Constraint Programming with Unrestricted Quantification
نویسندگان
چکیده
Search problems occur widely in AI, and a number of generalpurpose constraint-based methods for solving them have been developed. Convenient modelling of many problems is enabled by use of quantifiers of various sorts, but the most prominent approaches support only limited use of quantifiers. A recently proposed constraint programming framework, based on classical logic and the notion of expansion of a finite structure with new relations, supports unrestricted use of both first-order and second-order quantifiers. The framework can be parameterized to capture various complexity classes, including NP and Σ k for any k. Second-order quantifiers can be used to concisely model search problems at any of these complexity levels. First-order quantifiers can be used freely for modelling convenience, without affecting the complexity level which is determined by the second-order quantifiers. We explain this framework, discuss the roles of quantifiers, and give some examples.
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