Citations of:
Add citations
You must login to add citations.


This paper presents a sound and complete fivesided sequent calculus for firstorder weak Kleene valuations which permits not only elegant representations of four logics definable on firstorder weak Kleene valuations, but also admissibility of five cut rules by proof analysis. 

Paraconsistent Weak Kleene Logic is the 3valued propositional logic defined on the weak Kleene tables and with two designated values. Most of the existing proof systems for PWK are characterised by the presence of linguistic restrictions on some of their rules. This feature can be seen as a shortcoming. We provide a cutfree calculus for PWK that is devoid of such provisos. Moreover, we introduce a Prieststyle tableaux calculus for PWK. 

In this paper, we study logical systems which represent entailment relations of two kinds. We extend the approach of finding ‘exactly true’ and ‘nonfalsity’ versions of fourvalued 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). DualBelnap logic and anything but falsehood. Journal of Logics and their Applications, 6, 413–433; Shramko et al. (2017). Firstdegree entailment and its relatives. Studia Logica, 105(6), 1291–1317] to the case (...) 

Paraconsistent weak Kleene logic is the $3$valued logic based on the weak Kleene matrices and with two designated values. In this paper, we investigate the poset of prevarieties of generalized involutive bisemilattices, focussing in particular on the order ideal generated by Α$\textrm{lg} $. Applying to this poset a general result by Alexej Pynko, we prove that, exactly like Priest’s logic of paradox, $\textrm{PWK}$ has only one proper nontrivial extension apart from classical logic: $\textrm{PWK}_{\textrm{E}}\textrm{,}$ PWK logic plus explosion. This $6$valued logic, (...) 

In this paper we discuss the extent to which conjunction and disjunction can be rightfully regarded as such, in the context of infectious logics. Infectious logics are peculiar manyvalued logics whose underlying algebra has an absorbing or infectious element, which is assigned to a compound formula whenever it is assigned to one of its components. To discuss these matters, we review the philosophical motivations for infectious logics due to Bochvar, Halldén, Fitting, Ferguson and Beall, noticing that none of them discusses (...) 