{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T20:45:43Z","timestamp":1783111543773,"version":"3.54.6"},"reference-count":47,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2019,10,9]],"date-time":"2019-10-09T00:00:00Z","timestamp":1570579200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In recent work, Stalnaker proposes a logical framework in which belief is realized as a weakened form of knowledge 35. Building on Stalnaker\u2019s core insights, and using frameworks developed in 11 and 3, we employ<jats:italic>topological<\/jats:italic>tools to refine and, we argue, improve on this analysis. The structure of topological subset spaces allows for a natural distinction between what is<jats:italic>known<\/jats:italic>and (roughly speaking) what is<jats:italic>knowable<\/jats:italic>; we argue that the foundational axioms of Stalnaker\u2019s system rely intuitively on<jats:italic>both<\/jats:italic>of these notions. More precisely, we argue that the plausibility of the principles Stalnaker proposes relating knowledge and belief relies on a subtle equivocation between an \u201cevidence-in-hand\u201d conception of knowledge and a weaker \u201cevidence-out-there\u201d notion of what<jats:italic>could come to be known<\/jats:italic>. Our analysis leads to a trimodal logic of knowledge, knowability, and belief interpreted in topological subset spaces in which belief is definable in terms of<jats:italic>knowledge and knowability<\/jats:italic>. We provide a sound and complete axiomatization for this logic as well as its uni-modal belief fragment. We then consider weaker logics that preserve suitable translations of Stalnaker\u2019s postulates, yet do not allow for any reduction of belief. We propose novel topological semantics for these irreducible notions of belief, generalizing our previous semantics, and provide sound and complete axiomatizations for the corresponding logics.<\/jats:p>","DOI":"10.1017\/s1755020319000509","type":"journal-article","created":{"date-parts":[[2019,10,9]],"date-time":"2019-10-09T08:18:59Z","timestamp":1570609139000},"page":"748-775","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":8,"title":["LOGIC AND TOPOLOGY FOR KNOWLEDGE, KNOWABILITY, AND 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