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Rev. Symb. Log., 2020, Volume 13, Issue 2, Pages 416–435 (Mi rsc4)  

Belnap-Dunn modal logics: truth constants vs. truth values

S. P. Odintsova, S. O. Speranskib

a Sobolev Inst. Math., 4 Koptyug Ave., Novosibirsk 630090, Russia
b St. Petersburg State Univ., 29B Line 14th, St. Petersburg 199178, Russia

Abstract: 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-501-12019
This work was supported by the Russian Foundation for Basic Research (Project No. 18-501-12019).



English version:
DOI: https://doi.org/10.1017/S1755020319000121

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