Complete axiomatizations of the algebras of finite, rational and infinite trees

@article{Maher1988CompleteAO,
  title={Complete axiomatizations of the algebras of finite, rational and infinite trees},
  author={Michael J. Maher},
  journal={[1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science},
  year={1988},
  pages={348-357}
}
  • Michael J. Maher
  • Published 1988
  • Mathematics, Computer Science
  • [1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science
  • Complete axiomizations for the algebras of infinite trees and infinite trees are presented. The axiomizations are parameterized by the alphabet of function symbols for both the finite trees and infinite trees. There are two main cases, depending on whether the number of function symbols is finite or infinite. In the former case an extra axiom is necessary to obtain completeness. The method of proof is an elimination of quantifiers. Although a full elimination of quantifiers is not possible, the… CONTINUE READING
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    References

    SHOWING 1-10 OF 17 REFERENCES
    Semantics of Infinite Tree Logic Programming
    • 47
    Reasoning About Recursively Defined Data Structures
    • D. Oppen
    • Mathematics, Computer Science
    • J. ACM
    • 1980
    • 35
    An Efficient Unification Algorithm
    • 868
    • PDF
    Foundations of Logic Programming
    • 2,993
    Complete Logic Programs with Domain-Closure Axiom
    • 29
    • PDF
    Fundamental properties of infinite trees
    • 221
    Negation in Logic Programming
    • K. Kunen
    • Mathematics, Computer Science
    • J. Log. Program.
    • 1987
    • 540
    • PDF
    Initial Algebra Semantics and Continuous Algebras
    • 871
    • PDF
    Negation as Failure
    • K. Clark
    • Computer Science, Mathematics
    • Logic and Data Bases
    • 1977
    • 1,747
    • PDF
    Constraint logic programming
    • 1,483