{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:56:24Z","timestamp":1750308984505,"version":"3.41.0"},"reference-count":45,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[1983,7,1]],"date-time":"1983-07-01T00:00:00Z","timestamp":425865600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["SIGACT News"],"published-print":{"date-parts":[[1983,7]]},"abstract":"<jats:p>We introduce classes of interpretations. We characterize the free and Herbrand interpretations for a class. We define the algebraic, equational, relational and first-order classes of interpretations, study their properties and relate them to the literature. We apply this study to derive complete proof systems for deducing (in some (in) equational logic) all (in) equalitions valid in a class.<\/jats:p>","DOI":"10.1145\/1008933.1008936","type":"journal-article","created":{"date-parts":[[2004,10,12]],"date-time":"2004-10-12T15:20:46Z","timestamp":1097594446000},"page":"45-71","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Survey on classes of interpretations and some of their applications"],"prefix":"10.1145","volume":"15","author":[{"given":"Ir\u00e8ne","family":"Guessarian","sequence":"first","affiliation":[{"name":"Universit\u00e9 Paris 7, UER de Math\u00e9matiques, Paris"}]}],"member":"320","published-online":{"date-parts":[[1983,7]]},"reference":[{"volume-title":"I-adic theories and program semantics, Proc. 3rd Workshop on Categorical and Algebraic methods in Computer Science","year":"1980","key":"e_1_2_1_1_1","unstructured":"\/ADJ\/ ADJ , Algebraic theories , I-adic theories and program semantics, Proc. 3rd Workshop on Categorical and Algebraic methods in Computer Science , Dortmund University - Report no 114 ( 1980 ), 109--114. \/ADJ\/ ADJ, Algebraic theories, I-adic theories and program semantics, Proc. 3rd Workshop on Categorical and Algebraic methods in Computer Science, Dortmund University - Report no 114 (1980), 109--114."},{"key":"e_1_2_1_2_1","volume-title":"Dissertations Mathematicae (Rozprawy Math.) 204","author":"Andreka H.","year":"1982","unstructured":"\/AN\/ H. Andreka , I. Nemeti , Generalization of variety and quasi-variety concepts to partial algebras through category theory , Dissertations Mathematicae (Rozprawy Math.) 204 ( 1982 ). \/AN\/ H. Andreka, I. Nemeti, Generalization of variety and quasi-variety concepts to partial algebras through category theory, Dissertations Mathematicae (Rozprawy Math.) 204 (1982)."},{"key":"e_1_2_1_3_1","volume-title":"Model theory and categories in Computer Science, FCT 81, LNCS 117","author":"Andreka H.","year":"1981","unstructured":"\/AN1\/ H. Andreka , I. Nemeti , Applications of Universal Algebra , Model theory and categories in Computer Science, FCT 81, LNCS 117 , Berlin ( 1981 ), 16--23. \/AN1\/ H. Andreka, I. Nemeti, Applications of Universal Algebra, Model theory and categories in Computer Science, FCT 81, LNCS 117, Berlin (1981), 16--23."},{"key":"e_1_2_1_4_1","volume-title":"FCT 77, LNCS 56","author":"Arnold A.","year":"1977","unstructured":"\/ARN\/ A. Arnold , M. Nivat , Non-deterministic recursive program schemes , FCT 77, LNCS 56 , Berlin ( 1977 ), 12--21. \/ARN\/ A. Arnold, M. Nivat, Non-deterministic recursive program schemes, FCT 77, LNCS 56, Berlin (1977), 12--21."},{"key":"e_1_2_1_5_1","volume-title":"Algebraic solutions to recursion schemes","author":"Benson D.","year":"1981","unstructured":"\/BG1\/ D. Benson , I. Guessarian , Algebraic solutions to recursion schemes , LITP-Report no 81-66, Paris ( 1981 ), submitted for publication. \/BG1\/ D. Benson, I. Guessarian, Algebraic solutions to recursion schemes, LITP-Report no 81-66, Paris (1981), submitted for publication."},{"key":"e_1_2_1_7_1","unstructured":"\/BS\/ J. Bell A. Slomson Models and Ultraproducts North-Holland London (1971). \/BS\/ J. Bell A. Slomson Models and Ultraproducts North-Holland London (1971)."},{"key":"e_1_2_1_8_1","volume-title":"AMS coll","author":"Birkhoff G.","year":"1979","unstructured":"\/B\/ G. Birkhoff , Lattice theory , AMS coll ., 3 rd edition, New-York ( 1979 ) \/B\/ G. Birkhoff, Lattice theory, AMS coll., 3rd edition, New-York (1979)","edition":"3"},{"key":"e_1_2_1_9_1","volume-title":"IBM Report, Yorktown Heights","author":"Bloom S.","year":"1982","unstructured":"\/BL\/ S. Bloom , R. Tindell , Varieties of \"IF-THEN-ELSE \", IBM Report, Yorktown Heights ( 1982 ). \/BL\/ S. Bloom, R. Tindell, Varieties of \"IF-THEN-ELSE\", IBM Report, Yorktown Heights (1982)."},{"issue":"80","key":"e_1_2_1_10_1","first-page":"28","article-title":"g\u00e9brique des programmes r\u00e9cursifs non-d\u00e9terministes, Thesis","author":"Boudol G.","year":"1980","unstructured":"\/BD\/ G. Boudol , S\u00e9mantique op\u00e9rationnelle g\u00e9brique des programmes r\u00e9cursifs non-d\u00e9terministes, Thesis , LITP-Report no 80 - 28 ( 1980 ). \/BD\/ G. 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Courcelle, Infinite trees in normal form and recursive equations having a unique solution, MST 13 (1979), 131--180.","journal-title":"MST"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(78)90016-8"},{"key":"e_1_2_1_15_1","doi-asserted-by":"crossref","first-page":"105","DOI":"10.3233\/FI-1980-3109","article-title":"Raoult, Completions of ordered magmas","volume":"3","author":"Courcelle B.","year":"1980","unstructured":"\/CR\/ B. Courcelle , J.-C . Raoult, Completions of ordered magmas , Fundamentae Informaticae 3 ( 1980 ), 105 -- 116 . \/CR\/ B. Courcelle, J.-C. Raoult, Completions of ordered magmas, Fundamentae Informaticae 3 (1980), 105--116.","journal-title":"Fundamentae Informaticae"},{"key":"e_1_2_1_16_1","volume-title":"Paris","author":"Cousineau G.","year":"1977","unstructured":"\/COU\/ G. Cousineau , Les arbres \u00e0 feuilles indic\u00e9es: un cadre alg\u00e9brique des structures de controle, thesis , Paris ( 1977 ). \/COU\/ G. Cousineau, Les arbres \u00e0 feuilles indic\u00e9es: un cadre alg\u00e9brique des structures de controle, thesis, Paris (1977)."},{"key":"e_1_2_1_17_1","volume-title":"Logic colloquium 73","author":"Elgot C. C.","year":"1975","unstructured":"\/E\/ C. C. Elgot , Monadic computation and iterative algebraic theories , Logic colloquium 73 , North-Holland , Amsterdam ( 1975 ). \/E\/ C. C. Elgot, Monadic computation and iterative algebraic theories, Logic colloquium 73, North-Holland, Amsterdam (1975)."},{"key":"e_1_2_1_18_1","first-page":"71","article-title":"Guessarian, Terminaison et simplification de programmes","volume":"12","author":"Ermine F.","year":"1980","unstructured":"\/EG\/ F. Ermine , I . Guessarian, Terminaison et simplification de programmes , Revue Tech. Thomson-CSF , 12 ( 1980 ), 71 -- 90 . \/EG\/ F. Ermine, I. Guessarian, Terminaison et simplification de programmes, Revue Tech. Thomson-CSF, 12 (1980), 71--90.","journal-title":"Revue Tech. Thomson-CSF"},{"key":"e_1_2_1_19_1","volume-title":"Formal languages: perspectives and open problems","author":"Engelfriet J.","year":"1980","unstructured":"\/EN\/ J. Engelfriet , Some open questions and recent results on tree transducers and tree languages , in Formal languages: perspectives and open problems , Academic Press , London ( 1980 ), 241--286. \/EN\/ J. Engelfriet, Some open questions and recent results on tree transducers and tree languages, in Formal languages: perspectives and open problems, Academic Press, London (1980), 241--286."},{"key":"e_1_2_1_20_1","volume-title":"n-rational algebras","author":"Gallier J. H.","year":"1981","unstructured":"\/G\/ J. H. Gallier , n-rational algebras , Univ. of Pennsylvania report ( 1981 ), \/G\/ J. H. Gallier, n-rational algebras, Univ. of Pennsylvania report (1981),"},{"key":"e_1_2_1_21_1","unstructured":"\/GB\/ R. M. Burstall J. A. Goguen Institutions: Logic and specification this conference. \/GB\/ R. M. Burstall J. A. Goguen Institutions: Logic and specification this conference."},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(79)90032-1"},{"key":"e_1_2_1_23_1","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-77487-9","volume-title":"Universal Algebra","author":"Gr\u00e4tzer G.","year":"1979","unstructured":"\/GR\/ G. Gr\u00e4tzer , Universal Algebra , 2 nd edition, Springer-Verlag , Berlin ( 1979 ). \/GR\/ G. Gr\u00e4tzer, Universal Algebra, 2nd edition, Springer-Verlag, Berlin (1979).","edition":"2"},{"key":"e_1_2_1_24_1","doi-asserted-by":"crossref","unstructured":"\/GU\/ I. Guessarian Algebraic Semantics LNCS 99 Springer-Verlag Berlin (1981) \/GU\/ I. Guessarian Algebraic Semantics LNCS 99 Springer-Verlag Berlin (1981)","DOI":"10.1007\/3-540-10284-1"},{"key":"e_1_2_1_25_1","volume-title":"Sch\u00e9mas r\u00e9cursifs polyadiques: \u00e9quivalences et classes d'interpr\u00e9tation","author":"Guessarian I.","year":"1975","unstructured":"\/GU1\/ I. Guessarian , Sch\u00e9mas r\u00e9cursifs polyadiques: \u00e9quivalences et classes d'interpr\u00e9tation , Thesis , Paris ( 1975 ). \/GU1\/ I. Guessarian, Sch\u00e9mas r\u00e9cursifs polyadiques: \u00e9quivalences et classes d'interpr\u00e9tation, Thesis, Paris (1975)."},{"key":"e_1_2_1_26_1","volume-title":"Proc. US-French conference on applications of Algebraic methods in Language definition and compiling","author":"I.","year":"1982","unstructured":"\/GU2\/ I. Guessarian, Survey on classes of interpretations and some of their applications , Proc. US-French conference on applications of Algebraic methods in Language definition and compiling , Fontainebleau ( 1982 ), to appear. \/GU2\/ I. Guessarian, Survey on classes of interpretations and some of their applications, Proc. US-French conference on applications of Algebraic methods in Language definition and compiling, Fontainebleau (1982), to appear."},{"key":"e_1_2_1_27_1","unstructured":"\/GM\/ I. Guessarian J. Meseguer Remarks on the axiomatisation of \"if-then-else\" in preparation. \/GM\/ I. Guessarian J. Meseguer Remarks on the axiomatisation of \"if-then-else\" in preparation."},{"key":"e_1_2_1_28_1","unstructured":"\/GPP\/ I. Guessarian F. Parisi-Presicce A remark on iterative and regular factor algebras submitted for publication. \/GPP\/ I. Guessarian F. Parisi-Presicce A remark on iterative and regular factor algebras submitted for publication."},{"key":"e_1_2_1_29_1","volume-title":"Des substitutions dans les systemes d'\u00e9quations alg\u00e9briques sur le magma","author":"Kott L.","year":"1979","unstructured":"\/K\/ L. Kott , Des substitutions dans les systemes d'\u00e9quations alg\u00e9briques sur le magma ; application aux transformations de programme et \u00e0 leur correction, Thesis , Paris ( 1979 ). \/K\/ L. Kott, Des substitutions dans les systemes d'\u00e9quations alg\u00e9briques sur le magma; application aux transformations de programme et \u00e0 leur correction, Thesis, Paris (1979)."},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(82)90002-0"},{"key":"e_1_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)72018-4"},{"key":"e_1_2_1_32_1","volume-title":"Algebraic systems","author":"Mal'cev A. I.","year":"1973","unstructured":"\/MA\/ A. I. Mal'cev , Algebraic systems , North-Holland , Amsterdam ( 1973 ) \/MA\/ A. I. Mal'cev, Algebraic systems, North-Holland, Amsterdam (1973)"},{"key":"e_1_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(80)90106-1"},{"key":"e_1_2_1_34_1","volume-title":"LNCS 107","author":"Meseguer J.","year":"1981","unstructured":"\/M2\/ J. Meseguer , A. Birkhoff-like theorem for algebraic classes of interpretations of program schemes , LNCS 107 , Springer-Verlag , Berlin ( 1981 ), 152--168. \/M2\/ J. Meseguer, A. Birkhoff-like theorem for algebraic classes of interpretations of program schemes, LNCS 107, Springer-Verlag, Berlin (1981), 152--168."},{"key":"e_1_2_1_35_1","volume-title":"LNCS 92","author":"Milner R.","year":"1980","unstructured":"\/MI\/ R. Milner , A calculus of communication systems , LNCS 92 , Springer Verlag Berlin ( 1980 ). \/MI\/ R. Milner, A calculus of communication systems, LNCS 92, Springer Verlag Berlin (1980)."},{"volume-title":"Iterative algebras","author":"Nelson E.","key":"e_1_2_1_36_1","unstructured":"\/NE\/ E. Nelson , Iterative algebras , McMaster University Comp . Sci. Tec. Rep no 81 - CS - 12. \/NE\/ E. Nelson, Iterative algebras, McMaster University Comp. Sci. Tec. Rep no 81 - CS - 12."},{"key":"e_1_2_1_37_1","volume-title":"Proc. 1st ICALP, North Holland","author":"M.","year":"1972","unstructured":"\/NI\/ M. Nivat, Langages alg\u00e9briques sur le magma libre et s\u00e9mantique des shc\u00e9mas de programmes , Proc. 1st ICALP, North Holland , Amsterdam ( 1972 ). \/NI\/ M. Nivat, Langages alg\u00e9briques sur le magma libre et s\u00e9mantique des shc\u00e9mas de programmes, Proc. 1st ICALP, North Holland, Amsterdam (1972)."},{"key":"e_1_2_1_38_1","volume-title":"Symp. Mathematica 15","author":"M.","year":"1975","unstructured":"\/N\/ M. Nivat, On the interpretation of recursive polyadic program schemes , Symp. Mathematica 15 , Rome ( 1975 ), 255--281. \/N\/ M. Nivat, On the interpretation of recursive polyadic program schemes, Symp. Mathematica 15, Rome (1975), 255--281."},{"key":"e_1_2_1_39_1","volume-title":"Ph. D. thesis","author":"Oles F. J.","year":"1982","unstructured":"\/O\/ F. J. Oles , A category theoretic approach to the semantics of programming languages , Ph. D. thesis , Syracuse University ( 1982 ). \/O\/ F. J. Oles, A category theoretic approach to the semantics of programming languages, Ph. D. thesis, Syracuse University (1982)."},{"key":"e_1_2_1_40_1","unstructured":"\/P\/ A. Pasztor Chain-continuous algebras - a variety of partial algebras Stuttgart Univ. Report no 7-82. \/P\/ A. Pasztor Chain-continuous algebras - a variety of partial algebras Stuttgart Univ. Report no 7-82."},{"key":"e_1_2_1_41_1","volume-title":"Ph. D, Univ. of Connecticut","author":"Parisi-Presicce F.","year":"1981","unstructured":"\/PP\/ F. Parisi-Presicce , Uniqueness of solutions of fixedpoint equations in regular extensions of iterative algebras , Ph. D, Univ. of Connecticut ( 1981 ). \/PP\/ F. Parisi-Presicce, Uniqueness of solutions of fixedpoint equations in regular extensions of iterative algebras, Ph. D, Univ. of Connecticut (1981)."},{"key":"e_1_2_1_42_1","first-page":"257","article-title":"Rounds, Mappings and grammars on trees","volume":"4","author":"W.","year":"1970","unstructured":"\/R\/ W. C . Rounds, Mappings and grammars on trees , MST 4 ( 1970 ), 257 -- 287 . \/R\/ W. C. Rounds, Mappings and grammars on trees, MST 4 (1970), 257--287.","journal-title":"MST"},{"key":"e_1_2_1_43_1","doi-asserted-by":"publisher","DOI":"10.1137\/0205037"},{"key":"e_1_2_1_44_1","doi-asserted-by":"publisher","DOI":"10.1145\/322092.322105"},{"key":"e_1_2_1_45_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(80)90056-0"},{"key":"e_1_2_1_46_1","unstructured":"\/W\/ W. Wechler R-fuzzy computation to appear in Fuzzy Inf. and decision processes. \/W\/ W. Wechler R-fuzzy computation to appear in Fuzzy Inf. and decision processes."}],"container-title":["ACM SIGACT News"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1008933.1008936","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1008933.1008936","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T21:41:08Z","timestamp":1750282868000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1008933.1008936"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1983,7]]},"references-count":45,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1983,7]]}},"alternative-id":["10.1145\/1008933.1008936"],"URL":"https:\/\/doi.org\/10.1145\/1008933.1008936","relation":{},"ISSN":["0163-5700"],"issn-type":[{"type":"print","value":"0163-5700"}],"subject":[],"published":{"date-parts":[[1983,7]]},"assertion":[{"value":"1983-07-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}