Communications of the ACM
Learnability and the Vapnik-Chervonenkis dimension
Journal of the ACM (JACM)
Learning Conjunctions of Horn Clauses
Machine Learning - Computational learning theory
First-order jk-clausal theories are PAC-learnable
Artificial Intelligence
Generalized teaching dimensions and the query complexity of learning
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
Simple learning algorithms using divide and conquer
COLT '95 Proceedings of the eighth annual conference on Computational learning theory
Knowledge compilation and theory approximation
Journal of the ACM (JACM)
How many queries are needed to learn?
Journal of the ACM (JACM)
Artificial Intelligence
Logical settings for concept-learning
Artificial Intelligence
Conjunctions of unate DNF formulas: learning and structure
Information and Computation
Learning to Reason with a Restricted View
Machine Learning
Learning Function-Free Horn Expressions
Machine Learning - The Eleventh Annual Conference on computational Learning Theory
Exact learning of DNF formulas using DNF hypotheses
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Learning closed horn expressions
Information and Computation
Machine Learning
Machine Learning
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Learning Acyclic First-Order Horn Sentences from Entailment
ALT '97 Proceedings of the 8th International Conference on Algorithmic Learning Theory
Learning Horn Definitions with Equivalence and Membership Queries
ILP '97 Proceedings of the 7th International Workshop on Inductive Logic Programming
Learning First-Order Acyclic Horn Programs from Entailment
ILP '98 Proceedings of the 8th International Workshop on Inductive Logic Programming
On boolean functions and their orientations: learning, monotone dimension, and certificates
On boolean functions and their orientations: learning, monotone dimension, and certificates
Theoretical Computer Science - Special issue: Algorithmic learning theory
Learnability and Automatizability
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Query Learning and Certificates in Lattices
ALT '08 Proceedings of the 19th international conference on Algorithmic Learning Theory
Canonical horn representations and query learning
ALT'09 Proceedings of the 20th international conference on Algorithmic learning theory
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This paper studies the complexity of learning classes of expressions in propositional logic from equivalence queries and membership queries. In particular, we focus on bounding the number of queries that are required to learn the class ignoring computational complexity. This quantity is known to be captured by a combinatorial measure of concept classes known as the certificate complexity. The paper gives new constructions of polynomial size certificates for monotone expressions in conjunctive normal form (CNF), for unate CNF functions where each variable affects the function either positively or negatively but not both ways, and for Horn CNF functions. Lower bounds on certificate size for these classes are derived showing that for some parameter settings the new certificate constructions are optimal. Finally, the paper gives an exponential lower bound on the certificate size for a natural generalization of these classes known as renamable Horn CNF functions, thus implying that the class is not learnable from a polynomial number of queries.