Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Tree clustering for constraint networks (research note)
Artificial Intelligence
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Structure-driven algorithms for truth maintenance
Artificial Intelligence
Model-based diagnosis using causal networks
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
An improved constraint-propagation algorithm for diagnosis
IJCAI'87 Proceedings of the 10th international joint conference on Artificial intelligence - Volume 2
Clustering without (thinking about) triangulation
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Partition-based logical reasoning for first-order and propositional theories
Artificial Intelligence - Special volume on reformulation
Practical partition-based theorem proving for large knowledge bases
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Theorem proving with structured theories
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Partition-based logical reasoning for first-order and propositional theories
Artificial Intelligence - Special volume on reformulation
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Graph-based algorithms convert a knowledge base with a graph structure into one with a tree structure (a join-tree) and then apply tree-inference on the result. Nodes in the join-tree are cliques of variables and tree-inference is exponential in w*, the size of the maximal clique in the join-tree. A central property of join-trees that validates tree-inference is the running-intersection property: the intersection of any two cliques must belong to every clique on the path between them. We present two key results in connection to graph-based algorithms. First, we show that the running-intersection property, although sufficient, is not necessary for validating tree-inference. We present a weaker property for this purpose, called running-interaction, that depends on nonstructural (semantical) properties of a knowledge base. We also present a linear algorithm that may reduce w* of a join-tree, possibly destroying its running-intersection property, while maintaining its running-interaction property and, hence, its validity for tree-inference. Second, we develop a simple algorithm for generating trees satisfying the running-interaction property. The algorithm bypasses triangulation (the standard technique for constructing join-trees) and does not construct a join-tree first. We show that the proposed algorithm may in some cases generate trees that are more efficient than those generated by modifying a join-tree.