Artificial Intelligence
Journal of Complexity
A logic for reasoning about probabilities
Information and Computation - Selections from 1988 IEEE symposium on logic in computer science
Mining association rules between sets of items in large databases
SIGMOD '93 Proceedings of the 1993 ACM SIGMOD international conference on Management of data
Anytime deduction for probabilistic logic
Artificial Intelligence
Optimization of constrained frequent set queries with 2-variable constraints
SIGMOD '99 Proceedings of the 1999 ACM SIGMOD international conference on Management of data
Mining frequent patterns without candidate generation
SIGMOD '00 Proceedings of the 2000 ACM SIGMOD international conference on Management of data
Fast Algorithms for Mining Association Rules in Large Databases
VLDB '94 Proceedings of the 20th International Conference on Very Large Data Bases
Models and algorithms for probabilistic and Bayesian logic
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
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In data mining association rules are very popular. Most of the algorithms in the literature for finding association rules start by searching for frequent itemsets. The itemset mining algorithms typically interleave brute force counting of frequencies with a meta-phase for pruning parts of the search space. The knowledge acquired in the counting phases can be represented by frequent set expressions. A frequent set expression is a pair containing an itemset and a frequency indicating that the frequency of that itemset is greater than or equal to the given frequency. A system of frequent sets is a collection of such expressions. We give an axiomatization for these systems. This axiomatization characterizes complete systems. A system is complete when it explicitly contains all information that it logically implies. Every system of frequent sets has a unique completion. The completion of a system actually represents the knowledge that maximally can be derived in the meta-phase.