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A practical implementation of simple consequence relations using inductive definitions

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Automated Deduction—CADE-14 (CADE 1997)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1249))

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Abstract

Logical frameworks such as the Edinburgh LF or Isabelle are not suitable for general metatheory, since they do not allow induction. On the other hand it is hard to encode a logic in an inductive definition-style framework so that it is usable for object theory. We propose a solution to this problem that borrows techniques from the type-theory tradition of logical frameworks for use with a language of inductive definitions, providing us with a notation suitable for practical object and metatheory both.

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References

  1. A. Avron. Simple consequence relations. Information and Computation, 92:105–139, 1991.

    Article  MathSciNet  Google Scholar 

  2. A. Avron. Axiomatic systems, deduction and implication. J. Logic Computat., 2:51–98, 1992.

    Article  MathSciNet  Google Scholar 

  3. A. Avron, F. Honsell, I. Mason, and R. Pollack. Using typed lambda calculus to implement formal systems on a machine. J. Automated Reasoning, 9:309–352, 1992.

    Article  MathSciNet  Google Scholar 

  4. D. Basin and S. Matthews. Structuring metatheory on inductive definitions. In M. A. McRobbie and J. K. Slaney, editors, Proc. CADE-13. Springer, Berlin, 1996.

    Google Scholar 

  5. S. Feferman. Finitary inductive systems. In Logic Colloquium '88. North-Holland, Amsterdam, 1990.

    Google Scholar 

  6. J.-Y. Girard. Proof Theory and Logical Complexity, vol. 1. Bibliopolis, Naples, 1987.

    MATH  Google Scholar 

  7. R. Harper, F. Honsell, and G. Plotkin. A framework for defining logics. J. ACM, 40:143–184, 1993.

    Article  MathSciNet  Google Scholar 

  8. S. Matthews. Implementing FS0 in Isabelle: adding structure at the metalevel. In J. Calmet and C. Limongelli, editors, Proc. Disco'96. Springer, Berlin, 1996.

    Google Scholar 

  9. R. McDowell and D. Miller. A logic for reasoning with higher-order abstract syntax. In Proc. 12th IEEE Ann. Symp. Logic Comp. Sci. IEEE Computer Society Press, 1997.

    Google Scholar 

  10. R. P. Nederpelt, J. H. Geuvers, and R. C. de Vrijer, editors. Selected papers on Automath. Elsevier, Amsterdam, 1994.

    MATH  Google Scholar 

  11. L. C. Paulson. The foundation of a generic theorem prover. J. Automated Reasoning, 5:363–397, 1989.

    Article  MathSciNet  Google Scholar 

  12. L. C. Paulson. Isabelle: A generic theorem prover. Springer, Berlin, 1994.

    Book  Google Scholar 

  13. F. Pfenning. Elf: A language for logic definition and verified meta-programming. In Proc. 4th IEEE Ann. Symp. Logic Comp. Sci. IEEE Computer Society Press, 1989.

    Google Scholar 

  14. E. Rohwedder. Verifying the meta-theory of deductive systems. thesis proposal, CMU, 1994.

    Google Scholar 

  15. C. Talcott. A theory of binding structures, and applications to rewriting. Theoret. Comput. Sci., 112:99–143, 1993.

    Article  MathSciNet  Google Scholar 

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William McCune

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© 1997 Springer-Verlag Berlin Heidelberg

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Matthews, S. (1997). A practical implementation of simple consequence relations using inductive definitions. In: McCune, W. (eds) Automated Deduction—CADE-14. CADE 1997. Lecture Notes in Computer Science, vol 1249. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63104-6_31

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  • DOI: https://doi.org/10.1007/3-540-63104-6_31

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  • Print ISBN: 978-3-540-63104-0

  • Online ISBN: 978-3-540-69140-2

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