{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,4]],"date-time":"2026-02-04T20:48:47Z","timestamp":1770238127377,"version":"3.49.0"},"reference-count":23,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2021,3,8]],"date-time":"2021-03-08T00:00:00Z","timestamp":1615161600000},"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":[[2023,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The Quantified argument calculus (Quarc) has received a lot of attention recently as an interesting system of quantified logic which eschews the use of variables and unrestricted quantification, but nonetheless achieves results similar to the Predicate calculus (PC) by employing quantifiers applied directly to predicates instead. Despite this noted similarity, the issue of the relationship between Quarc and PC has so far not been definitively resolved. We address this question in the present paper, and then expand upon that result.<\/jats:p><jats:p>Utilizing recent developments in structural proof theory, we develop a G3-style sequent calculus for Quarc and briefly demonstrate its structural properties. We put these properties to use immediately to construct direct proofs of the meta-theoretical properties of the system. We then incorporate an abstract (and, as we shall see, logical) predicate into the system in a way that preserves all the structural properties. This allows us to identify a system of Quarc which is deductively equivalent to PC, and also yields a constructive method of demonstrating the Craig interpolation theorem (which speaks in favor of the aforementioned predicate being logical). We further generalize this extension to develop a bivalent system of Quarc with defining clauses that still maintains all the desirable properties of a good proof system.<\/jats:p>","DOI":"10.1017\/s175502032100006x","type":"journal-article","created":{"date-parts":[[2021,3,8]],"date-time":"2021-03-08T05:17:48Z","timestamp":1615180668000},"page":"449-479","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":6,"title":["ABSTRACT FORMS OF QUANTIFICATION IN THE QUANTIFIED ARGUMENT CALCULUS"],"prefix":"10.1017","volume":"16","author":[{"given":"EDI","family":"PAVLOVI\u0106","sequence":"first","affiliation":[]},{"given":"NORBERT","family":"GRATZL","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,3,8]]},"reference":[{"key":"S175502032100006X_r12","first-page":"173","volume-title":"First-Order Logic Revisited","author":"Lanzet","year":"2004"},{"key":"S175502032100006X_r9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01201353"},{"key":"S175502032100006X_r14","doi-asserted-by":"publisher","DOI":"10.18778\/0138-0680.48.2.04"},{"key":"S175502032100006X_r11","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020317000053"},{"key":"S175502032100006X_r18","doi-asserted-by":"publisher","DOI":"10.1515\/9783110657883-007"},{"key":"S175502032100006X_r13","first-page":"235","article-title":"Craig no interpolation theorem","volume":"12","author":"Maehara","year":"1960","journal-title":"Suugaku"},{"key":"S175502032100006X_r19","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020318000114"},{"key":"S175502032100006X_r20","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-020-09564-7"},{"key":"S175502032100006X_r15","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511527340"},{"key":"S175502032100006X_r1","volume-title":"Logic and Natural Language: On Plural Reference and Its Semantic and Logical Significance","author":"Ben-Yami","year":"2004"},{"key":"S175502032100006X_r2","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020313000373"},{"key":"S175502032100006X_r16","doi-asserted-by":"publisher","DOI":"10.2969\/msjmemoirs\/00201C060"},{"key":"S175502032100006X_r4","unstructured":"[4] Ben-Yami, H. , (2021). The Quantified argument calculus and natural logic. Dialectica. Forthcoming."},{"key":"S175502032100006X_r23","volume-title":"Grundlehren der mathematischen Wissenschaften","volume":"103","author":"Sch\u00fctte","year":"1960"},{"key":"S175502032100006X_r17","unstructured":"[17] Pavlovi\u0107, E. (2017). The Quantified Argument Calculus: An Inquiry into Its Logical Properties and Applications. Ph.D. Thesis, Central European University, Budapest."},{"key":"S175502032100006X_r6","volume-title":"Computability and logic","author":"Boolos","year":"1974"},{"key":"S175502032100006X_r7","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(98)80016-5"},{"key":"S175502032100006X_r5","unstructured":"[5] Ben-Yami, H. , & Pavlovi\u0107, E. (n.d.). Completeness of the Quantified Argument Calculus on the Truth-Valuational Approach. Forthcoming."},{"key":"S175502032100006X_r8","doi-asserted-by":"publisher","DOI":"10.2307\/2963594"},{"key":"S175502032100006X_r22","doi-asserted-by":"publisher","DOI":"10.1080\/01445340.2018.1467198"},{"key":"S175502032100006X_r21","unstructured":"[21] Raab, J. (2016). The Relationship of QUARC and Classical Logic. Master\u2019s Thesis, LMU, Munich."},{"key":"S175502032100006X_r3","doi-asserted-by":"publisher","DOI":"10.1007\/s11229-020-02771-4"},{"key":"S175502032100006X_r10","volume-title":"The Collected Papers","author":"Gentzen","year":"1969"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S175502032100006X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,16]],"date-time":"2023-05-16T10:34:05Z","timestamp":1684233245000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S175502032100006X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,8]]},"references-count":23,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["S175502032100006X"],"URL":"https:\/\/doi.org\/10.1017\/s175502032100006x","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,8]]},"assertion":[{"value":"\u00a9 The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}