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The logic MPLω

  • Part II The Design Language COLD
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Book cover Algebraic Methods: Theory, Tools and Applications (Algebraic Methods 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 394))

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Abstract

MPLω is many-sorted partial logic with countably infinite conjunctions and disjunctions. We show in this paper that MPLω satisfies the interpolation property and allows the explicit definition of inductively defined predicates and functions. By these properties, MPLω is useful as a semantic framework for the design language COLD.

The research for this paper was supported by ESPRIT project METEOR (nr. 432) through Philips Research Laboratories Eindhoven.

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References

  1. J. BARWISE, Admissible Sets and Structures, Springer-Verlag, Berlin (1975).

    Google Scholar 

  2. S. FEFERMAN, Lectures on Proof Theory, in: M.H. LÖB (Ed.), Proceedings of the Summer School in Logic, Leeds 1967, Lecture Notes in Mathematics 70, Springer-Verlag, Berlin (1968), 1–107.

    Google Scholar 

  3. H.B.M. JONKERS, C.P.J. KOYMANS, G.R. RENARDEL DE LAVALETTE, A Semantic Framework for the COLD-Family of Languages, Technical Report, ESPRIT project 432, Doc.Nr. METEOR/t2/PRLE/1 (1986).

    Google Scholar 

  4. C. KARP, Languages with Expressions of Infinite Length, North-Holland, Amsterdam (1964).

    Google Scholar 

  5. H.J. KEISLER, Model Theory for Infinitary Logic, North-Holland, Amsterdam (1971).

    Google Scholar 

  6. E.G.K. LOPEZ-ESCOBAR, An Interpolation Theorem for Denumerably Long Sentences, Fundamenta Mathematicae 57 (1965), 253–272.

    Google Scholar 

  7. G.R. RENARDEL DE LAVALETTE, Descriptions in Mathematical Logic, Studia Logica 43 (1984), 281–294.

    Google Scholar 

  8. K. SCHÜTTE, Der Interpolationssatz der Intuitionistischen Prädikatenlogik, Mathematische Annalen 148 (1962), 192–200.

    Article  Google Scholar 

  9. D.S. SCOTT, Existence and Description in Formal Logic, in: R. SCHOENMAN (Ed.), Bertrand Russell, Philosopher of the Century, Allen & Unwin, London (1967), 181–200.

    Google Scholar 

  10. D.S. SCOTT, Identity and Existence in Intuitionistic Logic, in: M.P. FOURMAN, C.J. MULVEY, D.S. SCOTT (Eds.), Applications of Sheaves, Lecture Notes in Mathematics 753, Springer Verlag, Berlin (1979), 660–696.

    Google Scholar 

  11. W.W. TAIT, Normal Derivability in Classical Logic, in: J. BARWISE (Ed.), The Syntax and Semantics of Infinitary Languages, Lecture Notes in Mathematics 72, Springer-Verlag, Berlin (1968), 204–236.

    Google Scholar 

  12. G. TAKEUTI, Proof Theory, North-Holland, Amsterdam (1975).

    Google Scholar 

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Martin Wirsing Jan A. Bergstra

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© 1989 Springer-Verlag Berlin Heidelberg

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Koymans, C.P.J., Renardel de Lavalette, G.R. (1989). The logic MPLω . In: Wirsing, M., Bergstra, J.A. (eds) Algebraic Methods: Theory, Tools and Applications. Algebraic Methods 1987. Lecture Notes in Computer Science, vol 394. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015041

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  • DOI: https://doi.org/10.1007/BFb0015041

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51698-9

  • Online ISBN: 978-3-540-46758-8

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