Positive logics are $\{ \wedge , \vee , \to \}$-fragments of intermediate logics. It is clear that the positive fragment of $Int$ is not structurally complete. We give a description of all hereditarily structurally complete positive logics, while the question whether there is a structurally complete positive logic which is not hereditarily structurally complete, remains open.

中文翻译：

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遗传结构完整的正逻辑

积极的逻辑是$\{ \wedge , \vee , \to \}$- 中间逻辑的片段。很明显，正片断$INT$结构不完整。我们描述了所有遗传上结构完整的实证逻辑，而是否存在结构上不完整的遗传上结构完备的实证逻辑的问题仍然悬而未决。