{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,18]],"date-time":"2024-08-18T23:40:04Z","timestamp":1724024404401},"reference-count":14,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2021,1,7]],"date-time":"2021-01-07T00:00:00Z","timestamp":1609977600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,3,21]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We introduce the concept of $\\textit{access-based}$ intuitionistic knowledge which relies on the intuition that agent $i$ knows $\\varphi$ if $i$ has found $\\textit{access to a proof}$ of $\\varphi$. Basic principles are distribution and factivity of knowledge as well as $\\square\\varphi\\rightarrow K_i\\varphi$ and $K_i(\\varphi\\vee\\psi) \\rightarrow (K_i\\varphi\\vee K_i\\psi)$, where $\\square\\varphi$ reads $`\\varphi$ is proved'. The formalization extends a family of classical modal logics (Lewitzka, 2017, Journal of Logic and Computation, 27, 201--212) designed as combinations of $\\mathit{IPC}$ and $\\mathit{CPC}$ and as systems for the reasoning about proof, i.e. intuitionistic truth. We adopt a formalization of common knowledge from (Lewitzka, 2011, Studia Logica, 97, 233--264) and interpret it here as access-based common knowledge. We compare our proposal with recent approaches to intuitionistic knowledge (Artemov and Protopopescu, 2016, The Review of Symbolic Logic, 9, 266--298; Lewitzka, 2019, Annals of Pure and Applied Logic, 170, 218--250) and bring together these different concepts in a unifying semantic framework based on Heyting algebra expansions.<\/jats:p>","DOI":"10.1093\/logcom\/exaa086","type":"journal-article","created":{"date-parts":[[2020,12,12]],"date-time":"2020-12-12T06:14:24Z","timestamp":1607753664000},"page":"473-493","source":"Crossref","is-referenced-by-count":0,"title":["Access-based intuitionistic knowledge"],"prefix":"10.1093","volume":"31","author":[{"given":"Steffen","family":"Lewitzka","sequence":"first","affiliation":[{"name":"Departamento de Ci\u00eancia da Computa\u00e7\u00e3o, Instituto de Matem\u00e1tica e Estatistica, Universidade Federal da Bahia-UFBA, 40170-110 Salvador BA, 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