{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,24]],"date-time":"2024-08-24T23:11:50Z","timestamp":1724541110854},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T00:00:00Z","timestamp":1717200000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T00:00:00Z","timestamp":1717200000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Log. Univers."],"published-print":{"date-parts":[[2024,6]]},"DOI":"10.1007\/s11787-024-00353-3","type":"journal-article","created":{"date-parts":[[2024,7,23]],"date-time":"2024-07-23T15:07:22Z","timestamp":1721747242000},"page":"125-156","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Mathematical Representation of Peterson\u2019s Rules for Fuzzy Peterson\u2019s Syllogisms"],"prefix":"10.1007","volume":"18","author":[{"given":"Petra","family":"Murinov\u00e1","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michal","family":"Burda","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Viktor","family":"Pavliska","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,7,23]]},"reference":[{"key":"353_CR1","first-page":"7","volume-title":"Context Dependency in the Analysis of Linguistic Meaning","author":"D Abusch","year":"2004","unstructured":"Abusch, D., Rooth, M.: Empty-domain effects for presuppositional and non-presuppositional determiners. In: Kamp, H., Partee, B. (eds.) Context Dependency in the Analysis of Linguistic Meaning, p. 7. Elsevier, Amsterdam (2004)"},{"key":"353_CR2","doi-asserted-by":"publisher","first-page":"54","DOI":"10.4304\/jcp.2.5.54-66","volume":"2","author":"M Afshar","year":"2007","unstructured":"Afshar, M., Dartnell, C., Luzeaux, D., Sallantin, J., Tognetti, Y.: Aristotle\u2019s square revisited to frame discovery science. J. Comput. 2, 54\u201366 (2007)","journal-title":"J. Comput."},{"key":"353_CR3","first-page":"939","volume-title":"The Handbook of Logic and Language","author":"D Beaver","year":"2004","unstructured":"Beaver, D.: Presupposition. In: van Benthem, J., ter Meulen, A. (eds.) The Handbook of Logic and Language, pp. 939\u20131008. Elsevier, Amsterdam (2004)"},{"key":"353_CR4","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1305\/ndjfl\/1093870683","volume":"25","author":"M Brown","year":"1984","unstructured":"Brown, M.: Generalized quantifiers and the square of opposition. Notre Dame J. Form. Log. 25, 303\u2013322 (1984)","journal-title":"Notre Dame J. Form. Log."},{"key":"353_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-9480-6","volume-title":"Algebraic Foundations of Many-valued Reasoning","author":"RLO Cignoli","year":"2000","unstructured":"Cignoli, R.L.O., D\u2019Ottaviano, I.M.L., Mundici, D.: Algebraic Foundations of Many-valued Reasoning. Kluwer, Dordrecht (2000)"},{"issue":"4","key":"353_CR6","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1007\/BF00961659","volume":"2","author":"D Dubois","year":"1993","unstructured":"Dubois, D., Godo, L., L\u00f3pez de M\u00e0ntaras, R., Prade, H.: Qualitative reasoning with imprecise probabilities. J. Intell. Inf. Syst. 2(4), 319\u2013363 (1993)","journal-title":"J. Intell. Inf. Syst."},{"key":"353_CR7","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1111\/j.1467-8640.1988.tb00120.x","volume":"4","author":"D Dubois","year":"1988","unstructured":"Dubois, D., Prade, H.: On fuzzy syllogisms. Comput. Intell. 4, 171\u2013179 (1988)","journal-title":"Comput. Intell."},{"key":"353_CR8","unstructured":"Gainor, J.: What is distribution in categorical syllogisms. https:\/\/www.youtube.com\/watch?v=7_Y-Bxr4apQ (2011)"},{"key":"353_CR9","volume-title":"Reason and Argumen","author":"P Geach","year":"1976","unstructured":"Geach, P.: Reason and Argumen. University of California Press, California (1976)"},{"key":"353_CR10","first-page":"155","volume-title":"CLS 33: The Main Session","author":"LR Horn","year":"1997","unstructured":"Horn, L.R.: All john\u2019s children are as bald as the king of france: existential import and the geometry of opposition. In: CLS 33: The Main Session, pp. 155\u2013179. Chicago Linguistic Society, Chicago (1997)"},{"key":"353_CR11","doi-asserted-by":"publisher","first-page":"837","DOI":"10.1016\/B978-044481714-3\/50020-5","volume-title":"Handbook of Logic and Language","author":"EL Keenan","year":"1997","unstructured":"Keenan, E.L., Westerst\u00e5hl, D.: Generalized quantifiers in linguistics and logic. In: Benthem, J.V., Meulen, A.T. (eds.) Handbook of Logic and Language, pp. 837\u2013893. Elsevier, Amsterdam (1997)"},{"key":"353_CR12","doi-asserted-by":"crossref","unstructured":"Miclet, L., Prade, H.: Analogical proportions and square of oppositions. In: Laurent, A., et al. (ed.) Proc. 15th Int. Conf. on Information Processing and Management of Uncer- tainty in Knowledge-Based Systems, July 15-19, pp. 324\u2013334. Montpellier, CCIS (2014)","DOI":"10.1007\/978-3-319-08855-6_33"},{"key":"353_CR13","doi-asserted-by":"publisher","first-page":"12","DOI":"10.4064\/fm-44-1-12-36","volume":"44","author":"A Mostowski","year":"1957","unstructured":"Mostowski, A.: On a generalization of quantifiers. Fundam. Math. 44, 12\u201336 (1957)","journal-title":"Fundam. Math."},{"key":"353_CR14","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1007\/s11787-020-00265-y","volume":"265","author":"P Murinov\u00e1","year":"2020","unstructured":"Murinov\u00e1, P.: Graded structures of opposition in fuzzy natural logic. Log. Univers. 265, 495\u2013522 (2020)","journal-title":"Log. Univers."},{"key":"353_CR15","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/j.fss.2011.07.004","volume":"186","author":"P Murinov\u00e1","year":"2013","unstructured":"Murinov\u00e1, P., Nov\u00e1k, V.: A formal theory of generalized intermediate syllogisms. Fuzzy Sets Syst. 186, 47\u201380 (2013)","journal-title":"Fuzzy Sets Syst."},{"key":"353_CR16","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1016\/j.fss.2013.05.006","volume":"242","author":"P Murinov\u00e1","year":"2014","unstructured":"Murinov\u00e1, P., Nov\u00e1k, V.: Analysis of generalized square of opposition with intermediate quantifiers. Fuzzy Sets Syst. 242, 89\u2013113 (2014)","journal-title":"Fuzzy Sets Syst."},{"key":"353_CR17","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1016\/j.fss.2014.01.009","volume":"247","author":"P Murinov\u00e1","year":"2014","unstructured":"Murinov\u00e1, P., Nov\u00e1k, V.: The structure of generalized intermediate syllogisms. Fuzzy Sets Syst. 247, 18\u201337 (2014)","journal-title":"Fuzzy Sets Syst."},{"key":"353_CR18","unstructured":"Murinov\u00e1, P., Nov\u00e1k, V.: Logical syllogisms with \u201calmost all, most, many, a few\u201d and several\u201d. Int. J. Approx. Reason. (submitted)"},{"key":"353_CR19","doi-asserted-by":"crossref","unstructured":"Murinov\u00e1, P., Pavliska, V., Burda, M.: Generalized peterson\u2019s rules in fuzzy natural logic. In: Atlantis Studies in Uncertainty Modelling 2021-09-19 Bratislava, pp. 383\u2013390. (2021)","DOI":"10.2991\/asum.k.210827.051"},{"key":"353_CR20","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1016\/j.fss.2004.03.027","volume":"149","author":"V Nov\u00e1k","year":"2005","unstructured":"Nov\u00e1k, V.: On fuzzy type theory. Fuzzy Sets Syst. 149, 235\u2013273 (2005)","journal-title":"Fuzzy Sets Syst."},{"issue":"22","key":"353_CR21","doi-asserted-by":"publisher","first-page":"2939","DOI":"10.1016\/j.fss.2008.02.023","volume":"159","author":"V Nov\u00e1k","year":"2008","unstructured":"Nov\u00e1k, V.: A comprehensive theory of trichotomous evaluative linguistic expressions. Fuzzy Sets Syst. 159(22), 2939\u20132969 (2008)","journal-title":"Fuzzy Sets Syst."},{"issue":"10","key":"353_CR22","doi-asserted-by":"publisher","first-page":"1229","DOI":"10.1016\/j.fss.2007.12.008","volume":"159","author":"V Nov\u00e1k","year":"2008","unstructured":"Nov\u00e1k, V.: A formal theory of intermediate quantifiers. Fuzzy Sets Syst. 159(10), 1229\u20131246 (2008)","journal-title":"Fuzzy Sets Syst."},{"key":"353_CR23","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2023.108994","volume":"161","author":"V Nov\u00e1k","year":"2023","unstructured":"Nov\u00e1k, V., Murinov\u00e1, P.: Verification of validity of syllogisms with intermediate quantifiers is equivalent with checking Peterson\u2019s rules. Int. J. Approx. Reason. 161, 108994 (2023)","journal-title":"Int. J. Approx. Reason."},{"key":"353_CR24","doi-asserted-by":"publisher","first-page":"122","DOI":"10.1016\/j.ijar.2022.08.002","volume":"150","author":"V Nov\u00e1k","year":"2022","unstructured":"Nov\u00e1k, V., Murinov\u00e1, P., Ferbas, P.: Formal analysis of Peterson\u2019s rules for checking validity of syllogisms with intermediate quantifiers. Int. J. Approx. Reason. 150, 122\u2013138 (2022)","journal-title":"Int. J. Approx. Reason."},{"key":"353_CR25","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-5217-8","volume-title":"Mathematical Principles of Fuzzy Logic","author":"V Nov\u00e1k","year":"1999","unstructured":"Nov\u00e1k, V., Perfilieva, I., Mo\u010dko\u0159, J.: Mathematical Principles of Fuzzy Logic. Kluwer, Boston (1999)"},{"key":"353_CR26","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s11787-007-0031-x","volume":"2","author":"T Parsons","year":"2008","unstructured":"Parsons, T.: Things that are right with the traditional square of opposition. Log. Univers. 2, 3\u201311 (2008)","journal-title":"Log. Univers."},{"key":"353_CR27","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1007\/s11787-008-0038-y","volume":"2","author":"R Pellissier","year":"2008","unstructured":"Pellissier, R.: \u201cSetting\u2019\u2019 n-opposition. Log. Univers. 2, 235\u2013263 (2008)","journal-title":"Log. Univers."},{"key":"353_CR28","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/j.fss.2013.02.007","volume":"234","author":"M Pereira-Fari\u00f1a","year":"2014","unstructured":"Pereira-Fari\u00f1a, M., Vidal, J.C., D\u00edaz-Hermida, F., Bugar\u00edn, A.: A fuzzy syllogistic reasoning schema for generalized quantifiers. Fuzzy Sets Syst. 234, 79\u201396 (2014)","journal-title":"Fuzzy Sets Syst."},{"key":"353_CR29","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1305\/ndjfl\/1093882414","volume":"20","author":"P Peterson","year":"1979","unstructured":"Peterson, P.: On the logic of \u201cfew\u2019\u2019, \u201cmany\u2019\u2019 and \u201cmost\u2019\u2019. Notre Dame J. Form. Log. 20, 155\u2013179 (1979)","journal-title":"Notre Dame J. Form. Log."},{"key":"353_CR30","volume-title":"Intermediate Quantifiers: Logic, Linguistics, and Aristotelian Semantics","author":"P Peterson","year":"2000","unstructured":"Peterson, P.: Intermediate Quantifiers: Logic, Linguistics, and Aristotelian Semantics. Ashgate, Aldershot (2000)"},{"key":"353_CR31","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1007\/BF00398801","volume":"16","author":"N Rescher","year":"1965","unstructured":"Rescher, N., Gallagher, N.: Venn diagrams for plurative syllogisms. Philos. Stud. 16, 49\u201355 (1965)","journal-title":"Philos. Stud."},{"key":"353_CR32","doi-asserted-by":"publisher","DOI":"10.1093\/actrade\/9780199244959.book.1","volume-title":"Aristotle\u2019s Prior and Posterior Analytics","author":"WD Ross","year":"1949","unstructured":"Ross, W.D.: Aristotle\u2019s Prior and Posterior Analytics. Clarendom Press, Oxford (1949)"},{"key":"353_CR33","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/S0004-3702(97)00020-9","volume":"93","author":"DG Schwartz","year":"1997","unstructured":"Schwartz, D.G.: Dynamic reasoning with qualified syllogisms. Artif. Intell. 93, 103\u2013167 (1997)","journal-title":"Artif. Intell."},{"key":"353_CR34","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1305\/ndjfl\/1093883568","volume":"23","author":"BE Thompson","year":"1982","unstructured":"Thompson, B.E.: Syllogisms using \u201cfew\u2019\u2019,\u201cmany\u2019\u2019 and \u201cmost\u2019\u2019. Notre Dame J. Form. Log. 23, 75\u201384 (1982)","journal-title":"Notre Dame J. Form. Log."},{"key":"353_CR35","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1305\/ndjfl\/1093636527","volume":"27","author":"B Thompson","year":"1986","unstructured":"Thompson, B.: Syllogisms with statistical quantifiers. Notre Dame J. Form. Log. 27, 93\u2013103 (1986)","journal-title":"Notre Dame J. Form. Log."},{"key":"353_CR36","doi-asserted-by":"publisher","first-page":"2431","DOI":"10.1007\/s00500-013-1216-2","volume":"18","author":"E Turunen","year":"2014","unstructured":"Turunen, E.: An algebraic study of Peterson\u2019s intermediate syllogisms. Soft Comput. 18, 2431\u20132444 (2014)","journal-title":"Soft Comput."},{"key":"353_CR37","unstructured":"Wikipedia: http:\/\/en.wikipedia.org\/wiki\/aristotle (2004)"},{"key":"353_CR38","first-page":"149","volume":"9","author":"LA Zadeh","year":"1983","unstructured":"Zadeh, L.A.: A computational approach to fuzzy quantifiers in natural languages. Comput. Math. 9, 149\u2013184 (1983)","journal-title":"Comput. Math."},{"key":"353_CR39","doi-asserted-by":"publisher","first-page":"754","DOI":"10.1109\/TSMC.1985.6313459","volume":"15","author":"LA Zadeh","year":"1985","unstructured":"Zadeh, L.A.: Syllogistic reasoning in fuzzy logic and its applications to usuality and reasoning with dispositions. IEEE Trans. Syst. Man Cybern. 15, 754\u2013765 (1985)","journal-title":"IEEE Trans. Syst. Man Cybern."}],"container-title":["Logica Universalis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11787-024-00353-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11787-024-00353-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11787-024-00353-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,24]],"date-time":"2024-08-24T22:04:18Z","timestamp":1724537058000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11787-024-00353-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6]]},"references-count":39,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["353"],"URL":"https:\/\/doi.org\/10.1007\/s11787-024-00353-3","relation":{},"ISSN":["1661-8297","1661-8300"],"issn-type":[{"type":"print","value":"1661-8297"},{"type":"electronic","value":"1661-8300"}],"subject":[],"published":{"date-parts":[[2024,6]]},"assertion":[{"value":"19 May 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 April 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 July 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}