AN EIGHT-VALUED PRACONSISTENT LOGIC Cover Image

AN EIGHT-VALUED PRACONSISTENT LOGIC
AN EIGHT-VALUED PRACONSISTENT LOGIC

Author(s): Norihiro Kamide
Subject(s): Philosophy, Logic
Published by: Wydawnictwo Uniwersytetu Jagiellońskiego
Keywords: paraconsistent logic; computer science

Summary/Abstract: It is known that many-valued paraconsistent logics are useful for expressing uncertain and inconsistency-tolerant reasoning in a wide range of Computer Science. Some four-valued and sixteen-valued logics have especially been well-studied. Some four-valued logics are not so ne-grained, and some sixteen-valued logics are enough ne-grained, but rather complex. In this paper, a natural eight-valued paraconsistent logic rather than four-valued and sixteen-valued logics is introduced as a Gentzen-type sequent calculus. This eight-valued logic is enough ne-grained and simpler than sixteen-valued logic. A triplet valuation semantics is introduced for this logic, and the completeness theorem for this semantics is proved. The cut-elimination theorem for this logic is proved, and this logic is shown to be decidable.

  • Issue Year: 2014
  • Issue No: 49
  • Page Range: 3-21
  • Page Count: 19
  • Language: English
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