{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,11]],"date-time":"2025-07-11T10:32:47Z","timestamp":1752229967737,"version":"3.32.0"},"publisher-location":"Berlin\/Heidelberg","reference-count":54,"publisher":"Springer-Verlag","isbn-type":[{"type":"print","value":"0387972889"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/bfb0043079","type":"book-chapter","created":{"date-parts":[[2006,8,17]],"date-time":"2006-08-17T16:46:04Z","timestamp":1155833164000},"page":"77-110","source":"Crossref","is-referenced-by-count":28,"title":["Dynamic algebras as a well-behaved fragment of relation algebras"],"prefix":"10.1007","author":[{"given":"Vaughan","family":"Pratt","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"5_CR1","doi-asserted-by":"crossref","unstructured":"G. Birkhoff. On the structure of abstract algebras. Proc. Cambridge Phil. Soc, 31, 1935.","DOI":"10.1017\/S0305004100013463"},{"key":"5_CR2","unstructured":"G. Birkhoff. Lattice Theory. Volume 25, A.M.S. Colloq. Publications, 1967."},{"key":"5_CR3","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1016\/0021-8693(81)90179-4","volume":"71","author":"C. Brink","year":"1981","unstructured":"C. Brink. Boolean modules. Journal of Algebra, 71:291\u2013313, 1981.","journal-title":"Journal of Algebra"},{"key":"5_CR4","volume-title":"Proc. Conf. on Category Theory and Computer Science, LNCS","author":"R.T Casley","year":"1989","unstructured":"R.T Casley, R.F. Crew, J. Meseguer, and V.R. Pratt. Temporal structures. In Proc. Conf. on Category Theory and Computer Science, LNCS, Springer-Verlag, Manchester, September 1989."},{"key":"5_CR5","volume-title":"Regular Algebra and Finite Machines","author":"J.H. Conway","year":"1971","unstructured":"J.H. Conway. Regular Algebra and Finite Machines. Chapman and Hall, London, 1971."},{"key":"5_CR6","first-page":"341","volume":"1","author":"L.H. Chin","year":"1951","unstructured":"L.H. Chin and A. Tarski. Distributive and modular laws in the arithmetic of relation algebras. Univ. Calif. Publ. Math., 1:341\u2013384, 1951.","journal-title":"Univ. Calif. Publ. Math."},{"key":"5_CR7","unstructured":"J.W. de Bakker and W.P. de Roever. A calculus for recursive program schemes. In M. Nivat, editor, Automata, Languages and Programming, pages 167\u2013196, North Holland, 1972."},{"key":"5_CR8","unstructured":"R. Dedekind. Essays on the Theory of Numbers. Open Court Publishing Company, 1901. Translation by W.W. Beman of Stetigkeit und irrationale Zahlen (1872) and Was sind und was sollen die Zahlen? (1888), reprinted 1963 by Dover Press."},{"key":"5_CR9","volume-title":"A Discipline of Programming","author":"E.W. Dijkstra","year":"1976","unstructured":"E.W. Dijkstra. A Discipline of Programming. Prentice-Hall, Englewood Cliffs, N.J., 1976."},{"key":"5_CR10","doi-asserted-by":"publisher","first-page":"426","DOI":"10.2307\/1989931","volume":"46","author":"R.P. Dilworth","year":"1939","unstructured":"R.P. Dilworth. Noncommutative residuated lattices. Trans. AMS, 46:426\u2013444, 1939.","journal-title":"Trans. AMS"},{"key":"5_CR11","first-page":"331","volume":"10","author":"A. Morgan De","year":"1864","unstructured":"A. De Morgan. On the syllogism, no. IV, and on the logic of relations. Trans. Cambridge Phil. Soc., 10:331\u2013358, 1864.","journal-title":"Trans. Cambridge Phil. Soc."},{"key":"5_CR12","doi-asserted-by":"crossref","unstructured":"P.C. Eklof. Ultraproducts for algebraists. In Handbook of Mathematical Logic, pages 105\u2013137, North Holland, 1977.","DOI":"10.1016\/S0049-237X(08)71099-1"},{"key":"5_CR13","doi-asserted-by":"crossref","unstructured":"M.J Fischer and R.E. Ladner. Propositional dynamic logic of regular programs. JCSS, 18(2), 1979.","DOI":"10.1016\/0022-0000(79)90046-1"},{"key":"5_CR14","unstructured":"L. Fuchs. Partially Ordered Algebraic Systems. Pergamon Press, 1963."},{"key":"5_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0304-3975(87)90045-4","volume":"50","author":"G. Jean-Yves","year":"1987","unstructured":"Jean-Yves Girard. Linear logic. Theoretical Computer Science, 50:1\u2013102, 1987.","journal-title":"Theoretical Computer Science"},{"key":"5_CR16","unstructured":"J.E. Hopcroft and J.D. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, 1979."},{"key":"5_CR17","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/BF02483728","volume":"15","author":"B. J\u00f3nsson","year":"1982","unstructured":"B. J\u00f3nsson. Varieties of relation algebras. Algebra Universalis, 15:273\u2013298, 1982.","journal-title":"Algebra Universalis"},{"issue":"80","key":"5_CR18","first-page":"1192","volume":"54","author":"B. J\u00f3nsson","year":"1948","unstructured":"B. J\u00f3nsson and A. Tarski. Representation problems for relation algebras. Bull. Amer. Math. Soc., 54:80,1192, 1948.","journal-title":"Bull. Amer. Math. Soc."},{"key":"5_CR19","doi-asserted-by":"publisher","first-page":"891","DOI":"10.2307\/2372123","volume":"73","author":"B. J\u00f3nsson","year":"1951","unstructured":"B. J\u00f3nsson and A. Tarski. Boolean algebras with operators. Part I. Amer. J. Math., 73:891\u2013939, 1951.","journal-title":"Amer. J. Math."},{"key":"5_CR20","doi-asserted-by":"publisher","first-page":"127","DOI":"10.2307\/2372074","volume":"74","author":"B. J\u00f3nsson","year":"1952","unstructured":"B. J\u00f3nsson and A. Tarski. Boolean algebras with operators. Part II. Amer. J. Math., 74:127\u2013162, 1952.","journal-title":"Amer. J. Math."},{"key":"5_CR21","first-page":"3","volume-title":"Automata Studies","author":"S.C. Kleene","year":"1956","unstructured":"S.C. Kleene. Representation of events in nerve nets and finite automata. In Automata Studies, pages 3\u201342, Princeton University Press, Princeton, NJ, 1956."},{"key":"5_CR22","doi-asserted-by":"crossref","unstructured":"D. Kozen. On the duality of dynamic algebras and Kripke models. In E. Engeler, editor, Proc. Workshop on Logic of Programs 1979, LNCS 125, pages 1\u201311, Springer-Verlag, 1979.","DOI":"10.1007\/3-540-11160-3_1"},{"key":"5_CR23","doi-asserted-by":"crossref","unstructured":"D. Kozen. A representation theorem for models of *-free PDL. Technical Report RC7864, IBM, September 1979.","DOI":"10.1007\/3-540-10003-2_83"},{"key":"5_CR24","doi-asserted-by":"crossref","unstructured":"D. Kozen. A representation theorem for models of *-free PDL. May 1979. Manuscript.","DOI":"10.1007\/3-540-10003-2_83"},{"key":"5_CR25","doi-asserted-by":"crossref","unstructured":"D. Kozen. A representation theorem for models of *-free PDL. In Proc. 7th Colloq. on Automata, Languages, and Programming, pages 351\u2013362, July 1980.","DOI":"10.1007\/3-540-10003-2_83"},{"key":"5_CR26","doi-asserted-by":"crossref","unstructured":"D. Kozen. On induction vs. *-continuity. In D. Kozen, editor, Proc. Workshop on Logics of Programs 1981, LNCS 131, pages 167\u2013176, Springer-Verlag, 1981.","DOI":"10.1007\/BFb0025782"},{"key":"5_CR27","doi-asserted-by":"crossref","unstructured":"D. Kozen and R. Parikh. A decision procedure for the propositional \u03bc-calculus. In E. Clarke and Kozen D., editors, Proc. Workshop on Logics of Programs 1983, LNCS 164, pages 313\u2013325, Springer-Verlag, 1983.","DOI":"10.1007\/3-540-12896-4_370"},{"key":"5_CR28","unstructured":"D. Kozen and J. Tiuryn. Logics of Programs. Technical Report 89-962, Dept. of Computer Science, Cornell University, 1989. To appear in: van Leeuwen (ed.), Handbook of Theoretical Computer Science, North Holland, Amsterdam, 1989."},{"key":"5_CR29","doi-asserted-by":"publisher","first-page":"707","DOI":"10.2307\/1969375","volume":"51","author":"R.C. Lyndon","year":"1950","unstructured":"R.C. Lyndon. The representation of relational algebras. Ann. of Math., Ser 2, 51:707\u2013729, 1950.","journal-title":"Ann. of Math."},{"key":"5_CR30","doi-asserted-by":"crossref","unstructured":"S. Mac Lane. Categories for the Working Mathematician. Springer-Verlag, 1971.","DOI":"10.1007\/978-1-4612-9839-7"},{"key":"5_CR31","first-page":"159","volume":"9","author":"M. Makkai","year":"1964","unstructured":"M. Makkai. On PC\u0394 classes in the theory of models. Publications of Math. Inst. Hung. Acad. Sci., 9:159\u2013194, 1964.","journal-title":"Publications of Math. Inst. Hung. Acad. Sci."},{"key":"5_CR32","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1307\/mmj\/1028999131","volume":"11","author":"J.D. Monk","year":"1964","unstructured":"J.D. Monk. On representable relation algebras. Michigan Math. J., 11:207\u2013210, 1964.","journal-title":"Michigan Math. J."},{"key":"5_CR33","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1016\/0304-3975(82)90030-5","volume":"17","author":"I. N\u00e9meti","year":"1982","unstructured":"I. N\u00e9meti. Every free algebra in the variety generated by the representable dynamic algebras is separable and representable. Theoretical Computer Science, 17:343\u2013347, 1982.","journal-title":"Theoretical Computer Science"},{"key":"5_CR34","volume-title":"Relation Algebras with Transitive Closure","author":"K.C. Ng","year":"1984","unstructured":"K.C. Ng. Relation Algebras with Transitive Closure. PhD thesis, University of California, Berkeley, 1984. 157+iv pp."},{"key":"5_CR35","first-page":"A29","volume":"24","author":"K.C. Ng","year":"1977","unstructured":"K.C. Ng and A. Tarski. Relation algebras with transitive closure, Abstract 742-02-09. Notices Amer. Math. Soc., 24:A29\u2013A30, 1977.","journal-title":"Notices Amer. Math. Soc."},{"key":"5_CR36","doi-asserted-by":"crossref","unstructured":"R. Parikh. A completeness result for a propositional dynamic logic. In LNCS 64, pages 403\u2013415, Springer-Verlag, 1978.","DOI":"10.1007\/3-540-08921-7_88"},{"key":"5_CR37","unstructured":"C.S. Peirce. Description of a notation for the logic of relatives, resulting from an amplification of the conceptions of Boole's calculus of logic. In Collected Papers of Charles Sanders Peirce. III. Exact Logic, Harvard University Press, 1933."},{"key":"5_CR38","doi-asserted-by":"crossref","unstructured":"V.R. Pratt. Semantical considerations on Floyd-Hoare logic. In Proc. 17th Ann. IEEE Symp. on Foundations of Comp. Sci., pages 109\u2013121, October 1976.","DOI":"10.1109\/SFCS.1976.27"},{"key":"5_CR39","doi-asserted-by":"crossref","unstructured":"V.R. Pratt. A practical decision method for propositional dynamic logic. In Proc. 10th Ann. ACM Symp. on Theory of Computing, pages 326\u2013337, San Diego, May 1978.","DOI":"10.1145\/800133.804362"},{"key":"5_CR40","unstructured":"V.R. Pratt. Dynamic Algebras: Examples, Constructions, Applications. Technical Report MIT\/LCS\/TM-138, M.I.T. Laboratory for Computer Science, July 1979."},{"key":"5_CR41","doi-asserted-by":"crossref","unstructured":"V.R. Pratt. Models of program logics. In 20th Symposium on foundations of Computer Science, San Juan, October 1979.","DOI":"10.1109\/SFCS.1979.24"},{"key":"5_CR42","doi-asserted-by":"crossref","unstructured":"V.R. Pratt. Dynamic algebras and the nature of induction. In 12th ACM Symposium on Theory of Computation, Los Angeles, April 1980.","DOI":"10.1145\/800141.804649"},{"key":"5_CR43","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1016\/0022-0000(80)90061-6","volume":"2","author":"V.R. Pratt","year":"1980","unstructured":"V.R. Pratt. A near optimal method for reasoning about action. Journal of Computer and System Sciences, 2:231\u2013254, April 1980. Also MIT\/LCS\/TM-113, M.I.T., Sept. 1978.","journal-title":"Journal of Computer and System Sciences"},{"key":"5_CR44","doi-asserted-by":"crossref","unstructured":"V.R. Pratt. A decidable mu-calculus. In Proc. 22nd IEEE Conference on Foundations of Computer Science, pages 421\u2013427, October 1981.","DOI":"10.1109\/SFCS.1981.4"},{"issue":"1","key":"5_CR45","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/BF01379149","volume":"15","author":"V.R. Pratt","year":"1986","unstructured":"V.R. Pratt. Modeling concurrency with partial orders. International Journal of Parallel Programming, 15(1):33\u201371, February 1986.","journal-title":"International Journal of Parallel Programming"},{"key":"5_CR46","first-page":"120","volume":"16","author":"V.N. Redko","year":"1964","unstructured":"V.N. Redko. On defining relations for the algebra of regular events (Russian). Ukrain. Mat. Z., 16:120\u2013126, 1964.","journal-title":"Ukrain. Mat. Z."},{"key":"5_CR47","volume-title":"Vorlesungen \u00fcber die Algebra der Logik (Exakte Logik). Dritter Band: Algebra und Logik der Relative","author":"E. Schr\u00f6der","year":"1895","unstructured":"E. Schr\u00f6der. Vorlesungen \u00fcber die Algebra der Logik (Exakte Logik). Dritter Band: Algebra und Logik der Relative. B.G. Teubner, Leipzig, 1895."},{"issue":"6","key":"5_CR48","first-page":"A","volume":"24","author":"K. Segerberg","year":"1977","unstructured":"K. Segerberg. A completeness theorem in the modal logic of programs. Notices of the AMS, 24(6):A-552, October 1977.","journal-title":"Notices of the AMS"},{"key":"5_CR49","doi-asserted-by":"publisher","first-page":"37","DOI":"10.2307\/1989664","volume":"40","author":"M. Stone","year":"1936","unstructured":"M. Stone. The theory of representations for Boolean algebras. Trans. Amer. Math. Soc., 40:37\u2013111, 1936.","journal-title":"Trans. Amer. Math. Soc."},{"key":"5_CR50","doi-asserted-by":"publisher","first-page":"73","DOI":"10.2307\/2268577","volume":"6","author":"A. Tarski","year":"1941","unstructured":"A. Tarski. On the calculus of relations. J. Symbolic Logic, 6:73\u201389, 1941.","journal-title":"J. Symbolic Logic"},{"key":"5_CR51","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/S1385-7258(55)50009-6","volume":"17","author":"A. Tarski","year":"1955","unstructured":"A. Tarski. Contributions to the theory of models. III. Indag. Math, 17:56\u201364, 1955.","journal-title":"Indag. Math"},{"key":"5_CR52","doi-asserted-by":"crossref","unstructured":"A. Tarski and S. Givant. A Formalization of Set Theory Without Variables. American Math. Soc., 1987.","DOI":"10.1090\/coll\/041"},{"key":"5_CR53","doi-asserted-by":"crossref","unstructured":"A. Van Gelder. A satisfiability tester for non-clausal propositional calculus. Information and Computation, 79(1), October 1988.","DOI":"10.1016\/0890-5401(88)90014-4"},{"key":"5_CR54","doi-asserted-by":"publisher","first-page":"335","DOI":"10.2307\/1990008","volume":"45","author":"M. Ward","year":"1939","unstructured":"M. Ward and R.P. Dilworth. Residuated lattices. Trans. AMS, 45:335\u2013354, 1939.","journal-title":"Trans. AMS"}],"container-title":["Lecture Notes in Computer Science","Algebraic Logic and Universal Algebra in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BFb0043079.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,10]],"date-time":"2025-01-10T13:48:13Z","timestamp":1736516893000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BFb0043079"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["0387972889"],"references-count":54,"URL":"https:\/\/doi.org\/10.1007\/bfb0043079","relation":{},"subject":[]}}