{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T02:30:16Z","timestamp":1775097016049,"version":"3.50.1"},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2009,10,5]],"date-time":"2009-10-05T00:00:00Z","timestamp":1254700800000},"content-version":"unspecified","delay-in-days":34,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2009,9]]},"abstract":"<jats:p>The question of whether knowledge is definable in terms of belief, which has played an important role in epistemology for the last 50 years, is studied here in the framework of epistemic and doxastic <jats:italic>logics<\/jats:italic>. Three notions of definability are considered: explicit definability, implicit definability, and reducibility, where explicit definability is equivalent to the combination of implicit definability and reducibility. It is shown that if knowledge satisfies any set of axioms contained in S5, then it cannot be explicitly defined in terms of belief. S5 knowledge can be implicitly defined by belief, but not reduced to it. On the other hand, S4.4 knowledge and weaker notions of knowledge cannot be implicitly defined by belief, but can be reduced to it by defining knowledge as <jats:italic>true belief<\/jats:italic>. It is also shown that S5 knowledge cannot be reduced to belief <jats:italic>and<\/jats:italic> justification, provided that there are no axioms that involve both belief and justification.<\/jats:p>","DOI":"10.1017\/s1755020309990141","type":"journal-article","created":{"date-parts":[[2009,10,5]],"date-time":"2009-10-05T16:58:53Z","timestamp":1254761933000},"page":"469-487","source":"Crossref","is-referenced-by-count":30,"title":["DEFINING KNOWLEDGE IN TERMS OF BELIEF: THE MODAL LOGIC PERSPECTIVE"],"prefix":"10.1017","volume":"2","author":[{"given":"JOSEPH Y.","family":"HALPERN","sequence":"first","affiliation":[]},{"given":"DOV","family":"SAMET","sequence":"additional","affiliation":[]},{"given":"ELLA","family":"SEGEV","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,10,5]]},"reference":[{"key":"S1755020309990141_manual_ref-1","volume-title":"Epistemic Justification: Essays in the Theory of Knowledge","author":"Alston","year":"1989"},{"key":"S1755020309990141_manual_ref-9","first-page":"113","article-title":"Epistemic luck and the purely epistemic","volume":"21","author":"Foley","year":"1984","journal-title":"American Philosophical Quarterly"},{"key":"S1755020309990141_manual_ref-15","first-page":"1","article-title":"Recent work in epistemic logic","volume":"30","author":"Lenzen","year":"1978","journal-title":"Acta Philosophica Fennica"},{"key":"S1755020309990141_manual_ref-16","doi-asserted-by":"publisher","DOI":"10.1007\/BF00205012"},{"key":"S1755020309990141_manual_ref-18","doi-asserted-by":"publisher","DOI":"10.5840\/jpr_2004_18"},{"key":"S1755020309990141_manual_ref-5","doi-asserted-by":"publisher","DOI":"10.1016\/S1385-7258(53)50042-3"},{"key":"S1755020309990141_manual_ref-10","first-page":"297","article-title":"Semantics for S4.04, S4.4, and S4.3.2","volume":"17","author":"Georgacarakos","year":"1976","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"S1755020309990141_manual_ref-2","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/exi053"},{"key":"S1755020309990141_manual_ref-6","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107050884"},{"key":"S1755020309990141_manual_ref-4","doi-asserted-by":"publisher","DOI":"10.1007\/s11098-005-4052-0"},{"key":"S1755020309990141_manual_ref-12","article-title":"On definability in multimodal logic: Basic notions","author":"Halpern","year":"2008","journal-title":"Review of Symbolic Logic"},{"key":"S1755020309990141_manual_ref-19","doi-asserted-by":"publisher","DOI":"10.1093\/019928038X.001.0001"},{"key":"S1755020309990141_manual_ref-20","doi-asserted-by":"publisher","DOI":"10.1007\/s11098-005-4062-y"},{"key":"S1755020309990141_manual_ref-21","doi-asserted-by":"publisher","DOI":"10.1093\/0199243794.001.0001"},{"key":"S1755020309990141_manual_ref-17","doi-asserted-by":"publisher","DOI":"10.1023\/A:1024248828122"},{"key":"S1755020309990141_manual_ref-11","doi-asserted-by":"publisher","DOI":"10.1093\/analys\/23.6.121"},{"key":"S1755020309990141_manual_ref-7","volume-title":"Epistemic Justification: Internalism vs. Externalism, Foundations vs. Virtues","author":"BonJour","year":"2003"},{"key":"S1755020309990141_manual_ref-14","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/3.2.173"},{"key":"S1755020309990141_manual_ref-3","volume-title":"The Problem of Knowledge","author":"Ayer","year":"1956"},{"key":"S1755020309990141_manual_ref-13","volume-title":"Knowledge and Belief","author":"Hintikka","year":"1962"},{"key":"S1755020309990141_manual_ref-8","volume-title":"Perceiving: A Philosophical Study","author":"Chisholm","year":"1957"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020309990141","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T22:26:51Z","timestamp":1750458411000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020309990141\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9]]},"references-count":21,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,9]]}},"alternative-id":["S1755020309990141"],"URL":"https:\/\/doi.org\/10.1017\/s1755020309990141","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,9]]}}}