1988
DOI: 10.1016/0304-3975(88)90140-5
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Unification in commutative idempotent monoids

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Cited by 24 publications
(28 citation statements)
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“…In this paper we extend uni cation, the core mechanism of logic programming, to handle bags and sets. When bags and sets are represented with using the union operations, bag and set uni cation is a particular case of AC1and ACI1-uni cation, which has been extensively studied 44,25,24,10,33,18]. Recently, a n umber of uni cation algorithms have been introduced for various domains of bags and sets built with the bag and set constructors similar to the list constructor used in functional and logic programming 21,22,45,9].…”
Section: Introductionmentioning
confidence: 99%
“…In this paper we extend uni cation, the core mechanism of logic programming, to handle bags and sets. When bags and sets are represented with using the union operations, bag and set uni cation is a particular case of AC1and ACI1-uni cation, which has been extensively studied 44,25,24,10,33,18]. Recently, a n umber of uni cation algorithms have been introduced for various domains of bags and sets built with the bag and set constructors similar to the list constructor used in functional and logic programming 21,22,45,9].…”
Section: Introductionmentioning
confidence: 99%
“…The implication from left to right in (I); The pair ( * v * , * w) is the only pair from {h(v, w)} ∪ G such that both 1 The reduction given in [7] is slightly different. The first pair (v 0 , w 0 ) from G has two corresponding pairs (v * 0 , * w 0 ) and ( * v * 0 , * w 0 ) in G .…”
Section: Theorem 31 There Exists a Set Of Pairs Of Wordsmentioning
confidence: 97%
“…Unification modulo ACI is a well-studied problem. The paper [1] gives an algorithm for solving ACI-unification with constants and a doubly exponential upper bound on the number of most general ACI-unifiers. The doubly exponential upper bound is tight.…”
Section: Letmentioning
confidence: 99%
“…This work mostly deals with AC unification-by reducing it to the solution of Diophantine equations-and only in the end it suggests a solution of the ACI problem, by replacing arithmetic equations with Boolean equations. Direct solutions of the ACI problem have been proposed by Büttner (Büttner 1986) and Baader and Büttner (Baader and Büttner 1988).…”
Section: Unification Algorithmsmentioning
confidence: 99%
“…2. If the test succeeds, then a solution can be constructed by assigning to each variable X in s = t a term composed of the union of all the constants present in s = t . For further details the reader is referred to (Baader and Büttner 1988).…”
Section: Examplementioning
confidence: 99%