Theory revision with queries: Horn, read-once, and parity formulas

A theory, in this context, is a Boolean formula; it is used to classify instances, or truth assignments. Theories can model real-world phenomena, and can do so more or less correctly. The theory revision, or concept revision, problem is to correct a given, roughly correct concept. This problem is considered here in the model of learning with equivalence and membership queries. A revision algorithm is considered efficient if the number of queries it makes is polynomial in the revision distance between the initial theory and the target theory, and polylogarithmic in the number of variables and the size of the initial theory. The revision distance is the minimal number of syntactic revision operations, such as the deletion or addition of literals, needed to obtain the target theory from the initial theory. Efficient ∗Email: [email protected]. Computer Science Department, University of Kentucky, Lexington, KY 40506-0046, USA. Partially supported by NSF grant CCR-0100040. †Contact author. Email [email protected]. Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607-7053, USA. Partially supported by NSF grants CCR-9800070 and CCR-0100336. ‡Email: [email protected]. Hungarian Academy of Sciences and University of Szeged, Research Group on Artificial Intelligence, H-6720 Szeged, Aradi vértanúk tere 1., Hungary §Email: [email protected]. Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL 60607-7045, USA, and Hungarian Academy of Sciences and University of Szeged, Research Group on Artificial Intelligence, H-6720 Szeged, Aradi vértanúk tere 1., Hungary. Partially supported by NSF grants CCR-0100336 and CCR-9800070.