Bilattice-based triangle provides elegant algebraic structure for reasoning with vague and uncertain information. But the truth and knowledge ordering of intervals in bilattice-based triangle can not deal with nonmonotonic reasoning and are not always intuitive. In this work, we construct an alternative algebraic structure, namely poset-based triangle and we provide with proper logical connectives for this. It as an enhancement of the bilattice-based triangle to handle nonmonotonicity in logical reasoning.
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