## An Improved General E-Unification Method (1994)

Venue: | J. Symbolic Computation |

Citations: | 8 - 1 self |

### BibTeX

@INPROCEEDINGS{Dougherty94animproved,

author = {Daniel J. Dougherty and Patricia Johann},

title = {An Improved General E-Unification Method},

booktitle = {J. Symbolic Computation},

year = {1994},

pages = {261--275},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper considers the problem of E-unification for arbitrary equational theories E, and presents an inference rule approximating Paramodulation and leading to a complete E-unification procedure which generalizes Narrowing. This sheds some light on the boundary between arbitrary E-unification situations and E-unification under canonical E.

### Citations

346 | An Efficient Unification Algorithm
- Martelli, Montanari
- 1982
(Show Context)
Citation Context ...s. These transformations naturally define a non-deterministic procedure, which we denote Syntactic Unification, or simply SU : Write S SU =)S 0 if S 0 is obtained from S in one SU step. Theorem 2.3. (=-=Martelli and Montanari 1982-=-) Every SU computation terminates. If S is unifiable then every SU computation on S terminates in a solved system determining a most general unifier for S. If S is not unifiable then no SU computation... |

268 | Orderings for term rewriting systems
- Dershowitz
- 1982
(Show Context)
Citation Context ...t for all terms T and occurrences u in T , T [u / A]sT [u / B]. If =) is any relation, we write =) for its relexive transitive closure. Definitions and notation not presented here should be found in (=-=Dershowitz and Jounnaud, 1991-=-). We always assume that our sets of equations are consistent. 2. Systems and E-unification methods Transformation-based unification methods attempt to reduce systems representing unification problems... |

169 | Canonical Forms and Unification - Hullot - 1980 |

125 | Completion without failure - Bachmair, Dershowitz, et al. - 1989 |

118 | Canonical Equational Proofs - Bachmair - 1991 |

65 |
First-Order Unification in an Equational Theory
- Fay
- 1979
(Show Context)
Citation Context ...variable. The choice of witness pair represents a guess that an equational derivation between substitution instances of A and B has an initial step using equation L = R at occurrence u. Theorem 2.5. (=-=Fay 1979-=-) Narrowing is sound and complete for sets of equations whose left-to-right orientation induces a canonical rewrite system. We outline a proof at the end of Section 3. Gallier and Snyder prove that Na... |

65 | Completeness of many-sorted equational logic
- Goguen, Meseguer
- 1985
(Show Context)
Citation Context ...aper, we note in passing that a proper treatment of many-sorted equational logic similarly requires (for different reasons) an explicit indication of a set of "relevant" variables; see, for =-=example, (Goguen and Meseguer 1981-=-, 1985). Definition 2.1. A pair hA; Bi is a two-element multiset of terms. A system is a finite set S of pairs together with a finite set Vars(S ) of variables, including at least the variables occurr... |

49 |
Complete sets of transformations for general Eunification
- Gallier, Snyder
- 1989
(Show Context)
Citation Context ...f witness pair represents a guess that an equational derivation between substitution instances of A and B involves a step (not necessarily initial) using equation L = R at occurrence u. Theorem 2.8. (=-=Gallier and Snyder 1989-=-) The non-deterministic E-unification procedure determined by Lazy Paramodulation steps and Syntactic Unification steps is sound and complete for arbitrary sets E of equations. (Syntactic Unification ... |

28 | M'ethodes et outils de conception syst'ematique d'algorithmes d'unification dans les th'eories 'equationnelles. Th`ese de doctorat d"etat en informatique, Universit'e de Nancy 1 - Kirchner - 1985 |

27 | Canonical inference - Lankford - 1975 |

23 | Computing unification algorithms - Kirchner |

16 | Paramodulation and theorem-proving in first order theories with equality - Robinson, Wos |

2 | A new equational unification method: A generalization of martelli-montanari’s algorithm - Kirchner - 1984 |

2 | Building in equational theories', Machine Intelligence 7, 73-90. Pottier L. [1991], Minimal solutions of linear diophantine equations: Bounds and algorithms - Plotkin |

1 |
Proof Methods for Equational Theories, dissertation
- Bachmair
- 1987
(Show Context)
Citation Context ...e construction of these systems is essentially an unfailing completion procedure similar to those described in (Bachmair, Dershowitz, and Hsiang 1986), (Bachmair, Dershowitz, and Plaisted 1987), and (=-=Bachmair 1987-=-). Gallier and Snyder's first step might be roughly summarized as: replace variables by new constants, work in the more congenial ground setting, then translate back to variables. It seems to us that ... |

1 | Complete sets of unifiers and matchers - Fages, Huet - 1986 |

1 | Sur la Theorie de la Demonstration, dissertation - Herbrand - 1930 |

1 | An algorithm for unification - Martelli, Moiso, et al. - 1986 |