On compositionality and its limitations

  • Authors:
  • Alexander Rabinovich

  • Affiliations:
  • Tel Aviv University, Israel

  • Venue:
  • ACM Transactions on Computational Logic (TOCL)
  • Year:
  • 2007

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Abstract

The aim of this article is to examine the applicability of a compositional method developed for a generalized product construction by Feferman and Vaught to the field of program verification.We suggest an instance of the generalized product construction and prove an appropriate composition theorem for modal logic. We illustrate the usefulness of this generalized product by showing that many “parallel composition” operations are special cases of this generalized product.We obtain positive results (the compositional method works) for basic propositional modal logic, and negative results (the compositional method fails) for more expressive logics which can express EGp---“there is a path such that all the nodes of the path have the property p.”Applications of the composition theorem to the model-checking problem and to the parametric model-checking problem are provided.