ABSTRACTThe articles Maximality and Refutability Skura [. Maximality and refutability. Notre Dame Journal of Formal Logic, 45, 65–72] and Three-valued Maximal Paraconsistent Logics Skura and Tuziak [. Three-valued maximal paraconsistent logics. In Logika. Wydawnictwo Uniwersytetu Wrocławskiego] introduced a simple method of proving maximality of a given paraconsistent matrix. This method stemmed from the so-called refutation calculus, where the focus in on rejecting rather than accepting formulas. The article A Generalisation of a Refutation-related Method in Paraconsistent Logics Trybus [. A generalisation (...) of a refutation-related method in paraconsistent logics. Logic and Logical Philosophy, 27. doi:10.12775/llp.2018.002] was a first step towards generalising the method. In it, a number of 3-valued paraconsistent matrices were shown maximal. In this article we extend these results to cover a number of n-valued paraconsistent matrices using the same method. (shrink)

ABSTRACTThe paper deals with a problem posed by Mathieu Vidal to provide a formal representation for defective conditional in mathematics Vidal, M. [. The defective conditional in mathematics. Journal of Applied Non-Classical Logics, 24, 169–179]. The key feature of defective conditional is that its truth-value is indeterminate if its antecedent is false. In particular, we are interested in two explanations given by Vidal with the use of trivalent logics. By analysing a simple argument from plane geometry, where defective conditional is (...) in use, he gives two trivalent formal explanations for it. For both explanations, Vidal rigorously shows that trivalent logics cannot adequately represent defective conditional. Preserving Vidal's criteria of defective conditional ad max, we indicate some arguable points in his explanations and present an alternative explanation containing the original conjunction and disjunction in order to show that there are trivalent logics that might be an adequate formal explanation for defective conditional. (shrink)

Correspondence analysis is Kooi and Tamminga’s universal approach which generates in one go sound and complete natural deduction systems with independent inference rules for tabular extensions of many-valued functionally incomplete logics. Originally, this method was applied to Asenjo–Priest’s paraconsistent logic of paradox LP. As a result, one has natural deduction systems for all the logics obtainable from the basic three-valued connectives of LP -language) by the addition of unary and binary connectives. Tamminga has also applied this technique to the paracomplete (...) analogue of LP, strong Kleene logic \. In this paper, we generalize these results for the negative fragments of LP and \, respectively. Thus, the method of correspondence analysis works for the logics which have the same negations as LP or \, but either have different conjunctions or disjunctions or even don’t have them as well at all. Besides, we show that correspondence analyses for the negative fragments of \ and LP, respectively, are also suitable without any changes for the negative fragments of Heyting’s logic \ and its dual \ and LP). (shrink)

The paper presents the semantic model of logical content processing in the environment of tabooed sentences. Such sentences occur both in academic and colloquial discourses. They can be interpreted as infected formulas with the value of an insult. The proposed model assumes that the inferential mechanism of argumentative activities realised in discourses in the environment of such formulas is based on Bochvar's logical matrices and Kripke’s possible worlds semantic structures. This mechanism is determined by semantic consequence operators of three types. (...) The presented theory can be viewed as a formal tool for reconstructing the logical mental mechanism which stops deductive actions aiming at the development of narrative worlds in discourse practices during epistemic wars. It postulates that these practices, which occur in processes of developing science, are governed by special logical mechanisms of inference. (shrink)