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The rules are suitable to be added to a system of positive free logic. The paper extends the proof of a cut elimination theorem for this system by Indrzejczak by proving the cases for the rules of<jats:italic>I<\/jats:italic>. There are also brief comparisons of the present approach to the more common one that formalises definite descriptions with a term forming operator. In the final section rules for<jats:italic>I<\/jats:italic>for negative free and classical logic are also mentioned.<\/jats:p>","DOI":"10.1007\/s11225-021-09958-x","type":"journal-article","created":{"date-parts":[[2021,8,19]],"date-time":"2021-08-19T12:04:32Z","timestamp":1629374672000},"page":"219-239","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Binary Quantifier for Definite Descriptions for Cut Free Free Logics"],"prefix":"10.1007","volume":"110","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3651-5458","authenticated-orcid":false,"given":"Nils","family":"K\u00fcrbis","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,8,19]]},"reference":[{"key":"9958_CR1","doi-asserted-by":"crossref","unstructured":"Bencivenga, E., Free logics, in D. Gabbay, and F. Guenther, (eds.), Handbook of Philosophical Logic. 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