{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T12:03:19Z","timestamp":1754481799384},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":15076,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1972,12]]},"abstract":"<jats:p>Since 1933, when Kolmogorov laid the foundations for probability and statistics as we know them today [1], it has been recognized that propositions asserting that such and such an event occurred as a consequence of the execution of a particular random experiment tend to band together and form a Boolean algebra. In 1936, Birkhoff and von Neumann [2] suggested that the so-called logic of quantum mechanics should not be a Boolean algebra, but rather should form what is now called a modular ortholattice [3]. Presumably, the departure from Boolean algebras encountered in quantum mechanics can be attributed to the fact that in quantum mechanics, one must consider more than one physical experiment, e.g., an experiment measuring position, an experiment measuring charge, an experiment measuring momentum, etc., and, because of the uncertainty principle, these experiments need not admit a common refinement in terms of which the Kolmogorov theory is directly applicable.<\/jats:p><jats:p>Mackey's Axioms I\u2013VI for quantum mechanics [4] imply that the logic of quantum mechanics should be a <jats:italic>\u03c3<\/jats:italic>-orthocomplete orthomodular poset [5]. Most contemporary practitioners of quantum logic seem to agree that a quantum logic is (at least) an orthomodular poset [6], [7], [8], [9], [10] or some variation thereof [11]. P. D. Finch [12] has shown that every completely orthomodular poset is the logic arising from sets of Boolean logics, where these sets have a structure similar to the structures generally given to quantum logic. In all of these versions of quantum logic, a fundamental relation, the relation of compatibility or commutativity, plays a decisive role.<\/jats:p>","DOI":"10.2307\/2272407","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:19:43Z","timestamp":1146950383000},"page":"641-645","source":"Crossref","is-referenced-by-count":13,"title":["The center of an orthologic"],"prefix":"10.1017","volume":"37","author":[{"given":"Barbara","family":"Jeffcott","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200078427_ref009","unstructured":"Pool J. C. T. , Simultaneous observability and the logic of quantum mechanics, Thesis, State University of Iowa, 1963."},{"key":"S0022481200078427_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(67)90105-9"},{"key":"S0022481200078427_ref005","first-page":"65","article-title":"A note on orthomodular lattices","volume":"27","author":"Foulis","year":"1962","journal-title":"Portugaliae Mathematica"},{"key":"S0022481200078427_ref002","doi-asserted-by":"publisher","DOI":"10.2307\/1968621"},{"key":"S0022481200078427_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BF01646019"},{"key":"S0022481200078427_ref001","volume-title":"Foundations of the theory of probability","author":"Kolmogorov","year":"1956"},{"key":"S0022481200078427_ref014","volume-title":"Operational statistics","author":"Randall","year":"1970"},{"key":"S0022481200078427_ref004","volume-title":"Mathematical foundations of quantum mechanics","author":"Mackey","year":"1963"},{"key":"S0022481200078427_ref003","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/002\/0177919"},{"key":"S0022481200078427_ref011","first-page":"59","article-title":"The problem of hidden variables in quantum mechanics","volume":"17","author":"Kochan","year":"1967","journal-title":"Journal of Mathematics and Mechanics"},{"key":"S0022481200078427_ref007","volume-title":"Geometry of quantum theory","volume":"1","author":"Varadarajan","year":"1968"},{"key":"S0022481200078427_ref012","first-page":"275","volume":"34","author":"Finch","year":"1969","journal-title":"On the structure of quantum logic"},{"key":"S0022481200078427_ref013","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1970.11992491"},{"key":"S0022481200078427_ref010","doi-asserted-by":"publisher","DOI":"10.2172\/4577721"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200078427","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,30]],"date-time":"2019-05-30T20:33:07Z","timestamp":1559248387000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200078427\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1972,12]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1972,12]]}},"alternative-id":["S0022481200078427"],"URL":"https:\/\/doi.org\/10.2307\/2272407","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1972,12]]}}}