{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T15:12:30Z","timestamp":1648739550679},"reference-count":29,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2020,8,25]],"date-time":"2020-08-25T00:00:00Z","timestamp":1598313600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2021,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>State spaces are, in the most general sense, sets of entities that contain information. Examples include states of dynamical systems, processes of observations, or possible worlds. We use domain theory to describe the structure of positive and negative information in state spaces. We present examples ranging from the space of trajectories of a dynamical system, over Dunn\u2019s aboutness interpretation of <jats:sc>fde<\/jats:sc>, to the space of open sets of a spectral space. We show that these information structures induce so-called <jats:sc>hype<\/jats:sc> models which were recently developed by Leitgeb (2019). Conversely, we prove a representation theorem: roughly, <jats:sc>hype<\/jats:sc> models can be represented as induced by an information structure. Thus, the well-behaved logic <jats:sc>hype<\/jats:sc> is a sound and complete logic for reasoning about information in state spaces.<\/jats:p><jats:p>As application of this framework, we investigate information fusion. We motivate two kinds of fusion. We define a groundedness and a separation property that allow a <jats:sc>hype<\/jats:sc> model to be closed under the two kinds of fusion. This involves a Dedekind\u2013MacNeille completion and a fiber-space like construction. The proof-techniques come from pointless topology and universal algebra.<\/jats:p>","DOI":"10.1017\/s1755020320000222","type":"journal-article","created":{"date-parts":[[2020,8,25]],"date-time":"2020-08-25T03:40:53Z","timestamp":1598326853000},"page":"155-186","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["THE LOGIC OF INFORMATION IN STATE SPACES"],"prefix":"10.1017","volume":"14","author":[{"given":"LEVIN","family":"HORNISCHER","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2020,8,25]]},"reference":[{"key":"S1755020320000222_r11","first-page":"1","article-title":"The ho-zhao problem","volume":"14","author":"Ho","year":"2018","journal-title":"Logical Methods in Computer Science"},{"key":"S1755020320000222_r15","volume-title":"Stone Spaces.","volume":"3","author":"Johnstone","year":"1982"},{"key":"S1755020320000222_r14","first-page":"133","volume-title":"The Logica Yearbook 2018","author":"Hornischer","year":"2019"},{"key":"S1755020320000222_r17","first-page":"357","article-title":"The duality of continous posets","volume":"5","author":"Lawson","year":"1979","journal-title":"Houston Journal of Mathematics"},{"key":"S1755020320000222_r16","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-5587-4_10"},{"key":"S1755020320000222_r21","doi-asserted-by":"publisher","DOI":"10.1016\/S1385-7258(87)80008-2"},{"key":"S1755020320000222_r1","volume-title":"Handbook of Logic in Computer Science","author":"Abramsky","year":"1994"},{"key":"S1755020320000222_r20","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1937-1501929-X"},{"key":"S1755020320000222_r9","doi-asserted-by":"publisher","DOI":"10.3233\/FI-1988-11206"},{"key":"S1755020320000222_r23","first-page":"265","article-title":"Partial monoids: Associativity and confluence","volume":"3","author":"Poinsot","year":"2010","journal-title":"Journal of Pure and Applied Mathematics"},{"key":"S1755020320000222_r25","doi-asserted-by":"publisher","DOI":"10.1007\/s10485-019-09565-x"},{"key":"S1755020320000222_r29","volume-title":"Topology via Logic","author":"Vickers","year":"1989"},{"key":"S1755020320000222_r8","first-page":"556","volume-title":"Truthmaker Semantics","author":"Fine","year":"2017"},{"key":"S1755020320000222_r6","first-page":"362","article-title":"An intuitive semantics for first degree relevant implications","volume":"36","author":"Dunn","year":"1971","journal-title":"Journal of Symbolic Logic"},{"key":"S1755020320000222_r26","unstructured":"Scott, D. 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