{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T08:14:27Z","timestamp":1649146467585},"reference-count":23,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2020,3,1]],"date-time":"2020-03-01T00:00:00Z","timestamp":1583020800000},"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":[[2020,3,16]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We present a labelled sequent calculus for a trimodal epistemic logic exhibitied in Baltag et al. (2017, Logic, Rationality, and Interaction, pp. 330\u2013346), an extension of the so called \u2018Topo-Logic\u2019. To the best of our knowledge, our calculus is the first proof-calculus for this logic. This calculus is obtained via an adaptation of the label technique by internalizing a semantics over topological spaces. This internalization leads to the generation of two kinds of labels in our calculus and the labelling of formulae by pairs of labels. These novelties give tools to provide a simple calculus that is intuitively connected to the semantics. We prove that this calculus enjoys many structural properties such as admissibility of cut, admissibility of contraction and invertibility of its rules. Finally, we exhibit a proof search strategy for our calculus that allows us to prove completeness in a direct way by the extraction of a countermodel from a failure of proof. To define this strategy, we design a tool for controlling the generation of labels in the construction of a search tree, although the termination of this strategy is still open.<\/jats:p>","DOI":"10.1093\/logcom\/exaa021","type":"journal-article","created":{"date-parts":[[2020,1,9]],"date-time":"2020-01-09T12:26:04Z","timestamp":1578572764000},"page":"663-696","source":"Crossref","is-referenced-by-count":0,"title":["A multi-labelled sequent calculus for Topo-Logic"],"prefix":"10.1093","volume":"30","author":[{"given":"Ian","family":"Shillito","sequence":"first","affiliation":[{"name":"Institute for Logic, Language and Computation, Universiteit van Amsterdam, Amsterdam, 1098 XG, The Netherlands"}]}],"member":"286","published-online":{"date-parts":[[2020,3,11]]},"reference":[{"key":"2020041308452806100_ref1","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/978-3-662-59533-6_11","volume-title":"Logic, Language, Information, and Computation","author":"Baltag","year":"2019"},{"key":"2020041308452806100_ref2","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s10992-018-9463-4","article-title":"A topological approach to full belief","volume":"48,","author":"Baltag","year":"2019","journal-title":"Journal of Philosophical Logic"},{"key":"2020041308452806100_ref3","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1007\/978-3-662-55665-8_23","volume-title":"Logic, Rationality, and Interaction","author":"Baltag","year":"2017"},{"key":"2020041308452806100_ref4","volume-title":"Topological subset space models for belief","author":"Bjorndahl","year":"2016"},{"key":"2020041308452806100_ref5","first-page":"88","article-title":"Logic and topology for knowledge, knowability, and belief - extended abstract","volume-title":"Proceedings Sixteenth Conference on Theoretical Aspects of Rationality and Knowledge","author":"Bjorndahl","year":"2017"},{"key":"2020041308452806100_ref6","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/0168-0072(95)00016-X","article-title":"Topological reasoning and the logic of knowledge","volume":"78,","author":"Dabrowski","year":"1996","journal-title":"Annals of Pure and Applied Logic"},{"key":"2020041308452806100_ref7","volume-title":"Advances in Modal Logic","author":"Dalmonte","year":"2018"},{"key":"2020041308452806100_ref8","volume-title":"Advances in Modal Logic","author":"Elbl","year":"2016"},{"key":"2020041308452806100_ref9","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1109\/LICS.2012.42","article-title":"Countermodels from sequent calculi in multi-modal logics","volume-title":"2012 27th Annual IEEE Symposium on Logic in Computer Science","author":"Garg","year":"2012"},{"key":"2020041308452806100_ref10","volume-title":"On the Proof Theory of Conditional Logics. 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