Аннотация:
We shall be concerned with the modal logic BK-which is based on the Belnap-Dunn four-valued matrix, and can be viewed as being obtained from the least normal modal logic K by adding 'strong negation'. Though all four values 'truth', 'falsity', 'neither' and 'both' are employed in its Kripke semantics, only the first two are expressible as terms. We show that expanding the original language of BK to include constants for 'neither' or/and 'both' leads to quite unexpected results. To be more precise, adding one of these constants has the effect of eliminating the respective value at the level of BK-extensions. In particular, if one adds both of these, then the corresponding lattice of extensions turns out to be isomorphic to that of ordinary normal modal logics.
Minghui Ma, Juntong Guo, “Kripke-Completeness and Sequent Calculus for Quasi-Boolean Modal Logic”, Stud Logica, 2024
А. В. Грефенштейн, С. О. Сперанский, “О кванторной версии модальной логики Белнапа–Данна”, Матем. сб., 215:3 (2024), 37–69 [A. V. Grefenshtein, S. O. Speranski, “On the quantified version of the Belnap–Dunn modal logic”, Mat. Sb., 215:3 (2024), 37–69]
А. В. Грефенштейн, С. О. Сперанский, “О кванторной версии модальной логики Белнапа–Данна”, Матем. сб., 215:3 (2024), 37–69; A. V. Grefenshtein, S. O. Speranski, “On the quantified version of the Belnap–Dunn modal logic”, Sb. Math., 215:3 (2024), 323–354
Hao Wu, Minghui Ma, Lecture Notes in Computer Science, 13963, Logic and Its Applications, 2023, 207
С. О. Сперанский, “О модальной логике бирешёток и её расширениях”, Алгебра и логика, 60:6 (2021), 612–635; S. O. Speranski, “Modal bilattice logic and its extensions”, Algebra and Logic, 60:6 (2022), 407–424
S. Drobyshevich, D. Skurt, “Neighbourhood Semantics for FDE-Based Modal Logics”, Stud Logica, 109:6 (2021), 1273
CARLO NICOLAI, JOHANNES STERN, “THE MODAL LOGICS OF KRIPKE–FEFERMAN TRUTH”, J. symb. log., 86:1 (2021), 362
Yuanlei Lin, Minghui Ma, “Belnap–Dunn Modal Logic with Value Operators”, Stud Logica, 109:4 (2021), 759
Igor Sedlár, Ondrej Majer, Synthese Library, 418, New Essays on Belnap-Dunn Logic, 2019, 293