Generalised state descriptions for strong first-degree entailment logic extensions

The article proposes a number of generalised state description semantics for certain Dunn—Belnap logic extensions. The extensions under investigation include the Rivieccio—Pietz (ETL) and Shramko—Zaitsev—Belikov (NFL) logics. Generalised state descriptions form the basis for defining entailment relations that enable us to formalise the corresponding logics.

References
[1] Dunn J.M., Restall G. Relevance logic. Handbook of philosophical logic. Springer Netherlands, 2002, рр. 1–128.
[2] Dunn J.M. Partiality and its dual. Studia Logica, 2000, vol. 66, no. 1, pp. 5–40.
[3] Voyshvillo E.K. Filosofsko-metodologicheskie aspekty relevantnoy logiki [Phiolosophical and methodological aspects of relevance logic]. Moscow, Editorial URSS Publ., 2011, 139 p.
[4] Smirnova E.D. Logika i filosofiya [Logic and philosophy]. Moscow, ROSSPEN; Russian Political Encyclopedia Press, 1996, 304 p.
[5] Pietz A., Rivieccio U. Nothing but the Truth. Journal of Philosophical Logic. 2013, no. 42, рр. 125–135.
[6] Marcos J. The value of the two values. In: Logic without Frontiers: Festschrift for Walter Alexandre Carnielli on the Occasion of his 60th Birthday (Tributes). J.Y. Beziau, M.E. Coniglio, eds. College Publications, 2011, pp. 277–294.
[7] Shramko Y., Zaitsev D., Belikov A. First-degree entailment and its relatives. Studia Logica, 2017, vol. 105, no. 6, рр. 1291–1347.