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Equivalences among various logical frameworks of partial algebras

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Computer Science Logic (CSL 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1092))

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Abstract

We examine a variety of liberal logical frameworks of partial algebras. Therefore we use simple, conjunctive and weak embeddings of institutions which preserve model categories and may map sentences to sentences, finite sets of sentences, or theory extensions using unique-existential quantifiers, respectively. They faithfully represent theories, model categories, theory morphisms, colimit of theories, reducts etc. Moreover, along simple and conjunctive embeddings, theorem provers can be re-used in a way that soundness and completeness is preserved. Our main result states the equivalence of all the logical frameworks with respect to weak embeddability. This gives us compilers between all frameworks. Thus it is a chance to unify the different branches of specification using liberal partial logics.

This is important for reaching the goal of formal interoperability of different specification languages for software development. With formal interoperability, a specification can contain parts written in different logical frameworks using a multiparadigm specification language, and one can re-use tools which are available for one framework also for other frameworks.

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Authors and Affiliations

  1. Dept. of Computer Science, University of Bremen, P.O.Box 33 04 40, D-28334, Bremen

    Till Mossakowski

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  1. Till Mossakowski
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Hans Kleine Büning

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© 1996 Springer-Verlag Berlin Heidelberg

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Mossakowski, T. (1996). Equivalences among various logical frameworks of partial algebras. In: Kleine Büning, H. (eds) Computer Science Logic. CSL 1995. Lecture Notes in Computer Science, vol 1092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61377-3_51

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  • DOI: https://doi.org/10.1007/3-540-61377-3_51

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61377-0

  • Online ISBN: 978-3-540-68507-4

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