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Logic

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Logic for Learning

Part of the book series: Cognitive Technologies ((COGTECH))

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Abstract

This chapter contains an account of the aspects of the syntax and semantics of higher-order logic that are most relevant to its application to learning.

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Bibliographical Notes

  1. A. Church. A formulation of the simple theory of types. Journal of Symbolic Logic, 5: 56–68, 1940.

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  2. L. Henkin. Completeness in the theory of types. Journal of Symbolic Logic, 15 (2): 81–91, 1950.

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  3. P.B. Andrews. An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof. Kluwer Academic Publishers, second edition, 2002.

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  4. D.A. Wolfram. The Clausal Theory of Types. Cambridge University Press, 1993.

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  5. J.L. Bell. Toposes and Local Set Theories. Oxford Science Publications, 1988.

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  6. J. Lambek and P.J. Scott. Introduction to Higher Order Categorical Logic. Cambridge University Press, 1986.

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  7. H.B. Curry and R. Feys. Combinatory Logic. North-Holland, 1958.

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  8. R. Hindley. The principal type scheme of an object in combinatory logic. Transactions of the American Mathematical Society, 146: 29–60, 1969.

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  9. R. Milner. A theory of type polymorphism in programming. Journal of Computer and System Sciences, 17: 348–375, 1978.

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  10. J.-L. Lassez, M.J. Maher, and K. Marriot. Unification revisited. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 587–625. Morgan Kaufmann, 1988.

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  11. J.W. Lloyd. Foundations of Logic Programming. Springer, second edition, 1987.

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  12. J.-L. Lassez, M.J. Maher, and K. Marriot. Unification revisited. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming, pages 587–625. Morgan Kaufmann, 1988.

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  13. J.W. Lloyd. Foundations of Logic Programming. Springer, second edition, 1987.

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  14. D.A. Wolfram. The Clausal Theory of Types. Cambridge University Press, 1993.

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Authors and Affiliations

  1. Research School of Information Sciences and Engineering, Computer Sciences Laboratory, The Australian National University, 0200, Canberra, ACT, Australia

    J. W. Lloyd

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  1. J. W. Lloyd
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© 2003 J. W. Lloyd

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Lloyd, J.W. (2003). Logic. In: Logic for Learning. Cognitive Technologies. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-08406-9_2

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  • DOI: https://doi.org/10.1007/978-3-662-08406-9_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-07553-7

  • Online ISBN: 978-3-662-08406-9

  • eBook Packages: Springer Book Archive

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