• 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.