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Publications (3)0.43 Total impact

  • Hitoshi Omori, Toshiharu Waragai
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    ABSTRACT: One of the well-known 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 3-valued 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 4-valued logic. More concretely, we develop the Belnapian 4-valued 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
  • Hitoshi Omori, Toshiharu Waragai
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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 01/2010; 51(4). · 0.43 Impact Factor
  • Hitoshi Omori, Toshiharu Waragai
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    ABSTRACT: In (1) Béziau developed the paraconsistent logic Z, which is def- initionally equivalent to the modal logic S5 (cf. Remark 2.3), 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 ax- iomatization of Z. We also discuss a new perspective on the relation between S5 and classical propositional logic (CPL) with the help of the new axiom- atization of Z. Then we conclude the paper by making a remark on the paraconsistency of HZ.