Abstract
We introduce a restricted version of second order logic SOω in which the second order quantifiers range over relations that are closed under the equivalence relation ≡k of k variable equivalence, for some k. This restricted second order logic is an effective fragment of the infinitary logic L ωαω , which differs from other such fragments in that it is not based on a fixpoint logic. We explore the relationship of SOω with fixpoint logics, showing that its inclusion relations with these logics are equivalent to problems in complexity theory. We also look at the expressibility of NP-complete problems in this logic.
Supported by EPSRC grant GR/H 81108.
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© 1995 Springer-Verlag Berlin Heidelberg
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Dawar, A. (1995). A restricted second order logic for finite structures. In: Leivant, D. (eds) Logic and Computational Complexity. LCC 1994. Lecture Notes in Computer Science, vol 960. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60178-3_94
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DOI: https://doi.org/10.1007/3-540-60178-3_94
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