Geodesic
Some remarks on Došen's logic $\mathsf{N}$ and its extensions
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 562-577 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper collects some observations about Došen's logic $\mathsf{N}$, where negation is treated as a modal operator, and its extensions. We shall see what happens when we add the contraposition axiom to several important extensions of $\mathsf{N}$, show that certain extensions of $\mathsf{N}$ are canonical, and also revisit the method of filtration.
Keywords: modal negation, intuitionistic modal logic, Heyting–Ockham logic, Hype, Routley star. 
@article{SEMR_2022_19_2_a1,
     author = {S. O. Speranski},
     title = {Some remarks on {Do\v{s}en's} logic $\mathsf{N}$ and its extensions},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {562--577},
     year = {2022},
     volume = {19},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a1/}
}
TY  - JOUR
AU  - S. O. Speranski
TI  - Some remarks on Došen's logic $\mathsf{N}$ and its extensions
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2022
SP  - 562
EP  - 577
VL  - 19
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a1/
LA  - en
ID  - SEMR_2022_19_2_a1
ER  - 
%0 Journal Article
%A S. O. Speranski
%T Some remarks on Došen's logic $\mathsf{N}$ and its extensions
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2022
%P 562-577
%V 19
%N 2
%U http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a1/
%G en
%F SEMR_2022_19_2_a1
S. O. Speranski. Some remarks on Došen's logic $\mathsf{N}$ and its extensions. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 562-577. http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a1/

[1] N. Bezhanishvili, A. Colacito, D. de Jongh, “A study of subminimal logics of negation and their modal companions”, Language, Logic, and Computation, Proceedings of the 12th International Tbilisi Symposium, LNCS, 11456, eds. A. Silva et al., Springer, 2019, 21–41 | MR

[2] P. Cabalar, S.P. Odintsov, D. Pearce, “Logical foundations of well-founded semantics”, Proceedings KR 2006, eds. P. Doherty (ed.) et al., AAAI Press, 2006, 25–35

[3] K. Došen, “Negation as a modal operator”, Rep. Math. Logic, 20 (1986), 15–28 | MR | Zbl

[4] S.A. Drobyshevich, S.P. Odintsov, “Finite model property for negative modalities”, Sib. Élektron. Mat. Izv., 10 (2013), 1–21 | MR | Zbl

[5] A.P. Hazen, Is even minimal negation constructive?, Analysis, Oxf., 55:2 (1995), 105–107 | DOI | MR | Zbl

[6] H. Leitgeb, “HYPE: a system of hyperintensional logic (with an application to semantic paradoxes)”, J. Philos. Log., 48:2 (2019), 305–405 | DOI | MR | Zbl

[7] G.C. Moisil, “Logique modale”, Disqu. Math. Phys., Bucuresti, 2 (1942), 3–98 | MR | Zbl

[8] S.P. Odintsov, H. Wansing, “Routley star and hyperintensionality”, J. Philos. Log., 50:1 (2021), 33–56 | DOI | MR | Zbl

[9] S.P. Odintsov, “Combining intuitionistic connectives and Routley negation”, Sib. Èlektron. Mat. Izv., 7 (2010), 21–41 | MR | Zbl

[10] K. Segerberg, “Propositional logics related to Heyting's and Johansson's”, Theoria, 34:1 (1968), 26–61 | DOI | MR

[11] S.O. Speranski, “Negation as a modality in a quantified setting”, J. Log. Comput., 31:5 (2021), 1330–1355 | DOI | MR | Zbl

[12] D. Vakarelov, “Consistency, completeness and negation”, Paraconsistent Logics. Essays on the Inconsistent, eds. G. Priest (ed.) et al., Philosophia Verlag, München etc, 1989, 238–363 | Zbl