## Ordering Constraints over Feature Trees Expressed in Second-order Monadic Logic (1998)

Venue: | Information and Computation |

Citations: | 8 - 4 self |

### BibTeX

@INPROCEEDINGS{Müller98orderingconstraints,

author = {Martin Müller and Joachim Niehren},

title = {Ordering Constraints over Feature Trees Expressed in Second-order Monadic Logic},

booktitle = {Information and Computation},

year = {1998},

pages = {196--210},

publisher = {Springer-Verlag}

}

### OpenURL

### Abstract

The language FT of ordering constraints over feature trees has been introduced as an extension of the system FT of equality constraints over feature trees. While the first-order theory of FT is well understood, only few decidability results are known for the first-order theory of FT . We introduce a new method for proving the decidability of fragments of the first-order theory of FT . This method is based on reduction to second order monadic logic that is decidable according to Rabin's famous tree theorem. The method applies to any fragment of the first-order theory of FT for which one can change the model towards sufficiently labeled feature trees -- a class of trees that we introduce. As we show, the first order-theory of ordering constraints over sufficiently labeled feature trees is equivalent to second-order monadic logic (S2S for infinite and WS2S for finite feature trees). We apply our method for proving that entailment of FT with existential quantifiers j 1 j=9x 1 : : :9x n j 2 is decidable. Previous results were restricted to entailment without existential quantifiers which can be solved in cubic time. Meanwhile, entailment with existential quantifiers has been shown PSPACE-complete (for finite and infinite feature trees respectively).