{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:55:26Z","timestamp":1750308926402,"version":"3.41.0"},"reference-count":16,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[1990,4,1]],"date-time":"1990-04-01T00:00:00Z","timestamp":638928000000},"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":["SIGSAM Bull."],"published-print":{"date-parts":[[1990,4]]},"abstract":"<jats:p>\n            In a number of books and articles [1,2], Lorenzen has developed a general kind of calculus for deriving character strings inductively, using finite systems of\n            <jats:italic>clauses<\/jats:italic>\n            , reminiscent of those that appear in logic programming. At the same time, these clauses are remarkably similar to the productions that appear in the multiple antecedent canonical systems of Post [3], as used originally to derive a computational basis for the formal notion of an algorithm. However, the interpretation is quite different in the case of the\n            <jats:bold>Lorenzen Calculus<\/jats:bold>\n            , where each successively derived word is a member of the\n            <jats:italic>theory<\/jats:italic>\n            , rather than (as in the case of Post, Turing [4], or Chomsky [5] productions) simply a \"way station\" on the route to a single generated \"terminal\" word. We intend to make a clear distinction between these two approaches at an appropriate point in the development, but it is well that a tentative appreciation of this fundamental difference be understood at the outset.\n          <\/jats:p>","DOI":"10.1145\/1089419.1089420","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"9-18","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["The relation of Lorenzen calculus to formal language theory"],"prefix":"10.1145","volume":"24","author":[{"given":"Ronald E.","family":"Prather","sequence":"first","affiliation":[{"name":"Trinity University, San Antonio, TX"}]}],"member":"320","published-online":{"date-parts":[[1990,4]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-01539-1"},{"key":"e_1_2_1_2_1","unstructured":"Lorenzen P. Metamathematik Bibliographisches Institut Mannheim 1962.  Lorenzen P. Metamathematik Bibliographisches Institut Mannheim 1962."},{"key":"e_1_2_1_3_1","first-page":"65","author":"Post E.","year":"1943","unstructured":"Post , E. , Formal Reductions of the General Combinatorial Decision Problem , Amer. Jour. of Math. , 65 , 1943 . Post, E., Formal Reductions of the General Combinatorial Decision Problem, Amer. Jour. of Math., 65, 1943.","journal-title":"Amer. Jour. of Math."},{"key":"e_1_2_1_4_1","volume-title":"On Computable Numbers, with an Application to the Entscheidungs Problem","author":"Turing A.","year":"1936","unstructured":"Turing , A. , On Computable Numbers, with an Application to the Entscheidungs Problem , Proc. London Math . Soc ., 2--42, 1936 . Turing, A., On Computable Numbers, with an Application to the Entscheidungs Problem, Proc. London Math. Soc., 2--42, 1936."},{"key":"e_1_2_1_5_1","first-page":"2","author":"Chomsky N.","year":"1959","unstructured":"Chomsky , N. , On Certain Formal Properties of Grammars , Inform and Control , 2 , 1959 . Chomsky, N., On Certain Formal Properties of Grammars, Inform and Control, 2, 1959.","journal-title":"Inform and Control"},{"key":"e_1_2_1_6_1","first-page":"12","author":"Curry H.","year":"1958","unstructured":"Curry , H. , Calculuses and Formal Systems , Dialectica , 12 , 1958 . Curry, H., Calculuses and Formal Systems, Dialectica, 12, 1958.","journal-title":"Dialectica"},{"key":"e_1_2_1_7_1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-96826-6","volume-title":"Foundations of Logic Programming","author":"Lloyd J.","year":"1984","unstructured":"Lloyd , J. , Foundations of Logic Programming , Springer-Verlag , Berlin , 1984 . Lloyd, J., Foundations of Logic Programming, Springer-Verlag, Berlin, 1984."},{"key":"e_1_2_1_8_1","volume-title":"Logic for Problem Solving","author":"Kowalski R.","year":"1979","unstructured":"Kowalski , R. , Logic for Problem Solving , North Holland , New York , 1979 . Kowalski, R., Logic for Problem Solving, North Holland, New York, 1979."},{"key":"e_1_2_1_9_1","unstructured":"Salomaa A. Formal Languages Academic Press New York 1973.   Salomaa A. Formal Languages Academic Press New York 1973."},{"key":"e_1_2_1_10_1","volume-title":"Houghton Mifflin","author":"Prather R.","year":"1986","unstructured":"Prather , R. , Elements of Discrete Mathematics , Houghton Mifflin , Boston , 1986 . Prather, R., Elements of Discrete Mathematics, Houghton Mifflin, Boston, 1986."},{"key":"e_1_2_1_11_1","unstructured":"Prather R. The Relation of Lorenzen Calculus to Logic Programming and Formal Language Theory submitted to Jour. of Logic Programming.  Prather R. The Relation of Lorenzen Calculus to Logic Programming and Formal Language Theory submitted to Jour. of Logic Programming."},{"key":"e_1_2_1_12_1","volume-title":"Algebraic Theory of Automata","author":"Ginsburg A.","year":"1968","unstructured":"Ginsburg , A. , Algebraic Theory of Automata , Academic Press , New York , 1968 . Ginsburg, A., Algebraic Theory of Automata, Academic Press, New York, 1968."},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-115350-2.50013-0"},{"key":"e_1_2_1_14_1","volume-title":"Theory of Computation","author":"Brainerd W.","year":"1974","unstructured":"Brainerd , W. and Landweber , L. , Theory of Computation . John Wiley and Sons , New York , 1974 . Brainerd, W. and Landweber, L., Theory of Computation. John Wiley and Sons, New York, 1974."},{"key":"e_1_2_1_15_1","volume-title":"Asilomar","author":"Prather R.","year":"1989","unstructured":"Prather , R. , The Lorenzen Calculus as a Logic Programming Language, submitted to Fourth Annual Logic in Computer Science Symposium , Asilomar , California , June 1989 . Prather, R., The Lorenzen Calculus as a Logic Programming Language, submitted to Fourth Annual Logic in Computer Science Symposium, Asilomar, California, June 1989."},{"key":"e_1_2_1_16_1","volume-title":"MR 76","author":"van Wijngaarden A.","year":"1965","unstructured":"van Wijngaarden , A. , Orthogonal Design and Description of a Formal Language, Mathematisch Centrum , MR 76 , Amsterdam , 1965 . van Wijngaarden, A., Orthogonal Design and Description of a Formal Language, Mathematisch Centrum, MR 76, Amsterdam, 1965."}],"container-title":["ACM SIGSAM Bulletin"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1089419.1089420","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1089419.1089420","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T21:36:45Z","timestamp":1750282605000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1089419.1089420"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,4]]},"references-count":16,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1990,4]]}},"alternative-id":["10.1145\/1089419.1089420"],"URL":"https:\/\/doi.org\/10.1145\/1089419.1089420","relation":{},"ISSN":["0163-5824"],"issn-type":[{"type":"print","value":"0163-5824"}],"subject":[],"published":{"date-parts":[[1990,4]]},"assertion":[{"value":"1990-04-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}