Реферат: The goal of this talk is to compare various modal logics based on Belnap and Dunn's paraconsistent four-valued logic FDE. One of such logics is the modal logic BK defined by S. Odintsov and H. Wansing in 2010. Its extension BS4 (a natural counterpart of S4) relates to the paraconsistent Nelson's logic N4⊥ in the same way as S4 relates to intuitionistic logic. Other versons of FDE-based modal logics are the paraconsistent modal logic KN4 by L. Goble whose non-modal base coincides with R. Brady's BD4 and the modal bilattice logic MBL introduced and investigated by A. Jung, U. Rivieccio, and R. Jansana. MBL is a generalization of BK that in its Kripke semantics makes use of a four-valued accessibility relation. On the way from BK to MBL, the Fischer Servi–style modal logic BKFS is defined as the set of all modal formulas valid under a modified standard translation into first-order FDE. To compare the expressive power of these logics having the strong negation ∼ in the language we must weaken the notion of definitional equivalence in a suitable way. It is proved, e.g., that BKFS is weakly definitionally equivalent to BK×BK and that MBL is faithfully embedded into BK×BK via a weakly structural translation.

Библиографическая ссылка: Odintsov S. , Wansing H.
FDE-Modalities and weak definability
Workshop on Proof Theory, Modal Logic and Reflection Principles 17-20 Oct 2017