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In the light of this, a formal system that is an extension of classical first-order logic is developed here, and is equipped with an appropriate semantics. An ontological interpretation of the new logic is then also provided, with several categories of object and notions of existence being distinguished. Last but not least, a modal version of the logic, with some interesting formal features, is proposed.<\/jats:p>","DOI":"10.1007\/s10849-023-09395-0","type":"journal-article","created":{"date-parts":[[2023,3,10]],"date-time":"2023-03-10T11:03:13Z","timestamp":1678446193000},"page":"473-487","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Names and Quantifiers: Bringing Them Together in Classical Logic"],"prefix":"10.1007","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1778-7167","authenticated-orcid":false,"given":"Jacek","family":"Pa\u015bniczek","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,3,10]]},"reference":[{"key":"9395_CR1","doi-asserted-by":"crossref","unstructured":"Akiba, K. (2018). 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