Abstract: The relationships between various modal logics based on Belnap and Dunn’s paraconsistent four-valued logic FDE are investigated. It is shown that the paraconsistent modal logic BK□, which lacks a primitive possibility operator ◊, is definitionally equivalent with the logic BK, which has both and ◊ as primitive modalities. Next, a tableau calculus for the paraconsistent modal logic KN4 introduced by L. Goble is defined and used to show that KN4 is definitionally equivalent with BK□ without the absurdity constant. Moreover, a tableau calculus is defined for 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. It is shown that MBL can be faithfully embedded into the bimodal logic BK□ × BK□ over the non-modal vocabulary of MBL. 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, and BKFS is shown to be characterized by the class of all models for BK□ × BK□. Moreover, BKFS is axiomatized and this axiom system is proved to be strongly sound and complete with respect to the class of models for BK□ x BK□. Moreover, the notion of definitional equivalence is suitably weakened, so as to show that BKFS and BK□ × BK□ are weakly definitionally equivalent. © Springer Science+Business Media B.V. 2017.

Cite: Odintsov S.P. , Wansing H.
Disentangling FDE-based paraconsistent modal logics
Studia Logica. 2017. V.105. N6. P.1221-1254. DOI: 10.1007/s11225-017-9753-9 WOS Scopus OpenAlex

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Web of science:	WOS:000415716400008
Scopus:	2-s2.0-85029773059
OpenAlex:	W2758805975

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Scopus	37
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Web of science	32

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