Lattices of Logical Fragments over Words

(Extended Abstract)
  • Manfred Kufleitner
  • Alexander Lauser
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7392)

Abstract

This paper introduces an abstract notion of fragments of monadic second-order logic. This concept is based on purely syntactic closure properties. We show that over finite words, every logical fragment defines a lattice of languages with certain closure properties. Among these closure properties are residuals and inverse \(\mathcal C\)-morphisms. Here, depending on certain closure properties of the fragment, \(\mathcal C\) is the family of arbitrary, non-erasing, length-preserving, length-multiplying, or lengthreducing morphisms. In particular, definability in a certain fragment can often be characterized in terms of the syntactic morphism. This work extends a result of Straubing in which he investigated certain restrictions of first-order formulae.

As motivating examples, we present (1) a fragment which captures the stutter-invariant part of piecewise-testable languages and (2) an acyclic fragment of Σ2. As it turns out, the latter has the same expressive power as two-variable first-order logic FO2.

Keywords

Expressive Power Atomic Formula Regular Language Comparison Graph Closure Property 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Manfred Kufleitner
    • 1
  • Alexander Lauser
    • 1
  1. 1.FMIUniversity of StuttgartGermany

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