{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T05:08:40Z","timestamp":1761541720274,"version":"3.41.2"},"reference-count":63,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2024,8,27]],"date-time":"2024-08-27T00:00:00Z","timestamp":1724716800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,3,11]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper introduces a sequent calculus, $\\textbf{M}_{\\textbf{S}}$, the minimal structural logic, which includes all structural rules while excluding operational ones. Despite its limited calculus, $\\textbf{M}_{\\textbf{S}}$ unexpectedly shares a property with intuitionistic logic and modal logics between $\\textsf{S1}$ and $\\textsf{S5}$: it lacks sound and complete finitely-valued (deterministic) semantics. Mirroring G\u00f6del\u2019s and Dugundji\u2019s findings, we demonstrate that $\\textbf{M}_{\\textbf{S}}$ does possess a natural finitely-valued non-deterministic semantics. In fact, we show that $\\textbf{M}_{\\textbf{S}}$ is sound and complete with respect to any semantics belonging to a natural class of maximally permissive non-deterministic matrices. We close by examining the case of subsystems of $\\textbf{M}_{\\textbf{S}}$, including the \u201cstructural kernels\u201d of the strict-tolerant and tolerant-strict logics $\\textbf{ST}$ and $\\textbf{TS}$, and strengthen this result to also preclude finitely-valued deterministic semantics with respect to variable designated value frameworks.<\/jats:p>","DOI":"10.1093\/logcom\/exae045","type":"journal-article","created":{"date-parts":[[2024,8,27]],"date-time":"2024-08-27T12:33:28Z","timestamp":1724762008000},"source":"Crossref","is-referenced-by-count":1,"title":["A G\u00f6del-Dugundji-style theorem for the minimal structural logic"],"prefix":"10.1093","volume":"35","author":[{"given":"Pawel","family":"Pawlowski","sequence":"first","affiliation":[{"name":"CLPS, Ghent University ,","place":["Belgium"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thomas M","family":"Ferguson","sequence":"additional","affiliation":[{"name":"Department of Cognitive Science , Rensselaer 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