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The value of free algebras

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Algebraic Logic and Universal Algebra in Computer Science (ALUACS 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 425))

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References

  • R. Balbes and Ph. Dwinger [1974], Distributive Lattices, U. of Missouri Press.

    Google Scholar 

  • N.D. Belnap, Jr. [1976], How a Computer Should Think, in Contemporary Aspects of Philosophy, ed. G. Ryle.

    Google Scholar 

  • J. Berman and W.J. Blok, [1988] Positive Boolean dependencies, Inf. Processing Letters, 27, 147–150.

    Article  MATH  MathSciNet  Google Scholar 

  • J. Berman and W.J. Blok, [1989], Equational Dependencies, Research Report no. 32, Dept. of Math., Stat., and C.S., Univ. of Illinois at Chicago.

    Google Scholar 

  • J. Berman and M. Mukaidono [1984], Enumerating fuzzy switching functions and free Kleene algebras, Comp. and Math. with Applications10, pp. 25–35.

    Article  MATH  MathSciNet  Google Scholar 

  • S. Blamey [1986], Partial Logic, in Handbook of Philosophical Logic, Vol. III, ed. D. Gabbay and F. Guenthner, D. Reidel Pub, pp. 1–70.

    MATH  Google Scholar 

  • D.A. Bochvar [1939], On a 3-valued logical calculus and its application to the analysis of contradictions, (Russian), Math. Sbornik 4, 287–308. Eng. Trans. in Hist. Philos. Logic 2(1981), 87–112.

    Google Scholar 

  • S. Burris and H.P. Sankappanavar [1981], A Course in Universal Algebra, Graduate Texts in Mathematics, vol. 78, Springer-Verlag.

    Google Scholar 

  • G. Czédli [1981], On dependencies in the relational model of data, Elektron. Informationsverab. u.Kybernet., 17, 103–112.

    MATH  Google Scholar 

  • J. Demetrovics and Gy. Gyepesi [1983], Some generalized type functional dependencies formalized as equality set on matrices, Discrete Applied Math., 6, 35–47.

    Article  MATH  MathSciNet  Google Scholar 

  • M.L. Ginsburg [1987], Multi-valued Logics, I,II,II. preprints.

    Google Scholar 

  • D. Gries [1981], The Science of Programming, Springer-Verlag.

    Google Scholar 

  • F. Guzman [1989], The implications in conditional logic, Proceedings of the Conference on Algebra and Computer Science, Iowa State University.

    Google Scholar 

  • F. Guzman and C. Squier [1989], The algebra of conditional logic, Algebra Universalis, to appear.

    Google Scholar 

  • D. Hobby and R. McKenzie [1988], The Structure of Finite Algebras, Contemporary Mathematics, 76, Amer. Math. Soc. Pub.

    Google Scholar 

  • S. Kleene [1952], Introduction to Metamathematics, pp. 332–340, Van Nostrand.

    Google Scholar 

  • A.D. Korshunov [1981], On the number of monotonic Boolean functions, (Russian), Problemy Kibernetiki 38, 5–108.

    MATH  MathSciNet  Google Scholar 

  • D. Maier [1983], The Theory of Relational Databases, Computer Science Press.

    Google Scholar 

  • J. McCarthy [1963], A basis for a mathematical theory of computation, in Computer Programming and Formal Systems, P. Braffort and D. Hirschberg eds., North-Holland Publishing Co., 33–70.

    Google Scholar 

  • J. McCarthy [1963a], Predicate calculus with “undefined” as a truth value, Stanford Artificial Intelligence Project, Memo 1, March 1963.

    Google Scholar 

  • R. McKenzie, G. McNulty and W. Taylor [1987], ALgebras, Lattices, Varieties, vol. 1, Wadsworth.

    Google Scholar 

  • M. Mukaidono and I.G. Rosenberg [1986], κ-valued functions for treating ambiquities: Their clone and a normal form. 18th Internat. Symposium on Multiple-valued Logic, IEEE.

    Google Scholar 

  • M. Nagata, M. Nakanishi, and T. Nishimura [1975], Implementation of Łukasiewicz's, Kleene's and McCarthy's 3-valued logics, Sci. Rep. Tokyo Kyoiku Daigaku Sect A 13, no. 347–365, 90–100. Math. Rev.53 #2055.

    Google Scholar 

  • A. Romanowska and A. Trakul [1989], On the structure of some bilattices, preprint.

    Google Scholar 

  • Y. Sagiv, C. Delobel, D.S. Parker and R. Fagin [1981], An equivalence between relational database dependencies and a fragment of propositional logic, J. ACM, 28, 435–453. Corrigendum J. ACM, 34(1987), 1016–1018.

    Article  MATH  MathSciNet  Google Scholar 

  • D.S. Scott [1973], Models of various type-free calculi, in Logic, Methodology and Philosophy of ScienceIV, ed. P. Suppes et al., North-Holland, 157–187.

    Google Scholar 

  • A. Szendrei [1986], Clones in Universal Algebra, SMS 99, University of Montreal Press.

    Google Scholar 

  • W. Taylor [1975], The fine spectrum of a variety, Algebra Universalis, 5, 263–303.

    MATH  MathSciNet  Google Scholar 

  • B. Thalheim, [1985], Funktionale Abhängigkeiten in relationalen Datenstrukturen, Elektron. Informationsverarb. u. Kybernet., 21, 23–33.

    MATH  MathSciNet  Google Scholar 

  • P.M. Winkler [1980], Classification of algebraic structures by work space, Algebra Universalis11, 320–33.

    MATH  MathSciNet  Google Scholar 

  • P.M. Winkler [1983], Polynomial Hyperforms, Algebra Universalis17, 101–109.

    Article  MATH  MathSciNet  Google Scholar 

  • I.D. Zaslavskii [1979], Realization of three-valued logical functions by means of recursive and Turing operators. (Russian), Studies in the theory of algorithms and mathematical logic, Nauka, 52–61. Math. Rev.81i:03031.

    Google Scholar 

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Clifford H. Bergman Roger D. Maddux Don L. Pigozzi

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© 1990 Springer-Verlag Berlin Heidelberg

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Berman, J. (1990). The value of free algebras. In: Bergman, C.H., Maddux, R.D., Pigozzi, D.L. (eds) Algebraic Logic and Universal Algebra in Computer Science. ALUACS 1988. Lecture Notes in Computer Science, vol 425. Springer, New York, NY. https://doi.org/10.1007/BFb0043076

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  • DOI: https://doi.org/10.1007/BFb0043076

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  • Print ISBN: 978-0-387-97288-6

  • Online ISBN: 978-0-387-34804-9

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