Onto-substitutability has been shown to be intrinsic to how a domain value is considered redundant in Constraint Satisfaction Problems (CSPs). A value is onto-substitutable if any solution involving that value remains a solution when that value is replaced by some other value. We redefine onto-substitutability to accommodate binary relationships and study its implication. Joint interchangeability, an extension of onto-substitutability to its interchangeability counterpart, emerges as one of the results. We propose a new way of removing interchangeable values by constructing a new value as an intermediate step, as well as introduce virtual interchangeability, a local reasoning that leads to joint interchangeability and allows values to be merged together. Algorithms for removing onto-substitutable values are also proposed. 1
Abstract.We consider configuration problems with preferences rather than just hard constraints, and we analyze and discuss the features that such configurators should have. In particular, these configurators should provide explanations for the current state, implications of a future choice, and also information about the quality of future solutions, all with the aim of guiding the user in the process of making the right choices to obtain a good solution. We then describe our implemented system, which, by taking the soft n-queens problem as an example, shows that it is indeed possible, even in this very general context of preference-based configurators, to automatically compute all the information needed for the desired features. This is done by keeping track of the inferences that are made during the constraint propagation enforcing phases.
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