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On the Expressive Power of Logics with Invariant Uses of Arithmetic Predicates

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7456)

Abstract

In this talk I consider first-order formulas (FO, for short) where, apart from the symbols in the given vocabulary, also predicates for linear order and arithmetic may be used. For example, order-invariant formulas are formulas for which the following is true: If a structure satisfies the formula with one particular linear order of the structure’s universe, then it satisfies the formula with any linear order of the structure’s universe. Arithmetic-invariant formulas are defined analogously, where apart from the linear order other arithmetic predicates may be used in an invariant way. The aim of this talk is to give an overview of the state-of-the art concerning the expressive power of order-invariant and arithmetic-invariant logics.

Keywords

  • Expressive Power
  • Graph Property
  • Invariant Logic
  • Regular Tree Language
  • Circuit Lower Bound

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Schweikardt, N. (2012). On the Expressive Power of Logics with Invariant Uses of Arithmetic Predicates. In: Ong, L., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2012. Lecture Notes in Computer Science, vol 7456. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32621-9_6

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  • DOI: https://doi.org/10.1007/978-3-642-32621-9_6

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