The implication problem for functional and inclusion dependencies
Information and Control
Equational theories and database constraints
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Computational consequences and partial solutions of a generalized unification problem
Proceedings of the Fourth Annual Symposium on Logic in computer science
The undecidability of the semi-unification problem
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Subsumption in KL-ONE is undecidable
Proceedings of the first international conference on Principles of knowledge representation and reasoning
On Type Inference for Object-Oriented Programming Languages
CSL '87 Proceedings of the 1st Workshop on Computer Science Logic
Computing with features as formulae
Computational Linguistics
Feature logic with weak subsumption constraints
ACL '91 Proceedings of the 29th annual meeting on Association for Computational Linguistics
ACL '95 Proceedings of the 33rd annual meeting on Association for Computational Linguistics
A larger decidable semiunification problem
Proceedings of the 9th ACM SIGPLAN international conference on Principles and practice of declarative programming
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We consider a generalization of term subsumption, or matching, to a class of mathematical structures which we call feature algebras. We show how these generalize both first-order terms and the feature structures used in computational linguistics. The notion of term subsumption generalizes to a natural notion of algebra homomorphism. In the setting of feature algebras, unification, corresponds naturally to solving constraints involving equalities between strings of unary function symbols, and semiunification also allows inequalities representing subsumption constraints. Our generalization allows us to show that the semiunification problem for finite feature algebras is undecidable. This implies that the corresponding problem for rational trees (cyclic terms) is also undecidable.