{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T18:01:36Z","timestamp":1765994496515,"version":"3.40.3"},"publisher-location":"Cham","reference-count":27,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319913759"},{"type":"electronic","value":"9783319913766"}],"license":[{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018]]},"DOI":"10.1007\/978-3-319-91376-6_50","type":"book-chapter","created":{"date-parts":[[2018,5,16]],"date-time":"2018-05-16T15:19:05Z","timestamp":1526483945000},"page":"549-564","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Weakening of Alpha Graphs: Quasi-Boolean Algebras"],"prefix":"10.1007","author":[{"given":"Minghui","family":"Ma","sequence":"first","affiliation":[]},{"given":"Ahti-Veikko","family":"Pietarinen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,5,17]]},"reference":[{"key":"50_CR1","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1017\/S1755020315000362","volume":"9","author":"F Bellucci","year":"2016","unstructured":"Bellucci, F., Pietarinen, A.-V.: Existential graphs as an instrument of logical analysis: part I. Alpha. Rev. Symb. Logic 9, 209\u2013237 (2016)","journal-title":"Rev. Symb. Logic"},{"issue":"4","key":"50_CR2","doi-asserted-by":"publisher","first-page":"539","DOI":"10.2979\/trancharpeirsoc.52.4.02","volume":"52","author":"F Bellucci","year":"2017","unstructured":"Bellucci, F., Pietarinen, A.-V.: From Mitchell to Carus: 14 years of logical graphs in the making. Trans. Charles S. Peirce Soc. 52(4), 539\u2013575 (2017a)","journal-title":"Trans. Charles S. Peirce Soc."},{"key":"50_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jal.2017.01.001","volume":"25","author":"F Bellucci","year":"2017","unstructured":"Bellucci, F., Pietarinen, A.-V.: Assertion and denial: a contribution from logical notations. J. Appl. Logics 25, 1\u201322 (2017b)","journal-title":"J. Appl. Logics"},{"key":"50_CR4","doi-asserted-by":"publisher","unstructured":"Bellucci, F., Chiffi, D., Pietarinen, A.-V.: Assertive graphs. J. Appl. Non-Class. Logics (2018). https:\/\/doi.org\/10.1080\/11663081.2017.1418101","DOI":"10.1080\/11663081.2017.1418101"},{"key":"50_CR5","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/978-94-010-1161-7_2","volume-title":"Modern Uses of Multiple-Valued Logic","author":"ND Belnap Jr","year":"1977","unstructured":"Belnap Jr., N.D.: A useful four-valued logic. In: Dunn, J.M., Epstein, G. (eds.) Modern Uses of Multiple-Valued Logic, pp. 5\u201337. Springer, Dordrecht (1977). https:\/\/doi.org\/10.1007\/978-94-010-1161-7_2"},{"key":"50_CR6","volume-title":"Deep Inference and Symmetry in Classical Proofs","author":"K Br\u00fcnnler","year":"2003","unstructured":"Br\u00fcnnler, K.: Deep Inference and Symmetry in Classical Proofs. Logos, Berlin (2003)"},{"issue":"4","key":"50_CR7","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1305\/ndjfl\/1093870147","volume":"23","author":"JM Dunn","year":"1982","unstructured":"Dunn, J.M.: A relational representation of quasi-Boolean algebras. Notre Dame J. Formal Logic 23(4), 353\u2013357 (1982)","journal-title":"Notre Dame J. Formal Logic"},{"key":"50_CR8","unstructured":"Guglielmi, A.: Deep Inference. http:\/\/alessio.guglielmi.name\/res\/cos\/"},{"key":"50_CR9","doi-asserted-by":"publisher","unstructured":"Ma, M., Fei, L.: Sequent calculi for semi-De Morgan and De Morgan algebras. Stud. Logica (2017). https:\/\/doi.org\/10.1007\/s11225-017-9755-7","DOI":"10.1007\/s11225-017-9755-7"},{"key":"50_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"168","DOI":"10.1007\/978-3-662-54069-5_13","volume-title":"Logic and Its Applications","author":"M Ma","year":"2017","unstructured":"Ma, M., Pietarinen, A.-V.: Peirce\u2019s sequent proofs of distributivity. In: Ghosh, S., Prasad, S. (eds.) ICLA 2017. LNCS, vol. 10119, pp. 168\u2013182. Springer, Heidelberg (2017). https:\/\/doi.org\/10.1007\/978-3-662-54069-5_13"},{"issue":"3","key":"50_CR11","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1007\/s11225-016-9703-y","volume":"105","author":"M Ma","year":"2017","unstructured":"Ma, M., Pietarinen, A.-V.: Proof analysis of Peirce\u2019s alpha system of graphs. Stud. Logica 105(3), 625\u2013647 (2017)","journal-title":"Stud. Logica"},{"key":"50_CR12","doi-asserted-by":"publisher","unstructured":"Ma, M., Pietarinen, A.-V.: Gamma graph calculi for modal logics. Synthese (2017). https:\/\/doi.org\/10.1007\/s11229-017-1390-3","DOI":"10.1007\/s11229-017-1390-3"},{"key":"50_CR13","unstructured":"Ma, M., Pietarinen, A.-V.: A graphical deep inference system for intuitionistic logic. Log. Anal. (in press)"},{"key":"50_CR14","first-page":"25","volume":"2","author":"A Oostra","year":"2010","unstructured":"Oostra, A.: Los gr\u00e1ficos Alfa de Peirce aplicados a la l\u00f3gica intuicionista. Cuad. Sist. Peirceana 2, 25\u201360 (2010)","journal-title":"Cuad. Sist. Peirceana"},{"key":"50_CR15","first-page":"250","volume":"7","author":"CS Peirce","year":"1867","unstructured":"Peirce, C.S.: On an improvement in Boole\u2019s calculus of logic. Proc. Am. Acad. Arts Sci. 7, 250\u2013261 (1867)","journal-title":"Proc. Am. Acad. Arts Sci."},{"issue":"1","key":"50_CR16","doi-asserted-by":"publisher","first-page":"15","DOI":"10.2307\/2369442","volume":"3","author":"CS Peirce","year":"1880","unstructured":"Peirce, C.S.: On the algebra of logic. Am. J. Math. 3(1), 15\u201357 (1880)","journal-title":"Am. J. Math."},{"issue":"2","key":"50_CR17","doi-asserted-by":"publisher","first-page":"180","DOI":"10.2307\/2369451","volume":"7","author":"CS Peirce","year":"1885","unstructured":"Peirce, C.S.: On the algebra of logic: a contribution to the philosophy of notation. Am. J. Math. 7(2), 180\u2013196 (1885)","journal-title":"Am. J. Math."},{"key":"50_CR18","unstructured":"Peirce, C.S.: Letter to Christine Ladd-Franklin, 9 November 1900. (R L 237)"},{"key":"50_CR19","unstructured":"Peirce, C.S.: Manuscripts in the Houghton Library of Harvard University, as identified by Richard Robin (1967). Cited as R followed by manuscript number"},{"key":"50_CR20","doi-asserted-by":"publisher","DOI":"10.1007\/1-4020-3729-5","volume-title":"Signs of Logic: Peircean Themes on the Philosophy of Language, Games, and Communication","author":"A-V Pietarinen","year":"2006","unstructured":"Pietarinen, A.-V.: Signs of Logic: Peircean Themes on the Philosophy of Language, Games, and Communication. Springer, Dordrecht (2006). https:\/\/doi.org\/10.1007\/1-4020-3729-5"},{"key":"50_CR21","volume-title":"Diagrammatology and Diagram Praxis","author":"A-V Pietarinen","year":"2010","unstructured":"Pietarinen, A.-V.: Is non-visual diagrammatic logic possible? In: Gerner, A. (ed.) Diagrammatology and Diagram Praxis. College Publications, London (2010)"},{"key":"50_CR22","doi-asserted-by":"publisher","first-page":"941","DOI":"10.1007\/s11229-015-0677-5","volume":"192","author":"A-V Pietarinen","year":"2015","unstructured":"Pietarinen, A.-V.: Exploring the Beta quadrant. Synthese 192, 941\u2013970 (2015)","journal-title":"Synthese"},{"key":"50_CR23","unstructured":"Roberts, D.D.: The existential graphs and natural deduction. In: Studies in the Philosophy of C. S. Peirce, pp. 109\u2013121. University of Massachusetts Press (1964)"},{"key":"50_CR24","doi-asserted-by":"crossref","DOI":"10.1515\/9783110226225","volume-title":"The Existential Graphs of Charles S. Peirce","author":"DD Roberts","year":"1973","unstructured":"Roberts, D.D.: The Existential Graphs of Charles S. Peirce. Mouton, The Hague (1973)"},{"key":"50_CR25","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/3633.001.0001","volume-title":"The Iconic Logic of Peirce\u2019s Graphs","author":"S-J Shin","year":"2002","unstructured":"Shin, S.-J.: The Iconic Logic of Peirce\u2019s Graphs. MIT Press, Cambridge (2002)"},{"key":"50_CR26","volume-title":"Knowledge Representation","author":"J Sowa","year":"2000","unstructured":"Sowa, J.: Knowledge Representation. Brooks, Pacific Grove (2000)"},{"key":"50_CR27","unstructured":"Zeman, J.: The Graphical Logic of Charles S. Peirce. Ph.D. dissertation, University of Chicago (1964)"}],"container-title":["Lecture Notes in Computer Science","Diagrammatic Representation and Inference"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-91376-6_50","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,2]],"date-time":"2020-11-02T02:10:14Z","timestamp":1604283014000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-91376-6_50"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018]]},"ISBN":["9783319913759","9783319913766"],"references-count":27,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-91376-6_50","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2018]]},"assertion":[{"value":"17 May 2018","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"Diagrams","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Theory and Application of Diagrams","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Edinburgh","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"United Kingdom","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2018","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18 June 2018","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 June 2018","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"10","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"diagrams2018","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/www.diagrams-conference.org\/2018\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}