2001/08/22 by Stefan Ratschan, Ratschan, Stefan
Computer Science · #Advanced Database Systems and Queries #Artificial Intelligence (cs.AI) #Constraint Satisfaction and Optimization #F.4.1 #FOS: Computer and information sciences #I.2.3 #Logic in Computer Science (cs.LO) #Logic, programming, and type systems #cs.AI #cs.LO
paper · pdf · doi:10.48550/arxiv.cs/0108013
openalex publication_date 2001/08/22 · arxiv created 2002/12/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate solutions instead of exact ones. However, the quantifiers of the first-order predicate language are an obstacle to allowing approximations to arbitrary small error bounds. In this paper we solve the problem by modifying the first-order language and replacing the classical quantifiers with approximate quantifiers. These also have two additional advantages: First, they are tunable, in the sense that they allow the user to decide on the trade-off between precision and efficiency. Second, they introduce additional expressivity into the first-order language by allowing reasoning over the size of solution sets.