{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T14:59:44Z","timestamp":1726412384345},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2005,11,21]],"date-time":"2005-11-21T00:00:00Z","timestamp":1132531200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Arch. Math. Logic"],"published-print":{"date-parts":[[2006,7]]},"DOI":"10.1007\/s00153-005-0324-9","type":"journal-article","created":{"date-parts":[[2005,11,21]],"date-time":"2005-11-21T08:37:53Z","timestamp":1132562273000},"page":"615-647","source":"Crossref","is-referenced-by-count":4,"title":["On two fragments with negation and without implication of the logic of residuated lattices"],"prefix":"10.1007","volume":"45","author":[{"given":"F\u00e9lix","family":"Bou","sequence":"first","affiliation":[]},{"given":"\u00c0ngel","family":"Garc\u00eda-Cerda\u00f1a","sequence":"additional","affiliation":[]},{"given":"Ventura","family":"Verd\u00fa","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2005,11,21]]},"reference":[{"key":"324_CR1","first-page":"11","volume":"65","author":"Adillon","year":"1","unstructured":"Adillon, R., Verd\u00fa, V.: On a contraction-less intuitionistic propositional logic with conjunction and fusion. Studia Logica, Special Issue on Abstract Algebraic Logic 65 (1), 11\u201330 (2000)","journal-title":"Studia Logica, Special Issue on Abstract Algebraic Logic"},{"key":"324_CR2","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/0304-3975(88)90037-0","volume":"570","author":"Avron","year":"1988","unstructured":"Avron, A.: The semantics and proof theory of linear logic. Theoretical Computer Science 570, 161\u2013184 (1988)","journal-title":"Theoretical Computer Science"},{"key":"324_CR3","unstructured":"Balbes, R., Dwinger, P.: Distributive lattices. University of Missouri Press, Columbia, Missouri, 1974"},{"key":"324_CR4","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1002\/malq.19560020803","volume":"2","author":"Banaschewski","year":"1956","unstructured":"Banaschewski, B.: H\u00fcllensysteme und Erweiterung von Quasi-Ordnungen. Zeitschrift f\u00fcr Mathematische Logik und Grundlagen der Mathematik 2, 117\u2013130 (1956)","journal-title":"Zeitschrift f\u00fcr Mathematische Logik und Grundlagen der Mathematik"},{"key":"324_CR5","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/s000120200000","volume":"48","author":"Blok","year":"3","unstructured":"Blok, W.J., van Alten, C.J.: The finite embeddability property for residuated lattices, pocrims and BCK-algebras. Algebra Universalis 48 (3), 253\u2013271 (2002)","journal-title":"Algebra Universalis"},{"key":"324_CR6","doi-asserted-by":"crossref","unstructured":"Blok, W.J., Pigozzi, D.: Algebraizable logics. Mem. Amer. Math. Soc. vol. 396, A.M.S., Providence, 1989","DOI":"10.1090\/memo\/0396"},{"key":"324_CR7","unstructured":"Bou, F., Garc\u00eda-Cerda\u00f1a, \u00c0., Verd\u00fa, V.: Analysis of two fragments of the logic of residuated lattices. In: W.A. Carnielli, F.M. Dion\u00edsio, P. Mateus (eds.) Proceedings of CombLog'04. Workshop on Combination of Logics: Theory and Applications, Lisbon, 2004, pp. 175\u2013186"},{"key":"324_CR8","doi-asserted-by":"crossref","unstructured":"Bou, F., Garc\u00eda-Cerda\u00f1a, \u00c0., Verd\u00fa, V.: On two fragments with negation and without implication of the logic of residuated lattices. Mathematics Preprint Series 369, IMUB University of Barcelona, 2005. Available on line at http:\/\/www.imub.es\/publications.html.","DOI":"10.1007\/s00153-005-0324-9"},{"key":"324_CR9","unstructured":"Burris, S., Sankappanavar, H.P.: A course in universal algebra. The Millennium Edn. (2000)"},{"key":"324_CR10","doi-asserted-by":"crossref","unstructured":"Cignoli, R., D'Ottaviano, I.M.L., Mundici, D.: Algebraic foundations of many-valued reasoning, Trends in Logic\u2013-Studia Logica Library, vol. 7. Kluwer Academic Publishers, Dordrecht, 2000","DOI":"10.1007\/978-94-015-9480-6"},{"key":"324_CR11","first-page":"105","volume":"4","author":"Cotlar","year":"1944","unstructured":"Cotlar, M.: A method of construction of structures and its application to topological spaces and abstract arithmetic (Spanish). Univ. Nac. Tucum\u00e1n Rev. Ser. A. 4, 105\u2013157 (1944)","journal-title":"Univ. Nac. Tucum\u00e1n Rev. Ser. A."},{"key":"324_CR12","doi-asserted-by":"crossref","first-page":"748","DOI":"10.1090\/S0002-9939-1962-0140451-2","volume":"13","author":"Crawley","year":"1962","unstructured":"Crawley, P.: Regular embeddings which preserve lattice structure. Proc. Amer. Math. Soc. 13, 748\u2013752 (1962)","journal-title":"Proc. Amer. Math. Soc."},{"key":"324_CR13","doi-asserted-by":"crossref","unstructured":"Czelakowski, J.: Protoalgebraic logics. Trends in Logic\u2013-Studia Logica Library, vol. 10, Kluwer Academic Publishers, Dordrecht, 2001","DOI":"10.1007\/978-94-017-2807-2"},{"key":"324_CR14","unstructured":"Devlin, K.: The joy of sets. Fundamentals of Contemporary Set Theory, second edn. Undergraduate Texts in Mathematics. Springer-Verlag, 1991"},{"key":"324_CR15","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1215\/S0012-7094-52-01972-8","volume":"19","author":"Dilworth","year":"1952","unstructured":"Dilworth, R.P., McLaughlin, J.E.: Distributivity in lattices. Duke Math. J. 19, 683\u2013693 (1952)","journal-title":"Duke Math. J."},{"key":"324_CR16","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/S0165-0114(01)00098-7","volume":"124","author":"Esteva","year":"2001","unstructured":"Esteva, F., Godo, L.: Monoidal t-norm based logic: towards a logic for left-continuous t-norms. Fuzzy Sets and Systems 124, 271\u2013288 (2001)","journal-title":"Fuzzy Sets and Systems"},{"key":"324_CR17","doi-asserted-by":"crossref","unstructured":"Esteva, F., Godo, L., Garc\u00eda-Cerda\u00f1a, \u00c0.: On the hierarchy of t-norm based residuated fuzzy logics. In: M. Fitting, E. Or\u0142owska (eds.) Beyond two: theory and applications of multiple-valued logic. Studies in Fuzziness and Soft Computing, vol. 114, Physica, Heidelberg, 2003, pp. 251\u2013272","DOI":"10.1007\/978-3-7908-1769-0_11"},{"key":"324_CR18","doi-asserted-by":"crossref","unstructured":"Font, J.M., Jansana, R., Pigozzi, D.: A survey on abstract algebraic logic. Studia Logica, Special Issue on Abstract Algebraic Logic, Part II 74 (1\/2), 13\u201397 (2003)","DOI":"10.1023\/A:1024621922509"},{"key":"324_CR19","doi-asserted-by":"crossref","first-page":"51","DOI":"10.2140\/pjm.1973.49.51","volume":"49","author":"Freese","year":"1973","unstructured":"Freese, R., Nation, J.B.: Congruence lattices of semilattices. Pacific J. Math. 49, 51\u201358 (1973). See also the manuscript Clarification to ``Congruence Lattices of Semilattices'', 1997","journal-title":"Pacific J. Math."},{"key":"324_CR20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3792\/pia\/1195573210","volume":"20","author":"Funayama","year":"1944","unstructured":"Funayama, N.: On the completion by cuts of distributive lattices. Proc. Imp. Acad. Tokyo 20, 1\u20132 (1944)","journal-title":"Proc. Imp. Acad. Tokyo"},{"key":"324_CR21","unstructured":"Gehrke, M., Harding, J., Venema, Y.: MacNeille completions and canonical extensions. Research Report PP-2004-05, Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, 2004"},{"key":"324_CR22","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1093\/logcom\/7.4.473","volume":"7","author":"Gil","year":"4","unstructured":"Gil, A.J., Torrens, A., Verd\u00fa, V.: On Gentzen systems associated with the finite linear MV-algebras. Journal of Logic and Computation 7 (4), 473\u2013500 (1997)","journal-title":"Journal of Logic and Computation"},{"key":"324_CR23","unstructured":"Gr\u00e4tzer, G.: General lattice theory, Second edition. Birkh\u00e4user Verlag, Basel, 1998"},{"key":"324_CR24","doi-asserted-by":"crossref","unstructured":"H\u00e1jek, P.: Metamathematics of fuzzy logic, Trends in Logic\u2013-Studia Logica Library, vol. 4. Kluwer Academic Publishers, Dordrecht, 1998","DOI":"10.1007\/978-94-011-5300-3"},{"key":"324_CR25","doi-asserted-by":"crossref","unstructured":"Halmos, P.R.: Lectures on Boolean algebras. Springer-Verlag 1974. Reprint of the ed. published by Van Nostrand, New York, 1963","DOI":"10.1007\/978-1-4612-9855-7_13"},{"key":"324_CR26","doi-asserted-by":"crossref","unstructured":"H\u00f6hle, U.: Commutative, residuated l-monoids. In: U. H\u00f6hle, E.P. Klement (eds.) Non-classical logics and their applications to fuzzy subsets (Linz, 1992), Theory Decis. Lib. Ser. B Math. Statist. Methods, vol. 32, Kluwer Acad. Publ. Dordrecht, 1995, pp. 53\u2013106","DOI":"10.1007\/978-94-011-0215-5_5"},{"key":"324_CR27","doi-asserted-by":"crossref","unstructured":"Jipsen, P., Tsinakis, C.: A survey of residuated lattices. In: J. Martinez (ed.) Ordered Algebraic Structures, Kluwer Academic Publishers, Dordrecht, 2002 pp. 19\u201356","DOI":"10.1007\/978-1-4757-3627-4_3"},{"key":"324_CR28","unstructured":"Kowalski, T., Ono, H.: The variety of residuated lattices is generated by its finite simple members. Reports on Mathematical Logic (34), 59\u201377 (2000). Algebra & substructural logics, Tatsunokuchi, 1999"},{"key":"324_CR29","unstructured":"Kowalski, T., Ono, H.: Residuated lattices: an algebraic glimpse at logics without contraction (preliminary report) (2001)"},{"key":"324_CR30","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1090\/S0002-9939-1973-0392730-9","volume":"37","author":"Lakser","year":"1973","unstructured":"Lakser, H.: Principal congruences of pseudocomplemented distributive lattices. Proceedings of the American Mathematical Society 37, 32\u201337 (1973)","journal-title":"Proceedings of the American Mathematical Society"},{"key":"324_CR31","doi-asserted-by":"crossref","unstructured":"Ono, H.: Semantics for substructural logics. In: K. Do\u0161en, P. Schroeder-Heister (eds.) Substructural logics, Oxford University Press, 1993, pp. 259\u2013291","DOI":"10.1093\/oso\/9780198537779.003.0010"},{"key":"324_CR32","doi-asserted-by":"crossref","unstructured":"Ono, H.: Proof-theoretic methods for nonclassical logic - an introduction. In: M. Takahashi, M. Okada, M. Dezani-Ciancaglini (eds.) Theories of Types and Proofs, MSJ Memoirs 2, Mathematical Society of Japan, 1998, pp. 207\u2013254","DOI":"10.2969\/msjmemoirs\/00201C060"},{"key":"324_CR33","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1023\/A:1025171301247","volume":"74","author":"Ono","year":"3","unstructured":"Ono, H.: Closure operators and complete embeddings of residuated lattices. Studia Logica 74 (3), 427\u2013440 (2003)","journal-title":"Studia Logica"},{"key":"324_CR34","unstructured":"Ono, H.: Completions of algebras and completeness of modal and substructural logics. pp. 335\u2013353 (2003)"},{"key":"324_CR35","doi-asserted-by":"crossref","unstructured":"Ono, H.: Substructural logics and residuated lattices - an introduction. In: V.F. Hendricks, J. Malinowski (eds.) 50 Years of Studia Logica Trends in Logic\u2013-Studia Logica Library. vol. 21, Dordrecht, 2003, pp. 193\u2013228","DOI":"10.1007\/978-94-017-3598-8_8"},{"key":"324_CR36","doi-asserted-by":"crossref","first-page":"169","DOI":"10.2307\/2273798","volume":"50","author":"Ono","year":"1","unstructured":"Ono, H., Komori, Y.: Logics without the contraction rule. The Journal of Symbolic Logic 50 (1), 169\u2013201 (1985)","journal-title":"The Journal of Symbolic Logic"},{"key":"324_CR37","first-page":"319","volume":"18","author":"Rebagliato","year":"1993","unstructured":"Rebagliato, J., Verd\u00fa, V.: On the algebraization of some Gentzen systems. Fundamenta Informaticae, Special Issue on Algebraic Logic and its Applications 18, 319\u2013338 (1993)","journal-title":"Fundamenta Informaticae, Special Issue on Algebraic Logic and its Applications"},{"key":"324_CR38","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1002\/malq.19940400109","volume":"40","author":"Rebagliato","year":"1994","unstructured":"Rebagliato, J., Verd\u00fa, V.: A finite Hilbert-style axiomatization of the implication-less fragment of the intuitionistic propositional calculus. Mathematical Logic Quarterly 40, 61\u201368 (1994)","journal-title":"Mathematical Logic Quarterly"},{"key":"324_CR39","unstructured":"Rebagliato, J., Verd\u00fa, V.: Algebraizable Gentzen systems and the deduction theorem for Gentzen systems. Mathematics Preprint Series 175, University of Barcelona, 1995"},{"key":"324_CR40","unstructured":"Russell, R.: The large deviations of random time-changes. Ph. D. Dissertation, University of Dublin, 1998"},{"key":"324_CR41","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/BF01900297","volume":"7","author":"Schmidt","year":"1956","unstructured":"Schmidt, J.: Zur Kennzeichnung der Dedekind-MacNeilleschen H\u00fclle einer geordneten H\u00fclle. Arch. Math. 7, 241\u2013249 (1956)","journal-title":"Arch. Math."},{"key":"324_CR42","doi-asserted-by":"crossref","unstructured":"W\u00f3jcicki, R.: Theory of logical calculi. Basic theory of consequence operations, Synthese Library, vol. 199. Reidel, Dordrecht, 1988","DOI":"10.1007\/978-94-015-6942-2"},{"key":"324_CR43","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1023\/A:1023360709757","volume":"73","author":"W\u00f3jcicki","year":"3","unstructured":"W\u00f3jcicki, R.: A logic is referential iff it is selfextensional. Studia Logica 73 (3), 323\u2013335 (2003)","journal-title":"Studia Logica"}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-005-0324-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00153-005-0324-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-005-0324-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,31]],"date-time":"2024-01-31T23:40:25Z","timestamp":1706744425000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00153-005-0324-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,11,21]]},"references-count":43,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2006,7]]}},"alternative-id":["324"],"URL":"https:\/\/doi.org\/10.1007\/s00153-005-0324-9","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"type":"print","value":"0933-5846"},{"type":"electronic","value":"1432-0665"}],"subject":[],"published":{"date-parts":[[2005,11,21]]}}}