{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,10,6]],"date-time":"2024-10-06T00:40:02Z","timestamp":1728175202821},"reference-count":23,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2010,8,12]],"date-time":"2010-08-12T00:00:00Z","timestamp":1281571200000},"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":[[2010,9]]},"abstract":"<jats:p>We consider a simple modal logic whose nonmodal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of axioms corresponding to the characteristic axioms of (e.g.) <jats:bold>T<\/jats:bold>, <jats:bold>S4<\/jats:bold>, and <jats:bold>S5<\/jats:bold>, such logics are useful, as shown in previous work by Baltag, Coecke, and the first author, for encoding and reasoning about information and misinformation in multiagent systems. For the propositional-only fragment of such a dynamic epistemic logic, we present an algebraic semantics, using lattices with agent-indexed families of adjoint pairs of operators, and a cut-free sequent calculus. The calculus exploits operators on sequents, in the style of \u201cnested\u201d or \u201ctree-sequent\u201d calculi; cut-admissibility is shown by constructive syntactic methods. The applicability of the logic is illustrated by reasoning about the muddy children puzzle, for which the calculus is augmented with extra rules to express the facts of the muddy children scenario.<\/jats:p>","DOI":"10.1017\/s1755020310000134","type":"journal-article","created":{"date-parts":[[2010,8,12]],"date-time":"2010-08-12T13:21:31Z","timestamp":1281619291000},"page":"351-373","source":"Crossref","is-referenced-by-count":8,"title":["POSITIVE LOGIC WITH ADJOINT MODALITIES: PROOF THEORY, SEMANTICS, AND REASONING ABOUT INFORMATION"],"prefix":"10.1017","volume":"3","author":[{"given":"MEHRNOOSH","family":"SADRZADEH","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ROY","family":"DYCKHOFF","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2010,8,12]]},"reference":[{"key":"S1755020310000134_ref23","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/4.2.125"},{"key":"S1755020310000134_ref22","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129598002540"},{"key":"S1755020310000134_ref21","unstructured":"Simpson A. (1993). The Proof Theory and Semantics of Intuitionistic Modal Logic. PhD Thesis, University of Edinburgh."},{"key":"S1755020310000134_ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.entcs.2009.07.102"},{"key":"S1755020310000134_ref19","doi-asserted-by":"publisher","DOI":"10.1007\/s11229-008-9414-7"},{"key":"S1755020310000134_ref18","unstructured":"Sadrzadeh M. (2006). Actions and Resources in Epistemic Logic. PhD Thesis, Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al."},{"key":"S1755020310000134_ref12","unstructured":"Kriener J. , Sadrzadeh M. , & Dyckhoff R. (2009). Implementation of a cut-free sequent calculus for logics with adjoint modalities. 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