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International Conference on Knowledge Science, Engineering and Management

KSEM 2018: Knowledge Science, Engineering and Management pp 89–101Cite as

Another Useful Four-Valued Logic

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11062))

Abstract

We propose a four-valued logic with intuitive semantics by the connectives that is useful for understanding the contradictions in knowledge representation. The intuitive semantics reflects that any assertion has dual character by whose information for or against the judgment. The four-valued logic is weakly paraconsistent and has the weak consistency to capture whether or not the contradictions are reconcilable with information. The four-valued logic is a normal extension of classical logic in a sense that it contains the schemata of classical axioms. We then propose an axiomatization of the four-valued logic. The soundness and completeness of the axiomatization with respect to the semantics are proved. The usefulness of the four-valued logic is discussed.

The work is supported in part by Natural Science Fund of China under numbers 61672049/61732001 and Advance Programs Fund of Ministry of Education of China.

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Notes

  1. 1.

    In classical logic, the material implication means that “if A, then B” is equal to “not A, or B”. The concept of material implication in F can be viewed as a natural extension from that in classical logic, that is, “if A, then B” is equal to “the opposite of A, or B”. That is, “\(v(A) \in D\) implies \(v(B) \in D\)” is equal to “\(v(A) \not \in D\), or \(v(B) \in D\)”.

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Authors and Affiliations

  1. Department of Information Science, School of Mathematical Science, Peking University, Beijing, 100871, China

    Zuoquan Lin & Zhaocong Jia

Authors
  1. Zuoquan Lin
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  2. Zhaocong Jia
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Correspondence to Zuoquan Lin .

Editor information

Editors and Affiliations

  1. University of Bristol, Bristol, United Kingdom

    Weiru Liu

  2. Università di Trento, Povo, Italy

    Fausto Giunchiglia

  3. Jilin University, Changchun, China

    Bo Yang

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Lin, Z., Jia, Z. (2018). Another Useful Four-Valued Logic. In: Liu, W., Giunchiglia, F., Yang, B. (eds) Knowledge Science, Engineering and Management. KSEM 2018. Lecture Notes in Computer Science(), vol 11062. Springer, Cham. https://doi.org/10.1007/978-3-319-99247-1_9

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  • DOI: https://doi.org/10.1007/978-3-319-99247-1_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99246-4

  • Online ISBN: 978-3-319-99247-1

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