{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,18]],"date-time":"2024-04-18T01:46:52Z","timestamp":1713404812018},"reference-count":43,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2009,3,1]],"date-time":"2009-03-01T00:00:00Z","timestamp":1235865600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Rev. symb. logic"],"published-print":{"date-parts":[[2009,3]]},"abstract":"<jats:p>The paper offers a matrix-based logic (relevant matrix quantum physics) for propositions which seems suitable as an underlying logic for empirical sciences and especially for quantum physics. This logic is motivated by two criteria which serve to clean derivations of classical logic from superfluous redundancies and uninformative complexities. It distinguishes those valid derivations (inferences) of classical logic which contain superfluous redundancies and complexities and are in this sense \u201cirrelevant\u201d from those which are \u201crelevant\u201d or \u201cnonredundant\u201d in the sense of allowing only the most informative consequences in the derivations. The latter derivations are strictly valid in<jats:italic>RMQ<\/jats:italic>, whereas the former are only materially valid.<jats:italic>RMQ<\/jats:italic>is a decidable matrix calculus which possesses a semantics and has the finite model property. It is shown in the paper how<jats:italic>RMQ<\/jats:italic>by its strictly valid derivations can avoid the difficulties with commensurability, distributivity, and Bell's inequalities when it is applied to quantum physics.<\/jats:p>","DOI":"10.1017\/s1755020309090169","type":"journal-article","created":{"date-parts":[[2009,5,28]],"date-time":"2009-05-28T08:30:51Z","timestamp":1243499451000},"page":"132-163","source":"Crossref","is-referenced-by-count":10,"title":["MATRIX-BASED LOGIC FOR APPLICATION IN PHYSICS"],"prefix":"10.1017","volume":"2","author":[{"given":"PAUL","family":"WEINGARTNER","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,3,1]]},"reference":[{"key":"S1755020309090169_ref43","first-page":"99","volume-title":"Naturwissenschaft und Weltbild","author":"Zeilinger","year":"1992"},{"key":"S1755020309090169_ref42","first-page":"3","article-title":"Paradoxes solved by simple relevance criteria","volume":"113","author":"Weingartner","year":"1986","journal-title":"Logique et Analyse"},{"key":"S1755020309090169_ref40","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-05679-0"},{"key":"S1755020309090169_ref39","first-page":"53","volume-title":"Zwischen traditioneller und moderner Logik","author":"Weingarnter","year":"2001"},{"key":"S1755020309090169_ref36","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-0548-2_24"},{"key":"S1755020309090169_ref35","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093893411"},{"key":"S1755020309090169_ref28","article-title":"Zwart and Franssen\u2019s impossibility theorem holds for possible-world-accounts but not for consequence-accounts to versimilitude","author":"Schurz","year":"2008","journal-title":"Synthese"},{"key":"S1755020309090169_ref27","first-page":"47","volume-title":"What is Closer-to-the-Truth?","author":"Schurz","year":"1987"},{"key":"S1755020309090169_ref26","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1163\/9789004457232","volume-title":"Advances in Scientific Philosophy. 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