Complete sets of transformations for general E-unification
Theoretical Computer Science - Second Conference on Rewriting Techniques and Applications, Bordeaux, May 1987
Foundations of Equational Logic Programming
Foundations of Equational Logic Programming
An improved general E-unification method
Journal of Symbolic Computation
Lazy narrowing: strong completeness and eager variable elimination
TAPSOFT '95 Selected papers from the 6th international joint conference on Theory and practice of software development
Term rewriting and all that
An Efficient Unification Algorithm
ACM Transactions on Programming Languages and Systems (TOPLAS)
A General Complete E-Unification Procedure
RTA '87 Proceedings of the 2nd International Conference on Rewriting Techniques and Applications
Improving Transformation Systems for General E-Unification
RTA '93 Proceedings of the 5th International Conference on Rewriting Techniques and Applications
A goal-oriented algorithm for unification in ELHR+ w.r.t. cycle-restricted ontologies
AI'12 Proceedings of the 25th Australasian joint conference on Advances in Artificial Intelligence
CADE'13 Proceedings of the 24th international conference on Automated Deduction
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We present a goal-directed E-unification procedure with eager Variable Elimination and a new rule, Cycle, for the case of collapsing equations --- that is, equations of the type x驴驴驴v where x 驴Var(v). Cycle replaces Variable Decomposition (or the so-called Root Imitation) and thus removes possibility of some obviously unnecessary infinite paths of inferences in the E-unification procedure. We prove that, as in other approaches, such inferences into variable positions in our goal-directed procedure are not needed. Our system is independent of selection rule and complete for any E-unification problem.