The First-Order Theory of Ordering Constraints over Feature Trees

The system FT of ordering constraints over feature trees has been introduced as an extension of the system FT of equality constraints over feature trees. We investigate the first-order theory of FT and its fragments, both over finite trees and over possibly infinite trees. We prove that the first-order theory of FT is undecidable, in contrast to the first-order theory of FT which is well-known to be decidable. We determine the complexity of the entailment problem of FT with existential quantification to be PSPACE-complete, by proving its equivalence to the inclusion problem of non-deterministic finite automata. Our reduction from the entailment problem to the inclusion problem is based on a new alogrithm that, given an existential formula of FT , computes a finite automaton which accepts all its logic consequences.