Yuguo He - On the strictness of the quantifier structure hierarchy in first-order logic

lmcs:965 - Logical Methods in Computer Science, November 13, 2014, Volume 10, Issue 4 - https://doi.org/10.2168/LMCS-10(4:3)2014
On the strictness of the quantifier structure hierarchy in first-order logic

Authors: Yuguo He

    We study a natural hierarchy in first-order logic, namely the quantifier structure hierarchy, which gives a systematic classification of first-order formulas based on structural quantifier resource. We define a variant of Ehrenfeucht-Fraisse games that characterizes quantifier classes and use it to prove that this hierarchy is strict over finite structures, using strategy compositions. Moreover, we prove that this hierarchy is strict even over ordered finite structures, which is interesting in the context of descriptive complexity.


    Volume: Volume 10, Issue 4
    Published on: November 13, 2014
    Accepted on: June 25, 2015
    Submitted on: January 6, 2011
    Keywords: Computer Science - Logic in Computer Science

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