- Author
- Marcelo E. Coniglio, Pawel Pawlowski (UGent) and Daniel Skurt
- Organization
- Project
- Abstract
- In previous publications, it was shown that finite non-deterministic matrices are quite powerful in providing semantics for a large class of normal and non-normal modal logics. However, some modal logics, such as those whose axiom systems contained the L & ouml;b axiom or the McKinsey formula, were not analyzed via non-deterministic semantics. Furthermore, other modal rules than the rule of necessitation were not yet characterized in the framework.In this paper, we will overcome this shortcoming and present a novel approach for constructing semantics for normal and non-normal modal logics that is based on restricted non-deterministic matrices. This approach not only offers a uniform semantical framework for modal logics, while keeping the interpretation of the involved modal operators the same, and thus making different systems of modal logic comparable. It might also lead to a new understanding of the concept of modality.
- Keywords
- SEMANTICS, S4, modal logics, non-deterministic semantics, swap structures, RNmatrices, decidability
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01KKDZ54Z99ZBNCR7GXFF5QE9X
- MLA
- Coniglio, Marcelo E., et al. “RNmatrices for Modal Logics.” REVIEW OF SYMBOLIC LOGIC, vol. 18, no. 3, 2025, pp. 744–74, doi:10.1017/S1755020325100737.
- APA
- Coniglio, M. E., Pawlowski, P., & Skurt, D. (2025). RNmatrices for modal logics. REVIEW OF SYMBOLIC LOGIC, 18(3), 744–774. https://doi.org/10.1017/S1755020325100737
- Chicago author-date
- Coniglio, Marcelo E., Pawel Pawlowski, and Daniel Skurt. 2025. “RNmatrices for Modal Logics.” REVIEW OF SYMBOLIC LOGIC 18 (3): 744–74. https://doi.org/10.1017/S1755020325100737.
- Chicago author-date (all authors)
- Coniglio, Marcelo E., Pawel Pawlowski, and Daniel Skurt. 2025. “RNmatrices for Modal Logics.” REVIEW OF SYMBOLIC LOGIC 18 (3): 744–774. doi:10.1017/S1755020325100737.
- Vancouver
- 1.Coniglio ME, Pawlowski P, Skurt D. RNmatrices for modal logics. REVIEW OF SYMBOLIC LOGIC. 2025;18(3):744–74.
- IEEE
- [1]M. E. Coniglio, P. Pawlowski, and D. Skurt, “RNmatrices for modal logics,” REVIEW OF SYMBOLIC LOGIC, vol. 18, no. 3, pp. 744–774, 2025.
@article{01KKDZ54Z99ZBNCR7GXFF5QE9X,
abstract = {{In previous publications, it was shown that finite non-deterministic matrices are quite powerful in providing semantics for a large class of normal and non-normal modal logics. However, some modal logics, such as those whose axiom systems contained the L & ouml;b axiom or the McKinsey formula, were not analyzed via non-deterministic semantics. Furthermore, other modal rules than the rule of necessitation were not yet characterized in the framework.In this paper, we will overcome this shortcoming and present a novel approach for constructing semantics for normal and non-normal modal logics that is based on restricted non-deterministic matrices. This approach not only offers a uniform semantical framework for modal logics, while keeping the interpretation of the involved modal operators the same, and thus making different systems of modal logic comparable. It might also lead to a new understanding of the concept of modality.}},
author = {{Coniglio, Marcelo E. and Pawlowski, Pawel and Skurt, Daniel}},
issn = {{1755-0203}},
journal = {{REVIEW OF SYMBOLIC LOGIC}},
keywords = {{SEMANTICS,S4,modal logics,non-deterministic semantics,swap structures,RNmatrices,decidability}},
language = {{eng}},
number = {{3}},
pages = {{744--774}},
title = {{RNmatrices for modal logics}},
url = {{http://doi.org/10.1017/S1755020325100737}},
volume = {{18}},
year = {{2025}},
}
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