{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,5]],"date-time":"2024-02-05T09:10:19Z","timestamp":1707124219802},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[2006,6,1]],"date-time":"2006-06-01T00:00:00Z","timestamp":1149120000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Stud Logica"],"published-print":{"date-parts":[[2006,6]]},"DOI":"10.1007\/s11225-006-8296-2","type":"journal-article","created":{"date-parts":[[2006,7,13]],"date-time":"2006-07-13T10:36:05Z","timestamp":1152786965000},"page":"15-30","source":"Crossref","is-referenced-by-count":7,"title":["Willem Blok and Modal Logic"],"prefix":"10.1007","volume":"83","author":[{"given":"W.","family":"Rautenberg","sequence":"first","affiliation":[]},{"given":"M.","family":"Zakharyaschev","sequence":"additional","affiliation":[]},{"given":"F.","family":"Wolter","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"8296_CR1","unstructured":"BLOK, W. J., Varieties of interior algebras, PhD thesis, University of Amsterdam, 1976."},{"key":"8296_CR2","first-page":"112","volume":"6","author":"W. J. BLOK","year":"1977","unstructured":"BLOK, W. J., \u2018The lattice of modal logics (abstract)\u2019, Bulletin of the Section of Logic of the Polish Academy of Sciences 6 (1977), 112\u2013115.","journal-title":"Bulletin of the Section of Logic of the Polish Academy of Sciences"},{"key":"8296_CR3","first-page":"167","volume":"7","author":"W. J. BLOK","year":"1978","unstructured":"BLOK, W. J., \u2018On the degree of incompleteness of modal logics (abstract)\u2019, Bulletin of the Section of Logic of the Polish Academy of Sciences 7 (1978), 167\u2013175.","journal-title":"Bulletin of the Section of Logic of the Polish Academy of Sciences"},{"key":"8296_CR4","unstructured":"BLOK, W. J., \u2018On the degree of incompleteness of modal logics and the covering relation in the lattice of modal logics\u2019, Technical Report 78\u201307, Department of Mathematics, University of Amsterdam, 1978."},{"key":"8296_CR5","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/BF00493671","volume":"38","author":"W. J. BLOK","year":"1979","unstructured":"BLOK, W. J., \u2018An axiomatization of the modal theory of the veiled recession frame\u2019, Studia Logica 38 (1979) 37\u201347.","journal-title":"Studia Logica"},{"key":"8296_CR6","doi-asserted-by":"crossref","first-page":"221","DOI":"10.2307\/2273184","volume":"45","author":"W. J. BLOK","year":"1980","unstructured":"BLOK, W. J., \u2018The lattice of modal logics: an algebraic investigation\u2019, Journal of Symbolic Logic 45 (1980), 221\u2013236.","journal-title":"Journal of Symbolic Logic"},{"key":"8296_CR7","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1007\/BF02483108","volume":"11","author":"W. J. BLOK","year":"1980","unstructured":"BLOK, W. J., \u2018The lattice of varieties of modal algebras is not strongly atomic\u2019, Algebra Universalis 11 (1980), 285\u2013294.","journal-title":"Algebra Universalis"},{"key":"8296_CR8","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1007\/BF00370315","volume":"39","author":"W. J. BLOK","year":"1980","unstructured":"BLOK, W. J., \u2018Pretabular varieties of modal algebras\u2019, Studia Logica 39 (1980), 101\u2013124.","journal-title":"Studia Logica"},{"key":"8296_CR9","unstructured":"BLOK, W. J., \u2018Reminiscences about modal logic in the seventies\u2019, 2000."},{"key":"8296_CR10","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/1385-7258(75)90033-5","volume":"37","author":"W. J. BLOK","year":"1975","unstructured":"BLOK, W. J., and P. DWINGER, \u2018Equational classes of closure algebras\u2019, Indagationes Mathematicae 37 (1975), 189\u2013198.","journal-title":"Indagationes Mathematicae"},{"key":"8296_CR11","doi-asserted-by":"crossref","first-page":"941","DOI":"10.2307\/2273660","volume":"48","author":"W. J. BLOK","year":"1983","unstructured":"BLOK, W. J., and P. KOHLER, \u2018Algebraic semantics for quasi-classical modal logics\u2019, Journal of Symbolic Logic 48 (1983), 941\u2013964.","journal-title":"Journal of Symbolic Logic"},{"key":"8296_CR12","volume-title":"Modal Logic, volume 35 of Oxford Logic Guides","author":"A. CHAGROV","year":"1997","unstructured":"CHAGROV, A., and M. ZAKHARYASCHEV, Modal Logic, volume 35 of Oxford Logic Guides, Clarendon Press, Oxford, 1997."},{"key":"8296_CR13","first-page":"105","volume-title":"Algebraic and Logical Constructions","author":"A. CHAGROV","year":"1989","unstructured":"CHAGROV, A., \u2018Nontabularity-pretabularity, antitabularity, co-antitabularity\u2019, in Algebraic and Logical Constructions, Kalinin State University, Kalinin, 1989, pp. 105\u2013111. (Russian)."},{"key":"8296_CR14","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/BF00370331","volume":"51","author":"A. CHAGROV","year":"1992","unstructured":"CHAGROV, A., and M. ZAKHARYASCHEV, \u2018Modal companions of intermediate prepositional logics\u2019, Studio, Logica 51 (1992), 49\u201382.","journal-title":"Studio, Logica"},{"key":"8296_CR15","unstructured":"CHAGROVA, L., \u2018On the degree of neighbourhood incompleteness of normal modal logics\u2019, in KRACHT, M., M. DE RIJKE, H. WANSING, and M. ZAKHARYASCHEV, (eds.) Advances in Modal Logic 1, CSLI Publications 1998, pp. 63\u201372."},{"key":"8296_CR16","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1002\/malq.19590051405","volume":"5","author":"M. DUMMETT","year":"1959","unstructured":"DUMMETT, M., and E. LEMMON, \u2018Modal logics between S4 and S5\u2019, Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik 5 (1959), 250\u2013264.","journal-title":"Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik"},{"key":"8296_CR17","first-page":"136","volume":"9","author":"W. DZIOBIAK","year":"1978","unstructured":"DZIOBIAK, W., \u2018A note on incompleteness of modal logics with respect to neighbourhood semantics\u2019, Bulletin of the Section of Logic 9 (1978), 136\u2013140.","journal-title":"Bulletin of the Section of Logic"},{"key":"8296_CR18","first-page":"257","volume-title":"Studies in Non-classical Logics and Set Theory","author":"L.L. ESAKIA","year":"1979","unstructured":"ESAKIA, L.L., \u2018On varieties of Grzegorczyk algebras\u2019, in MIKHAILOV, A. L, (ed.) Studies in Non-classical Logics and Set Theory, pp. 257\u2013287. Moscow, Nauka, 1979. (Russian)."},{"key":"8296_CR19","unstructured":"ESAKIA, L.L., \u2018To the theory of modal and superintuitionistic systems\u2019, in SMIRNOV, V. A., (ed.) Logical Inference. Proceedings of the USSR Symposium on the Theory of Logical Inference, pp. 147\u2013172. Nauka, Moscow, 1979. (Russian)."},{"key":"8296_CR20","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1111\/j.1755-2567.1977.tb00779.x","volume":"40","author":"L.L. ESAKIA","year":"1977","unstructured":"ESAKIA, L.L., and V. Yu. MESKHI, \u2018Five critical systems\u2019, Theoria 40 (1977), 52\u201360.","journal-title":"Theoria"},{"key":"8296_CR21","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1111\/j.1755-2567.1974.tb00076.x","volume":"40","author":"K. FINE","year":"1974","unstructured":"FINE, K., \u2018An incomplete logic containing S4\u2019, Theoria 40 (1974), 23\u201329.","journal-title":"Theoria"},{"key":"8296_CR22","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/S1570-8683(03)00008-9","volume":"1","author":"R. GOLDBLATT","year":"2003","unstructured":"GOLDBLATT, R., \u2018Mathematical modal logic: a view of its evolution\u2019, Journal of Applied Logic 1 (2003), 309\u2013392.","journal-title":"Journal of Applied Logic"},{"key":"8296_CR23","doi-asserted-by":"crossref","first-page":"223","DOI":"10.4064\/fm-60-3-223-231","volume":"60","author":"A. GRZEGORCZYK","year":"1967","unstructured":"GRZEGORCZYK, A., \u2018Some relational systems and the associated topological spaces\u2019, Fundamenta Mathematicae 60 (1967), 223\u2013231.","journal-title":"Fundamenta Mathematicae"},{"key":"8296_CR24","first-page":"1203","volume":"4","author":"V. A. JANKOV","year":"1963","unstructured":"JANKOV, V. A., \u2018The relationship between deducibility in the intuitionistic prepositional calculus and finite implicational structures\u2019, Soviet Mathematics Doklady 4 (1963), 1203\u20131204.","journal-title":"Soviet Mathematics Doklady"},{"key":"8296_CR25","doi-asserted-by":"crossref","unstructured":"JANSANA, R., \u2018Willem Blok's contribution to abstract algebraic logic\u2019, Studia Logica 31\u201348 of this issue.","DOI":"10.1007\/s11225-006-8297-1"},{"key":"8296_CR26","doi-asserted-by":"crossref","first-page":"110","DOI":"10.7146\/math.scand.a-10850","volume":"21","author":"B. JONSSON","year":"1967","unstructured":"JONSSON, B., \u2018Algebras whose congruence lattices are distributive\u2019, Mathematica Scandinavica 21 (1967), 110\u2013121.","journal-title":"Mathematica Scandinavica"},{"key":"8296_CR27","volume-title":"Tools and Techniques in Modal Logic, Studies in Logic","author":"M. KRACHT","year":"1999","unstructured":"KRACHT, M., Tools and Techniques in Modal Logic, Studies in Logic. Elsevier, North-Holland, 1999."},{"key":"8296_CR28","unstructured":"KUZNETSOV, A. V., \u2018Some properties of the structure of varieties of pseudo-Boolean algebras\u2019, in Proceedings of the Xlth USSR Algebraic Colloquium, pp. 255\u2013256, Kishinev, 1971. (Russian)."},{"key":"8296_CR29","unstructured":"LlTAK, T., An algebraic approach to incompleteness in modal logic, Ph. D. thesis, JAIST, 2005."},{"key":"8296_CR30","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1007\/BF01668553","volume":"14","author":"L. MAKSIMOVA","year":"1975","unstructured":"MAKSIMOVA, L., \u2018Modal logics of finite slices\u2019, Algebra and Logic 14 (1975), 188\u2013197.","journal-title":"Algebra and Logic"},{"key":"8296_CR31","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1007\/BF01668576","volume":"14","author":"L. MAKSIMOVA","year":"1975","unstructured":"MAKSIMOVA, L., \u2018Pretabular extensions of Lewis 54\u2019, Algebra and Logic 14 (1975), 16\u201333.","journal-title":"Algebra and Logic"},{"key":"8296_CR32","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/BF01463150","volume":"13","author":"L. MAKSIMOVA","year":"1974","unstructured":"MAKSIMOVA, L., and V. RYBAKOV, \u2018Lattices of modal logics\u2019, Algebra and Logic 13 (1974), 105\u2013122.","journal-title":"Algebra and Logic"},{"key":"8296_CR33","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0002-9947-1972-0313141-1","volume":"174","author":"R. McKENZIE","year":"1972","unstructured":"McKENZIE, R., \u2018Equational bases and non-modular lattice varieties\u2019, Transactions of the American Mathematical Society 174 (1972), 1\u201343.","journal-title":"Transactions of the American Mathematical Society"},{"key":"8296_CR34","doi-asserted-by":"crossref","first-page":"141","DOI":"10.2307\/1969080","volume":"45","author":"J. C. C. McKlNSEY","year":"1944","unstructured":"McKlNSEY, J. C. C., and A. TARSKI, \u2018The algebra of topology\u2019, Annals of Mathematics, 45 (1944), 141\u2013191.","journal-title":"Annals of Mathematics"},{"key":"8296_CR35","doi-asserted-by":"crossref","first-page":"122","DOI":"10.2307\/1969038","volume":"47","author":"J. C. C. McKlNSEY","year":"1946","unstructured":"McKlNSEY, J. C. C., and A. TARSKI, \u2018On closed elements in closure algebras\u2019, Annals of Mathematics 47 (1946), 122\u2013162.","journal-title":"Annals of Mathematics"},{"key":"8296_CR36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/2268135","volume":"13","author":"J. C. C. McKlNSEY","year":"1948","unstructured":"McKlNSEY, J. C. C., and A. TARSKI, \u2018Some theorems about the sentential calculi of Lewis and Heyting\u2019, Journal of Symbolic Logic 13 (1948), 1\u201315.","journal-title":"Journal of Symbolic Logic"},{"key":"8296_CR37","doi-asserted-by":"crossref","unstructured":"RAUTENBERG, W., Klassische und nichtklassische Aussagenlogik, Vieweg, Braunschweig-Wiesbaden, 1979.","DOI":"10.1007\/978-3-322-85796-5"},{"key":"8296_CR38","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/BF02021134","volume":"20","author":"W. RAUTENBERG","year":"1980","unstructured":"RAUTENBERG, W., \u2018Splitting lattices of logics\u2019, Archiv fur Mathematische Logik 20 (1980), 155\u2013159.","journal-title":"Archiv fur Mathematische Logik"},{"key":"8296_CR39","unstructured":"SEGERBERG, K., \u2018An essay in classical modal logic\u2019, Philosophical Studies 13 (1971)."},{"key":"8296_CR40","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1111\/j.1755-2567.1974.tb00077.x","volume":"40","author":"S. THOMASON","year":"1974","unstructured":"THOMASON, S., \u2018An incompleteness theorem in modal logic\u2019, Theoria 40 (1974), 30\u201334.","journal-title":"Theoria"},{"key":"8296_CR41","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/S0168-0072(96)00049-8","volume":"86","author":"P. WOLTER","year":"1997","unstructured":"WOLTER, P., \u2018The structure of lattices of subframe logics\u2019, Annals of Pure and Applied Logic 86 (1997), 47\u2013100.","journal-title":"Annals of Pure and Applied Logic"},{"key":"8296_CR42","doi-asserted-by":"crossref","unstructured":"WOLTER, P., and M. ZAKHARYASCHEV, \u2018Modal decision problems\u2019, in BLACKBURN, P., J. VAN BENTHEM, and F. WOLTER, (eds.) Handbook of Modal Logic, Elsevier, 2006.","DOI":"10.1016\/S1570-2464(07)80010-3"},{"key":"8296_CR43","doi-asserted-by":"crossref","unstructured":"ZAKHARYASCHEV, M., F. WOLTER, and A. CHAGROV, \u2018Advanced modal logic\u2019, in GABBAY, D., and F. GUENTHNER, (eds.) Handbook of Philosophical Logic, vol.3, pp. 83\u2013266. Kluwer Academic Publishers, 2nd edition, 2001.","DOI":"10.1007\/978-94-017-0454-0_2"}],"container-title":["Studia Logica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11225-006-8296-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11225-006-8296-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11225-006-8296-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,5]],"date-time":"2024-02-05T08:33:40Z","timestamp":1707122020000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11225-006-8296-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,6]]},"references-count":43,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[2006,6]]}},"alternative-id":["8296"],"URL":"https:\/\/doi.org\/10.1007\/s11225-006-8296-2","relation":{},"ISSN":["0039-3215","1572-8730"],"issn-type":[{"value":"0039-3215","type":"print"},{"value":"1572-8730","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,6]]}}}