On the strictness of the quantifier structure hierarchy in first-order logic
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...
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| Format: | Article |
| Language: | English |
| Published: |
Logical Methods in Computer Science e.V.
2014-11-01
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| Series: | Logical Methods in Computer Science |
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| Online Access: | https://lmcs.episciences.org/965/pdf |
| Summary: | 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. |
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| ISSN: | 1860-5974 |