{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T20:40:47Z","timestamp":1757450447904,"version":"3.40.4"},"reference-count":31,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2013,10,14]],"date-time":"2013-10-14T00:00:00Z","timestamp":1381708800000},"content-version":"unspecified","delay-in-days":0,"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":[[2013,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In van Benthem (2008), van Benthem proposes a dynamic consequence relation defined as<jats:inline-formula><jats:alternatives><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S1755020313000294_inline1\"\/><jats:tex-math>${\\psi _1}, \\ldots ,{\\psi _n}{ \\models ^d}\\phi \\,{\\rm{iff}}{ \\models ^{pa}}[{\\psi _1}] \\ldots [{\\psi _n}]\\phi ,$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>where the latter denotes consequence in public announcement logic, a dynamic epistemic logic. In this paper we investigate the structural properties of a conditional dynamic consequence relation<jats:inline-formula><jats:alternatives><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S1755020313000294_inline2\"\/><jats:tex-math>$\\models _{\\rm{\\Gamma }}^d$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>extending van Benthem\u2019s proposal. It takes into account a set of background conditions \u0393, inspired by Makinson (2003) wherein Makinson calls this reasoning \u2018modulo\u2019 a set \u0393. In the presence of common knowledge, conditional dynamic consequence is definable from (unconditional) dynamic consequence. An open question is whether dynamic consequence is compact. We further investigate a dynamic consequence relation for soft instead of hard announcements. Surprisingly, it shares many properties with (hard) dynamic consequence. Dynamic consequence relations provide a novel perspective on reasoning about protocols in multi-agent systems.<\/jats:p>","DOI":"10.1017\/s1755020313000294","type":"journal-article","created":{"date-parts":[[2013,10,14]],"date-time":"2013-10-14T14:15:54Z","timestamp":1381760154000},"page":"659-679","source":"Crossref","is-referenced-by-count":3,"title":["DYNAMIC CONSEQUENCE AND PUBLIC ANNOUNCEMENT"],"prefix":"10.1017","volume":"6","author":[{"given":"ANDR\u00c9S CORD\u00d3N","family":"FRANCO","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"HANS VAN","family":"DITMARSCH","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ANGEL","family":"NEPOMUCENO","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2013,10,14]]},"reference":[{"key":"S1755020313000294_ref30","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-5839-4"},{"key":"S1755020313000294_ref28","doi-asserted-by":"publisher","DOI":"10.1007\/s11229-005-3384-9"},{"key":"S1755020313000294_ref27","doi-asserted-by":"publisher","DOI":"10.26686\/ajl.v6i0.1801"},{"volume-title":"On the Concept of Logical Consequence","year":"1936","author":"Tarski","key":"S1755020313000294_ref24"},{"key":"S1755020313000294_ref22","doi-asserted-by":"publisher","DOI":"10.4324\/9780203252642"},{"key":"S1755020313000294_ref20","doi-asserted-by":"publisher","DOI":"10.1093\/jigpal\/11.1.69"},{"key":"S1755020313000294_ref19","article-title":"The Church-Fitch knowability paradox in the light of structural proof theory","author":"Maffezioli","year":"2012","journal-title":"Synthese"},{"key":"S1755020313000294_ref17","first-page":"217","volume-title":"Semantics","author":"Kracht","year":"2002"},{"key":"S1755020313000294_ref16","first-page":"178","volume-title":"Advances in Modal Logic","volume":"8","author":"Holliday","year":"2010"},{"key":"S1755020313000294_ref14","unstructured":"Gerbrandy J. D . (1999). Bisimulations on Planet Kripke. PhD Thesis, University of Amsterdam. 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