{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T18:47:14Z","timestamp":1768070834486,"version":"3.49.0"},"reference-count":17,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2014,2,1]],"date-time":"2014-02-01T00:00:00Z","timestamp":1391212800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"Instituto Tecnol\u00f3gico Aut\u00f3nomo de M\u00e9xico"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Comput. Logic"],"published-print":{"date-parts":[[2014,2]]},"abstract":"\n Dynamic topological logic<\/jats:italic>\n (DTL) is a polymodal logic designed for reasoning about\n dynamic topological systems<\/jats:italic>\n . These are pairs \u2329\n X<\/jats:italic>\n ,\n f<\/jats:italic>\n \u232a, where\n X<\/jats:italic>\n is a topological space and\n f<\/jats:italic>\n :\n X<\/jats:italic>\n \u2192\n X<\/jats:italic>\n is continuous. DTL uses a language L which combines the topological S4 modality \u25a1 with temporal operators from linear temporal logic.\n <\/jats:p>\n \n Recently, we gave a sound and complete axiomatization DTL\n *<\/jats:sup>\n for an extension of the logic to the language L\n *<\/jats:sup>\n , where \u25ca is allowed to act on finite sets of formulas and is interpreted as a tangled closure operator. No complete axiomatization is known in the language L, although one proof system, which we shall call KM, was conjectured to be complete by Kremer and Mints.\n <\/jats:p>\n \n In this article, we show that given any language L' such that L \u2286 L' \u2286 L\n *<\/jats:sup>\n , the set of valid formulas of L' is not finitely axiomatizable. It follows, in particular, that KM is incomplete.\n <\/jats:p>","DOI":"10.1145\/2489334","type":"journal-article","created":{"date-parts":[[2014,3,4]],"date-time":"2014-03-04T13:24:59Z","timestamp":1393939499000},"page":"1-18","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Non-finite axiomatizability of dynamic topological logic"],"prefix":"10.1145","volume":"15","author":[{"given":"David","family":"Fern\u00e1ndez-Duque","sequence":"first","affiliation":[{"name":"Universidad de Sevilla"}]}],"member":"320","published-online":{"date-parts":[[2014,3,6]]},"reference":[{"key":"e_1_2_1_1_1","first-page":"97","article-title":"Modal logics and topological semantics for hybrid systems. 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