• Title/Summary/Keyword: Baaz projection and its variant

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Weakening-free fuzzy logics with the connective Δ (II): a variant of Baaz projection

  • Yang, Eunsuk
    • Korean Journal of Logic
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    • v.16 no.1
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    • pp.1-15
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    • 2013
  • Yang [12] investigated weakening-free fuzzy logics expanded by the delta connective $\Delta$, which can be interpreted as Baaz's projection and its generalizations. In this paper, we keep investigating such logics with an alternative delta connective $\Delta$, which can be regarded as a variant of the Baaz projection. The main difference is that although our new $\Delta$ satisfies many properties of Baaz projection, it can nether be interpreted as Baaz's projection itself nor its generalizations. For this, we first introduce several weakening-free fuzzy logics with the alternative connective $\Delta$. The algebraic structures corresponding to the systems are then defined, and their algebraic completeness is proved.

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Algebraic completeness results for sKD and its Extensions

  • Yang, Eun-Suk
    • Korean Journal of Logic
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    • v.9 no.1
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    • pp.1-29
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    • 2006
  • This paper investigates algebraic semantics for sKD and its extensions $sKD_\triangle$, $sKD\forall$, and $sKD\forall{_\triangle}$: sKD is a variant of the infinite -valued Kleene- Diense logic KD; $sKD_\triangle$ is the sKD with the Baaz's projection A; and $sKD\forall$ and $sKD\forall{_\triangle}$: are the first order extensions of sKD and $sKD_\triangle$, respectively. I first provide algebraic completeness for each of sKD and $sKD_\triangle$. Next I show that each $sKD\forall$ and $sKD\forall{_\triangle}$: is algebraically complete.

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