The notion of a non-deterministic logical matrix (where connectives are interpreted as multi-functions) extends the traditional semantics for propositional logics based on logical matrices (where connectives are interpreted as functions). This extension allows for finitely characterizing a much wider class of logics, and has proven decisive in a myriad of recent compositionality results. In this paper we show that the added expressivity brought by non-determinism also has its drawbacks, and in particular that the problem of determining whether two given finite non-deterministic matrices are equivalent, in the sense that they induce the same logic, becomes undecidable. We also discuss some workable sufficient conditions and particular cases, namely regarding rexpansion homomorphisms and bridges to calculi.

翻译：非确定性逻辑矩阵（其中联结词被解释为多值函数）的概念扩展了基于逻辑矩阵（其中联结词被解释为函数）的传统命题逻辑语义。这一扩展允许有限地表征更广泛的逻辑类，并已在近期大量可组合性结果中被证明具有决定性意义。本文证明，非确定性带来的额外表达能力也存在其弊端，特别是判定两个给定的有限非确定性矩阵是否等价（即它们导出相同逻辑）的问题成为不可判定的。我们还讨论了一些可行的充分条件和特殊情况，特别是关于可扩展同态以及与演算的桥梁关系。