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

Abstract

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

Projective DNF formulae and their revision

“…In view of this relationship, it is an interesting general question whether attribute-efficient learnability results can be extended to results on efficient revision. Previously we gave a positive answer in the case of parity function, where the relationship between the two tasks is simple [5]. As a next step, we show here that Winnow is in fact an efficient algorithm for revising disjunctions as well.…”

“…An efficient revision algorithm is required to be polynomial in the number of literals that need to be modified and polylogarithmic in the total number of literals. Wrobel gives a general survey of the theory revision literature [19,20]; efficient revision in the framework of learning with queries is discussed in detail in [5,6].…”

Collaborative Concept Learning: Non Individualistic vs Individualistic Agents

“…From a computational learning theory perspective, collaborative consistent learning as proposed here has links with Query Learning and more precisely with theory revision with queries [6]. Critics as defined here may be seen as incomplete oracles answering equivalence queries: when the learner does not receive counterexamples from critics (acting as incomplete oracles), he has to wait for examples coming from the environment.…”

Projective DNF Formulae and Their Revision

“…Previously we gave a positive answer in the case of parity function, where the relationship between the two tasks is simple [5]. As a next step, we show here that Winnow is in fact an efficient algorithm for revising disjunctions as well.…”

“…An efficient revision algorithm is required to be polynomial in the number of literals that need to be modified and polylogarithmic in the total number of literals. Wrobel gives a general survey of the theory revision literature [19,20]; efficient revision in the framework of learning with queries is discussed in detail in [5,6].…”