{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:28Z","timestamp":1753894408469,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,4,4]]},"abstract":"<jats:p>We incorporate strong negation in the theory of computable functionals TCF, a common extension of Plotkin's PCF and G\\&amp;quot;{o}del's system $\\mathbf{T}$, by defining simultaneously strong negation $A^{\\mathbf{N}}$ of a formula $A$ and strong negation $P^{\\mathbf{N}}$ of a predicate $P$ in TCF. As a special case of the latter, we get strong negation of an inductive and a coinductive predicate of TCF. We prove appropriate versions of the Ex falso quodlibet and of double negation elimination for strong negation in TCF. We introduce the so-called tight formulas of TCF i.e., formulas implied by the weak negation of their strong negation, and the relative tight formulas. We present various case-studies and examples, which reveal the naturality of our definition of strong negation in TCF and justify the use of TCF as a formal system for a large part of Bishop-style constructive mathematics.<\/jats:p>","DOI":"10.46298\/lmcs-21(2:1)2025","type":"journal-article","created":{"date-parts":[[2025,4,4]],"date-time":"2025-04-04T10:10:10Z","timestamp":1743761410000},"source":"Crossref","is-referenced-by-count":0,"title":["Strong negation in the theory of computable functionals TCF"],"prefix":"10.46298","volume":"Volume 21, Issue 2","author":[{"given":"Nils","family":"K\u00f6pp","sequence":"first","affiliation":[]},{"given":"Iosif","family":"Petrakis","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2025,4,4]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/2210.05491v8","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/2210.05491v8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,4]],"date-time":"2025-04-04T10:10:10Z","timestamp":1743761410000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/11400"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,4]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-21(2:1)2025","relation":{"has-preprint":[{"id-type":"arxiv","id":"2210.05491v6","asserted-by":"subject"},{"id-type":"arxiv","id":"2210.05491v5","asserted-by":"subject"},{"id-type":"arxiv","id":"2210.05491v4","asserted-by":"subject"},{"id-type":"arxiv","id":"2210.05491v3","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2210.05491","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2210.05491","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2025,4,4]]},"article-number":"11400"}}