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ABSTRACT: One of the wellknown systems of para consistent logic called {\bf LFI1} is designed to be a base system in constructing evolutionary databases. This system {\bf LFI1} is proved to be a 3valued logic and also maximal relative to classical logic enriched with inconsistency operator in an obvious manner. The present paper aims to examine the system {\bf LFI1} from the viewpoint of Belnap's 4valued logic. More concretely, we develop the Belnapian 4valued system of Logics of Formal Inconsistency (LFIs) which can be seen as a natural generalization of {\bf LFI1}. As a consequence, from the viewpoint of the Belnapian logic, we obtain a formalization which contains the notion of ``normality'' instead of the constant $\perp$. On the other hand, from the viewpoint of LFIs, we lose the maximality but might be able to cope with more data in constructing databases. This is because the fourth value of the Belnapian matrix corresponds to incomplete data which cannot be dealt with in {\bf LFI1}. Our results contain an axiomatization of the Belnapian LFI, a characterization of ``normality'' in the system, and a translation result between the existing Belnapian system and the system we introduce. 2011 Database and Expert Systems Applications, DEXA, International Workshops, Toulouse, France, August 29  Sept. 2, 2011; 01/2011

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ABSTRACT: The present note offers a proof that systems developed by Majkić are
actually extensions of intuitionistic logic, and therefore not paraconsistent. Notre Dame Journal of Formal Logic 10/2010; 51(4). DOI:10.1215/002945272010032 · 0.36 Impact Factor

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ABSTRACT: In [T. Waragai and T. Shidori, “A system of paraconsistent logic that has the notion of behaving classically in terms of the law of double negation and its relation to S5”, in: Handbook of paraconsistency. London: College Publications. Studies in Logic (London) 9. Logic and Cognitive Systems, 177–187 (2007; Zbl 1230.03061)], a system of paraconsistent logic, called PCL1, which takes a similar approach to that of da Costa, is proposed. The present paper gives further results on this system and its related systems. Those results include the concrete condition to enrich the system PCL1 with the classical negation, a comparison of the concrete notion of “behaving classically” given by da Costa and by Waragai and Shidori, and a characterisation of the notion of “behaving classically” given by Waragai and Shidori. Logic and Logical Philosophy 06/2010; 19(1). DOI:10.12775/LLP.2010.006

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ABSTRACT: In [Log. Log. Philos. 15, No. 2, 99–111 (2006; Zbl 1134.03018)], J.Y. Béziau developed the paraconsistent logic Z, which is definitionally equivalent to the modal logic S5, and gave an axiomatization of the logic Z: the system HZ. In the present paper, we prove that some axioms of HZ are not independent and then propose another axiomatization of Z. We also discuss a new perspective on the relation between S5 and classical propositional logic (CPL) with the help of the new axiomatization of Z. Then we conclude the paper by making a remark on the paraconsistency of HZ. Logic and Logical Philosophy 03/2009; 17(4). DOI:10.12775/LLP.2008.017

Logic and Logical Philosophy 01/2009; 18(1).