{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T04:10:30Z","timestamp":1747195830657},"reference-count":92,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2008,6]]},"abstract":"<jats:p>A translation in an algebraic signature is a finite conjunction of equations in one variable. On a quasivariety K, a translation \u03c4 naturally induces a deductive system, called the \u03c4-assertional logic of K. Two quasivarieties are \u03c4-assertionally equivalent if they have the same \u03c4-assertional logic. This paper is a study of assertional equivalence. It characterizes the quasivarieties equivalent to ones with various desirable properties, such as \u03c4-regularity (a general form of point regularity). Special attention is paid to structural properties of quasivarieties that are assertionally equivalent to their varietal closures under an indicated translation.<\/jats:p>","DOI":"10.1142\/s0218196708004627","type":"journal-article","created":{"date-parts":[[2008,6,24]],"date-time":"2008-06-24T09:38:40Z","timestamp":1214300320000},"page":"589-681","source":"Crossref","is-referenced-by-count":33,"title":["ASSERTIONALLY EQUIVALENT QUASIVARIETIES"],"prefix":"10.1142","volume":"18","author":[{"given":"W. J.","family":"BLOK","sequence":"first","affiliation":[{"name":"Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, Illinois 60607-7045, USA"}]},{"given":"J. G.","family":"RAFTERY","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X54001, Durban 4000, South Africa"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"397","volume":"64","author":"Agliano P.","journal-title":"Acta Sci. Math. (Szeged)"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700035436"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01234106"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/s000120050020"},{"key":"rf5","volume-title":"Entailment: The Logic of Relevance and Necessity","volume":"1","author":"Anderson A. R.","year":"1975"},{"key":"rf6","volume-title":"Entailment: The Logic of Relevance and Necessity","volume":"2","author":"Anderson A. R.","year":"1992"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19980440304"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(88)90037-0"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.2307\/2274660"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093635414"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1093\/jigpal\/5.2.181"},{"key":"rf12","volume-title":"Distributive Lattices","author":"Balbes R.","year":"1974"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022873713616"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1080\/16073606.1997.9632225"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1023\/B:STUD.0000037127.15182.2a"},{"key":"rf17","first-page":"387","volume":"66","author":"Bignall R. J.","journal-title":"Scientia Math. Japonicae"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1007\/BF00375898"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370269"},{"key":"rf21","series-title":"Memoirs of the American Mathematical Society","volume-title":"Algebraizable Logics","volume":"396","author":"Blok W. J.","year":"1989"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1007\/BF01190766"},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1996.6834"},{"key":"rf26","unstructured":"W. J.\u00a0Blok and J. G.\u00a0Raftery, Models, Algebras and Proofs, Lecture Notes in Pure and Applied Mathematics\u00a0203, eds. X.\u00a0Caicedo and C. H.\u00a0Montenegro (Marcel Dekker, New York, 1999)\u00a0pp. 167\u2013186."},{"key":"rf27","doi-asserted-by":"publisher","DOI":"10.1007\/s000120050198"},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-005-0106-8"},{"key":"rf29","doi-asserted-by":"publisher","DOI":"10.1023\/A:1024626023417"},{"key":"rf30","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8130-3"},{"key":"rf31","doi-asserted-by":"publisher","DOI":"10.1007\/BF02483883"},{"key":"rf32","doi-asserted-by":"crossref","first-page":"505","DOI":"10.21136\/CMJ.1983.101905","volume":"33","author":"Chajda I.","journal-title":"Czechoslovak Math. J."},{"key":"rf33","doi-asserted-by":"publisher","DOI":"10.1007\/BF01898144"},{"key":"rf34","volume-title":"Foundations of Mathematical Logic","author":"Curry H. B.","year":"1963"},{"key":"rf35","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-2807-2"},{"key":"rf36","doi-asserted-by":"publisher","DOI":"10.2307\/2586559"},{"key":"rf37","doi-asserted-by":"crossref","first-page":"197","DOI":"10.21136\/CMJ.1987.102149","volume":"37","author":"Duda J.","journal-title":"Czechoslovak Math. J."},{"key":"rf38","doi-asserted-by":"publisher","DOI":"10.2307\/2271149"},{"key":"rf39","doi-asserted-by":"publisher","DOI":"10.4064\/fm-133-1-47-57"},{"key":"rf40","doi-asserted-by":"publisher","DOI":"10.1007\/BF02681565"},{"key":"rf41","first-page":"445","volume":"75","author":"Fichtner K.","journal-title":"Mat. Sbornik"},{"key":"rf42","first-page":"21","volume":"12","author":"Fichtner K.","journal-title":"Monatsch. d. deutsch. Akad. d. Wiss."},{"key":"rf43","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(88)90065-8"},{"key":"rf44","doi-asserted-by":"publisher","DOI":"10.1023\/A:1024621922509"},{"key":"rf45","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19900360606"},{"key":"rf46","series-title":"London Mathematical Society Lecture Note Series","volume-title":"Commutator Theory for Congruence Modular Varieties","volume":"125","author":"Freese R.","year":"1987"},{"key":"rf47","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1973.49.51"},{"key":"rf48","volume-title":"Residuated Lattices. An Algebraic Glimpse at Substructural Logics","author":"Galatos N.","year":"2007"},{"key":"rf49","doi-asserted-by":"publisher","DOI":"10.1023\/B:STUD.0000037126.29193.09"},{"key":"rf50","doi-asserted-by":"publisher","DOI":"10.1007\/BF01157527"},{"key":"rf51","doi-asserted-by":"publisher","DOI":"10.1007\/BF01191491"},{"key":"rf53","doi-asserted-by":"publisher","DOI":"10.1007\/BF02945100"},{"key":"rf54","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196702001048"},{"key":"rf55","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370843"},{"key":"rf56","doi-asserted-by":"publisher","DOI":"10.1023\/A:1004979825733"},{"key":"rf57","first-page":"69","volume":"29","author":"Higgs D.","journal-title":"Math. Japonica"},{"key":"rf58","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/076"},{"key":"rf59","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200610018"},{"key":"rf60","doi-asserted-by":"publisher","DOI":"10.3792\/pja\/1195522171"},{"key":"rf61","doi-asserted-by":"publisher","DOI":"10.1023\/B:STUD.0000032089.54776.63"},{"key":"rf62","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3627-4_3"},{"key":"rf63","first-page":"130","volume":"12","author":"Kabzi\u0144ski J. K.","journal-title":"Bull. Sect. Log., Polish Acad. Sci., Inst. Philos. Sociol."},{"key":"rf65","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1992-1062872-X"},{"key":"rf66","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196798000247"},{"key":"rf68","first-page":"391","volume":"29","author":"Komori Y.","journal-title":"Math. Japonica"},{"key":"rf69","doi-asserted-by":"publisher","DOI":"10.1007\/BF01057936"},{"key":"rf71","doi-asserted-by":"publisher","DOI":"10.1007\/BF01188995"},{"key":"rf72","doi-asserted-by":"publisher","DOI":"10.1007\/BF01190927"},{"key":"rf73","first-page":"177","volume":"20","author":"\u0141o\u015b J.","journal-title":"Indag. Math."},{"key":"rf74","volume-title":"Equivalence in Intensional Logics","author":"Malinowski J.","year":"1989"},{"key":"rf75","doi-asserted-by":"publisher","DOI":"10.2307\/2273106"},{"key":"rf76","doi-asserted-by":"publisher","DOI":"10.1007\/BF02120525"},{"key":"rf77","first-page":"407","volume":"15","author":"Meyer R. K.","journal-title":"Logique et Analyse N. S."},{"key":"rf78","doi-asserted-by":"publisher","DOI":"10.1007\/BF01054710"},{"key":"rf79","first-page":"696","volume":"29","author":"Nurakunov A. M.","journal-title":"Algebra i Logika"},{"key":"rf80","doi-asserted-by":"publisher","DOI":"10.2307\/2273798"},{"key":"rf81","first-page":"130","volume":"13","author":"Pa\u0142asinski M.","journal-title":"Bull. Sect. Log., Polish Acad. Sci., Inst. Philos. Sociol."},{"key":"rf82","first-page":"749","volume":"10","author":"Pa\u0142asinski M.","journal-title":"Math. Sem. Notes Kobe Univ."},{"key":"rf83","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093894720"},{"key":"rf84","unstructured":"D.\u00a0Pigozzi, Algebraic Logic, Colloquia Mathematica Societatis J\u00e1nos Bolyai\u00a054, eds. H.\u00a0Andr\u00e9ka, J. D.\u00a0Monk and I.\u00a0Nemeti (Budapest, Hungary, 1988)\u00a0pp. 473\u2013502."},{"key":"rf85","first-page":"30","volume":"3","author":"Prucnal T.","journal-title":"Bull. Sect. Log., Polish Acad. Sci., Inst. Philos. Sociol."},{"key":"rf86","doi-asserted-by":"publisher","DOI":"10.1007\/BF01236524"},{"key":"rf87","first-page":"95","volume":"41","author":"Raftery J. G.","journal-title":"Rep. Math. Log."},{"key":"rf88","first-page":"71","volume":"42","author":"Raftery J. G.","journal-title":"Rep. Math. Log."},{"key":"rf90","doi-asserted-by":"crossref","first-page":"727","DOI":"10.21136\/CMJ.1992.128368","volume":"42","author":"Raftery J. G.","journal-title":"Czechoslovak Math. J."},{"key":"rf92","first-page":"23","volume":"1","author":"Soboci\u0144ski B.","journal-title":"J. Comput. Syst."},{"key":"rf93","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008237600846"},{"key":"rf95","series-title":"CSLI Lecture Notes","volume-title":"Lectures on Linear Logic","volume":"29","author":"Troelstra A. S.","year":"1992"},{"key":"rf97","doi-asserted-by":"publisher","DOI":"10.1007\/BF01236518"},{"key":"rf98","doi-asserted-by":"publisher","DOI":"10.1023\/B:STUD.0000032087.02579.e2"},{"key":"rf99","doi-asserted-by":"publisher","DOI":"10.1007\/BF01874706"},{"key":"rf100","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1939-1501995-3"},{"key":"rf101","first-page":"303","volume":"44","author":"Wei S. M.","journal-title":"Math. Japonica"},{"key":"rf102","first-page":"211","volume":"28","author":"Wro\u0144ski A.","journal-title":"Math. Japonica"},{"key":"rf103","first-page":"215","volume":"28","author":"Wro\u0144ski A.","journal-title":"Math. Japonica"},{"key":"rf104","first-page":"115","volume":"29","author":"Wro\u0144ski A.","journal-title":"Math. Japonica"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196708004627","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,12]],"date-time":"2021-09-12T15:12:00Z","timestamp":1631459520000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196708004627"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,6]]},"references-count":92,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2008,6]]}},"alternative-id":["10.1142\/S0218196708004627"],"URL":"https:\/\/doi.org\/10.1142\/s0218196708004627","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,6]]}}}