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Modular non-deterministic semantics for T, TB, S4, S5 and more

Pawel Pawlowski (UGent) and Elio La Rosa
(2022) JOURNAL OF LOGIC AND COMPUTATION. 32(1). p.158-171
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Abstract
In this paper, a modular approach for non-deterministic semantics for (non-normal) modal logics is developed. In particular, our aim is to improve and reinterpret some results from Omori and Shirt (2016, IfCoLog J. Logics Appl., 3, 815-845) and Coniglio et al. (2015, J. Appl. Non-Class. Log., 25, 20-45) regarding modal systems T, TB, S4 and S5. More economical axiomatizations make the rule of necessitation modular, thus providing non-deterministic semantics for (NEC)-free fragments for all the investigated systems. Moreover, by fixing the interpretation of all connectives but the modal ones, a combinatorial outlook at their matrices is provided to the effect that a new modal system and simplification of those for T and S4 are achieved.
Keywords
MODAL SEMANTICS, LOGICS

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MLA
Pawlowski, Pawel, and Elio La Rosa. “Modular Non-Deterministic Semantics for T, TB, S4, S5 and More.” JOURNAL OF LOGIC AND COMPUTATION, vol. 32, no. 1, 2022, pp. 158–71, doi:10.1093/logcom/exab079.
APA
Pawlowski, P., & La Rosa, E. (2022). Modular non-deterministic semantics for T, TB, S4, S5 and more. JOURNAL OF LOGIC AND COMPUTATION, 32(1), 158–171. https://doi.org/10.1093/logcom/exab079
Chicago author-date
Pawlowski, Pawel, and Elio La Rosa. 2022. “Modular Non-Deterministic Semantics for T, TB, S4, S5 and More.” JOURNAL OF LOGIC AND COMPUTATION 32 (1): 158–71. https://doi.org/10.1093/logcom/exab079.
Chicago author-date (all authors)
Pawlowski, Pawel, and Elio La Rosa. 2022. “Modular Non-Deterministic Semantics for T, TB, S4, S5 and More.” JOURNAL OF LOGIC AND COMPUTATION 32 (1): 158–171. doi:10.1093/logcom/exab079.
Vancouver
1.
Pawlowski P, La Rosa E. Modular non-deterministic semantics for T, TB, S4, S5 and more. JOURNAL OF LOGIC AND COMPUTATION. 2022;32(1):158–71.
IEEE
[1]
P. Pawlowski and E. La Rosa, “Modular non-deterministic semantics for T, TB, S4, S5 and more,” JOURNAL OF LOGIC AND COMPUTATION, vol. 32, no. 1, pp. 158–171, 2022.
@article{8746786,
  abstract     = {{In this paper, a modular approach for non-deterministic semantics for (non-normal) modal logics is developed. In particular, our aim is to improve and reinterpret some results from Omori and Shirt (2016, IfCoLog J. Logics Appl., 3, 815-845) and Coniglio et al. (2015, J. Appl. Non-Class. Log., 25, 20-45) regarding modal systems T, TB, S4 and S5. More economical axiomatizations make the rule of necessitation modular, thus providing non-deterministic semantics for (NEC)-free fragments for all the investigated systems. Moreover, by fixing the interpretation of all connectives but the modal ones, a combinatorial outlook at their matrices is provided to the effect that a new modal system and simplification of those for T and S4 are achieved.}},
  author       = {{Pawlowski, Pawel and La Rosa, Elio}},
  issn         = {{0955-792X}},
  journal      = {{JOURNAL OF LOGIC AND COMPUTATION}},
  keywords     = {{MODAL SEMANTICS,LOGICS}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{158--171}},
  title        = {{Modular non-deterministic semantics for T, TB, S4, S5 and more}},
  url          = {{http://doi.org/10.1093/logcom/exab079}},
  volume       = {{32}},
  year         = {{2022}},
}
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