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A distinct notion in this context is that of Michie\u2019s definition of ultra-strong machine learning (USML). USML is demonstrated by a measurable increase in human performance of a task following provision to the human of a symbolic machine learned theory for task performance. A recent paper demonstrates the beneficial effect of a machine learned logic theory for a classification task, yet no existing work to our knowledge has examined the potential harmfulness of machine\u2019s involvement for human comprehension during learning. This paper investigates the explanatory effects of a machine learned theory in the context of simple two person games and proposes a framework for identifying the harmfulness of machine explanations based on the Cognitive Science literature. The approach involves a cognitive window consisting of two quantifiable bounds and it is supported by empirical evidence collected from human trials. Our quantitative and qualitative results indicate that human learning aided by a symbolic machine learned theory which satisfies a <jats:italic>cognitive window<\/jats:italic> has achieved significantly higher performance than human self learning. Results also demonstrate that human learning aided by a symbolic machine learned theory that fails to satisfy this window leads to significantly worse performance than unaided human learning.<\/jats:p>","DOI":"10.1007\/s10994-020-05941-0","type":"journal-article","created":{"date-parts":[[2021,3,11]],"date-time":"2021-03-11T21:02:36Z","timestamp":1615496556000},"page":"695-721","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["Beneficial and harmful explanatory machine learning"],"prefix":"10.1007","volume":"110","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2731-482X","authenticated-orcid":false,"given":"Lun","family":"Ai","sequence":"first","affiliation":[]},{"given":"Stephen H.","family":"Muggleton","sequence":"additional","affiliation":[]},{"given":"C\u00e9line","family":"Hocquette","sequence":"additional","affiliation":[]},{"given":"Mark","family":"Gromowski","sequence":"additional","affiliation":[]},{"given":"Ute","family":"Schmid","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,3,11]]},"reference":[{"key":"5941_CR1","doi-asserted-by":"publisher","first-page":"52138","DOI":"10.1109\/ACCESS.2018.2870052","volume":"6","author":"A Adadi","year":"2018","unstructured":"Adadi, A., & Berrada, M. 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