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Dependency calculus: Reasoning in a general point relation algebra
 KI 2005: ADVANCES IN ARTIFICIAL INTELLIGENCE, PROCEEDINGS OF THE 28TH ANNUAL GERMAN CONFERENCE ON AI
, 2005
"... Reasoning about complex dependencies between events is a crucial task. However, qualitative reasoning has so far concentrated on spatial and temporal issues. In contrast, we present a new dependency calculus (DC) that is created for specific questions of reasoning about causal relations and consequ ..."
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Reasoning about complex dependencies between events is a crucial task. However, qualitative reasoning has so far concentrated on spatial and temporal issues. In contrast, we present a new dependency calculus (DC) that is created for specific questions of reasoning about causal relations and consequences. Applications in the field of spatial representation and reasoning are, for instance, modeling traffic networks, ecological systems, medical diagnostics, and Bayesian Networks. Several extensions of the fundamental linear point algebra have been investigated, for instance on trees or on nonlinear structures. DC is an improved generalization that meets all requirements to describe dependencies on networks. We investigate this structure with respect to satisfiability problems, construction problems, tractable subclassses, and embeddings into other relation algebras. Finally, we analyze the associated interval algebra on network structures.
Disjunctions, Independence, Refinements
"... An important question in constraint satisfaction is how to restrict the problem to ensure tractability (since the general problem is NPhard). The use of ..."
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An important question in constraint satisfaction is how to restrict the problem to ensure tractability (since the general problem is NPhard). The use of
Disjunctions
"... An important question in constraint satisfaction is how to restrict the problem to ensure tractability (since the general problem is NPhard). The use of disjunctions has proven to be a useful method for constructing tractable constraint classes from existing classes; the wellknown `maxclosed &apo ..."
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An important question in constraint satisfaction is how to restrict the problem to ensure tractability (since the general problem is NPhard). The use of disjunctions has proven to be a useful method for constructing tractable constraint classes from existing classes; the wellknown `maxclosed ' and `ORDHorn ' constraints are examples of tractable classes that can be constructed this way. Three sucient conditions (the guaranteed satisfaction property, 1independence and 2independence) that each ensure the tractability of constraints combined by disjunctions have been proposed in the literature. We show that these conditions are both necessary and sucient for tractability in three dierent natural classes of disjunctive constraints. This suggests that deciding this kind of property is a very important task when dealing with disjunctive constraints. We provide a simple, automatic method for checking the 1independence propertythis method is applicable whenever the consistency of the constraints under consideration can be decided by pathconsistency. Our method builds on a connection between independence and renements (which is a way of reducing one constraint satisfaction problem to another.)