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Two-Variable Logic with Counting is Decidable (1996)
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by
Erich Grädel
,
Martin Otto
,
Eric Rosen
| Citations: | 77 - 4 self |
BibTeX
@MISC{Grädel96two-variablelogic,
author = {Erich Grädel and Martin Otto and Eric Rosen},
title = {Two-Variable Logic with Counting is Decidable},
year = {1996}
}
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Abstract
We prove that the satisfiability problem for C² is decidable. C² is first-order logic with only two variables in the presence of arbitrary counting quantifiers 9 ?m , m ? 1. It considerably extends L², plain first-order with only two variables, which is known to be decidable by a result of Mortimer. Unlike L², C² does not have the finite model property. As C² extends L² by expressive means for counting, significant applications arise from the fact that C² embeds corresponding counting extensions of modal logics.
