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Modal Logics -- RNmatrices vs. Nmatrices

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Abstract
In this short paper we will discuss the similarities and differences between two semantic approaches to modal logics - non-deterministic semantics and restricted non-deterministic semantics. Generally speaking, both kinds of semantics are similar in the sense that they employ non-deterministic matrices as a starting point but differ significantly in the way extensions of the minimal modal logic M are constructed. Both kinds of semantics are many-valued and truth-values are typically expressed in terms of tuples of 0s and 1s, where each dimension of the tuple represents either truth/falsity, possibility/non-possibility, necessity/non-necessity etc. And while non-deterministic semantics for modal logic offers an intuitive interpretation of the truth-values and the concept of modality, with restricted non-deterministic semantics are more general in terms of providing extensions of M, including normal ones, in an uniform way. On the example of three modal logics, MK, MKT and MKT4, we will show the differences and similarities of those two approaches. Additionally, we will briefly discuss (current) restrictions of both approaches.

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Please use this url to cite or link to this publication:

MLA
E. Coniglio, Marcelo, et al. “Modal Logics -- RNmatrices vs. Nmatrices.” EPTCS 415, 2024, Pp. 138-149, 2024, doi:10.4204/EPTCS.415.14.
APA
E. Coniglio, M., Pawlowski, P., & Skurt, D. (2024). Modal Logics -- RNmatrices vs. Nmatrices. EPTCS 415, 2024, Pp. 138-149. https://doi.org/10.4204/EPTCS.415.14
Chicago author-date
E. Coniglio, Marcelo, Pawel Pawlowski, and Daniel Skurt. 2024. “Modal Logics -- RNmatrices vs. Nmatrices.” EPTCS 415, 2024, Pp. 138-149. https://doi.org/10.4204/EPTCS.415.14.
Chicago author-date (all authors)
E. Coniglio, Marcelo, Pawel Pawlowski, and Daniel Skurt. 2024. “Modal Logics -- RNmatrices vs. Nmatrices.” EPTCS 415, 2024, Pp. 138-149. doi:10.4204/EPTCS.415.14.
Vancouver
1.
E. Coniglio M, Pawlowski P, Skurt D. Modal Logics -- RNmatrices vs. Nmatrices. EPTCS 415, 2024, pp 138-149. 2024;
IEEE
[1]
M. E. Coniglio, P. Pawlowski, and D. Skurt, “Modal Logics -- RNmatrices vs. Nmatrices,” EPTCS 415, 2024, pp. 138-149, 2024.
@article{01JKFQFJPFAMJGPZDF7CRMKP7A,
  abstract     = {{  In this short paper we will discuss the similarities and differences between
two semantic approaches to modal logics - non-deterministic semantics and
restricted non-deterministic semantics. Generally speaking, both kinds of
semantics are similar in the sense that they employ non-deterministic matrices
as a starting point but differ significantly in the way extensions of the
minimal modal logic M are constructed. Both kinds of semantics are many-valued
and truth-values are typically expressed in terms of tuples of 0s and 1s, where
each dimension of the tuple represents either truth/falsity,
possibility/non-possibility, necessity/non-necessity etc. And while
non-deterministic semantics for modal logic offers an intuitive interpretation
of the truth-values and the concept of modality, with restricted
non-deterministic semantics are more general in terms of providing extensions
of M, including normal ones, in an uniform way. On the example of three modal
logics, MK, MKT and MKT4, we will show the differences and similarities of
those two approaches. Additionally, we will briefly discuss (current)
restrictions of both approaches.
}},
  author       = {{E. Coniglio, Marcelo and Pawlowski, Pawel and Skurt, Daniel}},
  journal      = {{EPTCS 415, 2024, pp. 138-149}},
  language     = {{und}},
  title        = {{Modal Logics -- RNmatrices vs. Nmatrices}},
  url          = {{http://doi.org/10.4204/EPTCS.415.14}},
  year         = {{2024}},
}

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