NDLI: Some Observations on the Systems LFI1 and LFI1

Content Provider	IEEE Xplore Digital Library
Author	Omori, H. Waragai, T.
Copyright Year	2011
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.
Starting Page	320
Ending Page	324
File Size	163809
Page Count	5
File Format	PDF
ISBN	9781457709821
ISSN	15294188
DOI	10.1109/DEXA.2011.77
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-08-29
Publisher Place	France
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Databases Complexity theory Educational institutions Semantics Electronic mail Conferences Logics of Formal Inconsistency paraconsistent logic Belnap's 4-valued logic
Content Type	Text
Resource Type	Article

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