In language learning in the limit we investigate computable devices (learners) learning formal languages. Through the years, many natural restrictions have been imposed on the studied learners. As such, monotonic restrictions always enjoyed particular attention as, although being a natural requirement, monotonic learners show significantly diverse behaviour when studied in different settings. A recent study thoroughly analysed the learning capabilities of strongly monotone learners imposed with memory restrictions and various additional requirements. The unveiled differences between explanatory and behaviourally correct such learners motivate our studies of monotone learners dealing with the same restrictions. We reveal differences and similarities between monotone learners and their strongly monotone counterpart when studied with various additional restrictions. In particular, we show that explanatory monotone learners, although known to be strictly stronger, do (almost) preserve the pairwise relation as seen in strongly monotone learning. Contrasting this similarity, we find substantial differences when studying behaviourally correct monotone learners. Most notably, we show that monotone learners, as opposed to their strongly monotone counterpart, do heavily rely on the order the information is given in, an unusual result for behaviourally correct learners.

中文翻译：

---

在归纳推理中映射单调限制

在有限的语言学习中，我们调查了学习正式语言的可计算设备（学习者）。多年来，对学习者施加了许多自然限制。因此，单调限制总是受到特别关注，因为虽然是自然要求，但单调学习者在不同环境中学习时表现出明显不同的行为。最近的一项研究彻底分析了强单调学习者在记忆限制和各种附加要求下的学习能力。解释性和行为正确的此类学习者之间的显着差异激发了我们对处理相同限制的单调学习者的研究。当使用各种附加限制进行研究时，我们揭示了单调学习者与其强单调对应者之间的差异和相似之处。特别是，我们证明了解释性单调学习器虽然已知严格更强，但确实（几乎）保留了在强单调学习中所见的成对关系。对比这种相似性，我们发现在研究行为正确的单调学习者时存在实质性差异。最值得注意的是，我们表明单调学习者，而不是他们的强单调学习者，确实严重依赖于信息给出的顺序，对于行为正确的学习者来说，这是一个不寻常的结果。对比这种相似性，我们发现在研究行为正确的单调学习者时存在实质性差异。最值得注意的是，我们表明单调学习者，而不是他们的强单调学习者，确实严重依赖于信息给出的顺序，对于行为正确的学习者来说，这是一个不寻常的结果。对比这种相似性，我们发现在研究行为正确的单调学习者时存在实质性差异。最值得注意的是，我们表明单调学习者，而不是他们的强单调学习者，确实严重依赖于信息给出的顺序，对于行为正确的学习者来说，这是一个不寻常的结果。