{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:55:40Z","timestamp":1760057740001,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,23]],"date-time":"2025-02-23T00:00:00Z","timestamp":1740268800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Centre","award":["2021\/43\/B\/HS1\/03187"],"award-info":[{"award-number":["2021\/43\/B\/HS1\/03187"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>With his research on Aristotle\u2019s syllogistic, Jan \u0141ukasiewicz initiates the branch of logic known as the calculus of names. This field deals with axiomatic systems that analyse various fragments of the logic of names, i.e., that branch of logic that studies various forms of names and functors acting on them, as well as logical relationships between sentences in which these names and functors occur. In this work, we want not only to present the genesis of the calculus of names and its first system created by \u0141ukasiewicz, but we also want to deliver systems that extend the first. In this work, we will also show that, from the point of view of modern logic, \u0141ukasiewicz\u2019s approach to the syllogistic is not the only possible one. However, this does not diminish \u0141ukasiewicz\u2019s role in the study of syllogism. We believe that the calculus of names is undoubtedly the legacy of \u0141ukasiewicz.<\/jats:p>","DOI":"10.3390\/axioms14030160","type":"journal-article","created":{"date-parts":[[2025,2,24]],"date-time":"2025-02-24T05:36:47Z","timestamp":1740375407000},"page":"160","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Calculus of Names\u2014The Legacy of Jan \u0141ukasiewicz"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9133-5081","authenticated-orcid":false,"given":"Andrzej","family":"Pietruszczak","sequence":"first","affiliation":[{"name":"Department of Logic, Nicolaus Copernicus University, 87-100 Toru\u0144, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,23]]},"reference":[{"key":"ref_1","unstructured":"Presburger, M. (1929). 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