Entailment is undecidable in general for Separation (SL) Logic formulæ with inductive definitions, but it has been shown to be decidable [1] if the inductive rules satisfy three conditions, namely progress, connectivity and establishment. We show that entailment is undecidable if the latter condition is dropped, thus drawing a much clearer frontier for (un)decidability.

中文翻译：

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具有非建立归纳规则的符号堆分离逻辑公式的蕴涵是不可判定的

对于具有归纳定义的分离 (SL) 逻辑公式，蕴涵通常是不可判定的，但如果归纳规则满足三个条件，即进度、连通性和建立，它已被证明是可判定的 [1] 。我们表明，如果放弃后一个条件，蕴涵是不可判定的，从而为（不可）判定性绘制了更清晰的边界。