzeh Mohammadi0https://orcid.org/0000-0002-7726-3074Isfahan University of Technology, Department of Mathematical SciencesA 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.https://czasopisma.uni.lodz.pl/bulletin/article/view/13976many-valued logicmodal logicabelian logichypersequent calculuscut-elimination |
| spellingShingle | Hamzeh Mohammadi Linear Abelian Modal Logic Bulletin of the Section of Logic many-valued logic modal logic abelian logic hypersequent calculus cut-elimination |
| title | Linear Abelian Modal Logic |
| title_full | Linear Abelian Modal Logic |
| title_fullStr | Linear Abelian Modal Logic |
| title_full_unstemmed | Linear Abelian Modal Logic |
| title_short | Linear Abelian Modal Logic |
| title_sort | linear abelian modal logic |
| topic | many-valued logic modal logic abelian logic hypersequent calculus cut-elimination |
| url | https://czasopisma.uni.lodz.pl/bulletin/article/view/13976 |
| work_keys_str_mv | AT hamzehmohammadi linearabelianmodallogic |