Exactly true and non-falsity logics meeting infectious onesстатья
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Дата последнего поиска статьи во внешних источниках: 8 января 2021 г.
Аннотация:In this paper, we study logical systems which represent entailment relations of two kinds. We extend the approach of finding 'exactly true' and 'non-falsity' versions of four-valued logics that emerged in series of recent works [Pietz & Rivieccio (2013). Nothing but the truth. Journal of Philosophical Logic, 42(1), 125-135; Shramko (2019). Dual-Belnap logic and anything but falsehood. Journal of Logics and their Applications, 6, 413-433; Shramko et al. (2017). First-degree entail-ment and its relatives. Studia Logica, 105(6), 1291-1317] to the case of infectious logics, namely to the case of Deutsch's logic Sfde introduced in Deutsch [Relevant analytic entailment. The Relevance Logic Newsletter, 2(1), 26-44; The completeness of S. Studia Logica, 38(2), 137-147]. The particular systems obtained in this way are S etl and S nfl. We present them in the form of sequent calculi and prove corresponding soundness and completeness theorems. We illuminate the connection between Setl , Snfl and two well-known systems, strong Kleene three-valued logic K3 and Priest's Logic of Paradox LP. This connection allows us to investigate the characterisation of the entailment relations associated with Setl and Snfl as well as to introduce the notion of 'infectious analogue' of a certain logic. We also study implicative extensions of Setl and Snfl and prove soundness and completeness theorems for them as well.