{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T03:34:17Z","timestamp":1771472057866,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":28,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540759386","type":"print"},{"value":"9783540759393","type":"electronic"}],"license":[{"start":{"date-parts":[[2007,1,1]],"date-time":"2007-01-01T00:00:00Z","timestamp":1167609600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2007]]},"DOI":"10.1007\/978-3-540-75939-3_15","type":"book-chapter","created":{"date-parts":[[2007,10,27]],"date-time":"2007-10-27T05:47:10Z","timestamp":1193464030000},"page":"247-274","source":"Crossref","is-referenced-by-count":8,"title":["Notes on Strong Completeness in \u0141ukasiewicz, Product and BL Logics and in Their First-Order Extensions"],"prefix":"10.1007","author":[{"given":"Franco","family":"Montagna","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"15_CR1","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/S0022-4049(02)00329-8","volume":"181","author":"P. Aglian\u00f3","year":"2003","unstructured":"Aglian\u00f3, P., Montagna, F.: Varieties of basic algebras I: general properties. Journal of Pure and Applied Algebra\u00a0181, 105\u2013129 (2003)","journal-title":"Journal of Pure and Applied Algebra"},{"key":"15_CR2","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1007\/s000120050156","volume":"43","author":"W.J. Blok","year":"2000","unstructured":"Blok, W.J., Ferreirim, I.M.A.: On the structure of hoops. Algebra Universalis\u00a043, 233\u2013257 (2000)","journal-title":"Algebra Universalis"},{"key":"15_CR3","series-title":"Mem. Amer. Math. Soc. 396","volume-title":"Algebraizable Logics","author":"W. Blok","year":"1989","unstructured":"Blok, W., Pigozzi, D.: Algebraizable Logics. Mem. Amer. Math. Soc. 396, vol.\u00a077. Amer. Math. Soc., Providence (1989)"},{"key":"15_CR4","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1007\/s005000000044","volume":"4","author":"R. Cignoli","year":"2000","unstructured":"Cignoli, R., Esteva, F., Godo, L., Torrens, A.: Basic fuzzy logic is the logic of continuous t-norms and their residua. Soft Computing\u00a04, 106\u2013112 (2000)","journal-title":"Soft Computing"},{"key":"15_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-9480-6","volume-title":"Algebraic foundations of many-valued reasoning","author":"R. Cignoli","year":"2000","unstructured":"Cignoli, R., D\u2019Ottaviano, I.M.L., Mundici, D.: Algebraic foundations of many-valued reasoning. Kluwer, Dordrecht (2000)"},{"key":"15_CR6","first-page":"45","volume":"5","author":"R. Cignoli","year":"2000","unstructured":"Cignoli, R., Torrens, A.: An algebraic analysis of product logic. Mult. Val. Logic\u00a05, 45\u201365 (2000)","journal-title":"Mult. Val. Logic"},{"key":"15_CR7","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1093\/logcom\/13.4.532","volume":"13","author":"F. Esteva","year":"2003","unstructured":"Esteva, F., Godo, L., H\u00e1jek, P., Montagna, F.: Hoops and fuzzy logic. Journal of Logic and Computation\u00a013, 531\u2013555 (2003)","journal-title":"Journal of Logic and Computation"},{"key":"15_CR8","unstructured":"Ferreirim, I.M.A.: On varieties and quasi varieties of hoops and their reducts, PhD thesis, University of Illinois at Chicago (1992)"},{"key":"15_CR9","doi-asserted-by":"crossref","unstructured":"Flaminio, T., Godo, L.: A logic for reasoning about the probability of fuzzy events. In: Fuzzy Sets and Systems (preprint 2006, to appear)","DOI":"10.1016\/j.fss.2006.11.008"},{"key":"15_CR10","series-title":"Series in Algebra","doi-asserted-by":"crossref","DOI":"10.1142\/3811","volume-title":"Partially ordered groups","author":"A. Glass","year":"1999","unstructured":"Glass, A.: Partially ordered groups. Series in Algebra, vol.\u00a07. World Scientific, Singapore, New Jersey, London, Hong Kong (1999)"},{"key":"15_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-5300-3","volume-title":"Metamathematics of Fuzzy Logic","author":"P. H\u00e1jek","year":"1998","unstructured":"H\u00e1jek, P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht (1998)"},{"key":"15_CR12","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1016\/0165-0114(94)00299-M","volume":"73","author":"P. H\u00e1jek","year":"1995","unstructured":"H\u00e1jek, P.: Fuzzy Logic and Arithmetical Hierarchy. Fuzzy sets and Systems\u00a073, 359\u2013363 (1995)","journal-title":"Fuzzy sets and Systems"},{"key":"15_CR13","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1023\/A:1004948116720","volume":"58","author":"P. H\u00e1jek","year":"1997","unstructured":"H\u00e1jek, P.: Fuzzy Logic and Arithmetical Hierarchy II. Studia Logica\u00a058, 129\u2013141 (1997)","journal-title":"Studia Logica"},{"issue":"3","key":"15_CR14","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1007\/s005000050043","volume":"2","author":"P. H\u00e1jek","year":"1998","unstructured":"H\u00e1jek, P.: Basic logic and BL-algebras. Soft Computing\u00a02(3), 124\u2013128 (1998)","journal-title":"Soft Computing"},{"key":"15_CR15","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1023\/A:1011906423560","volume":"68","author":"P. H\u00e1jek","year":"2001","unstructured":"H\u00e1jek, P.: Fuzzy Logic and Arithmetical Hierarchy III. Studia Logica\u00a068, 129\u2013142 (2001)","journal-title":"Studia Logica"},{"key":"15_CR16","first-page":"1","volume":"30","author":"P. H\u00e1jek","year":"2005","unstructured":"H\u00e1jek, P.: Arithmetical complexity and fuzzy predicate logics: a survey. Soft Computing\u00a030, 1\u20137 (2005)","journal-title":"Soft Computing"},{"key":"15_CR17","first-page":"159","volume":"12","author":"P. H\u00e1jek","year":"2002","unstructured":"H\u00e1jek, P.: Some hedges for continuous t-norm logics. Neural Network World\u00a012, 159\u2013164 (2002)","journal-title":"Neural Network World"},{"key":"15_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-9540-7","volume-title":"Triangular norms","author":"E.P. Klement","year":"2000","unstructured":"Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. Kluwer Academic Publishers, Dordrecht (2000)"},{"key":"15_CR19","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1007\/s00153-005-0286-y","volume":"45","author":"T. Kroupa","year":"2006","unstructured":"Kroupa, T.: Representation and Extension of States on MV-algebras. Arch. Math. Log.\u00a045, 381\u2013392 (2006)","journal-title":"Arch. Math. Log."},{"key":"15_CR20","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1023\/A:1011958407631","volume":"68","author":"F. Montagna","year":"2001","unstructured":"Montagna, F.: Three complexity problems in quantified fuzzy logic. Studia Logica\u00a068, 143\u2013152 (2001)","journal-title":"Studia Logica"},{"key":"15_CR21","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1093\/logcom\/14.2.299","volume":"14","author":"F. Montagna","year":"2004","unstructured":"Montagna, F.: Storage Operators and Multiplicative Quantifiers in Many-valued Logics. Journal of Logic and Computation\u00a014, 299\u2013322 (2004)","journal-title":"Journal of Logic and Computation"},{"key":"15_CR22","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1016\/0022-1236(86)90015-7","volume":"65","author":"D. Mundici","year":"1986","unstructured":"Mundici, D.: Interpretations of AF C * algebras in \u0141ukasiewicz sentential calculus. Journal of Functional Analysis\u00a065, 15\u201363 (1986)","journal-title":"Journal of Functional Analysis"},{"key":"15_CR23","doi-asserted-by":"crossref","unstructured":"Mundici, D.: Averaging the truth value in \u0141ukasiewicz sentential logic. Studia Logica\u00a055, 113\u2013127 (special issue in honour of Helena Rasiowa) (1955)","DOI":"10.1007\/BF01053035"},{"key":"15_CR24","unstructured":"Mundici, D.: Bookmaking over infinitely-valued events. International Journal of Approximate Reasoning\u00a0(to appear)"},{"key":"15_CR25","unstructured":"Paris, J.: A note on the Dutch Book Method. In: De Cooman, G., Fine, T., Seidenfeleir, T. (eds.) Proceedings of the Second International Symposium on Imprecise Probabilities and their Applications, ISIPTA 2001, pp. 301\u2013306. Shaker Publishing Company, Ithaca, NY, USA (2001)"},{"key":"15_CR26","first-page":"869","volume-title":"Handbook of Measure Theory","author":"B. Rie\u010dan","year":"2001","unstructured":"Rie\u010dan, B., Mundici, D.: Probability on MV-algebras. In: Pap, E. (ed.) Handbook of Measure Theory, vol.\u00a0II, pp. 869\u2013900. North Holland, Amsterdam (2001)"},{"key":"15_CR27","unstructured":"Ragaz, M.E.: Arithmetische Klassification von Formelnmenge der unendlichwertigen Logik. ETH Z\u00fcrich, Thesis (1981)"},{"key":"15_CR28","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1090\/S0002-9947-1939-1501995-3","volume":"45","author":"M. Ward","year":"1939","unstructured":"Ward, M., Dilworth, R.P.: Residuated lattices. Transactions of American Mathematical Society\u00a045, 335\u2013354 (1939)","journal-title":"Transactions of American Mathematical Society"}],"container-title":["Lecture Notes in Computer Science","Algebraic and Proof-theoretic Aspects of Non-classical Logics"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-75939-3_15","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,4]],"date-time":"2019-05-04T02:01:25Z","timestamp":1556935285000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-75939-3_15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007]]},"ISBN":["9783540759386","9783540759393"],"references-count":28,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-75939-3_15","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007]]}}}