Automatic proofs by induction in theories without constructors
Information and Computation
CADE-10 Proceedings of the tenth international conference on Automated deduction
Handbook of theoretical computer science (vol. B)
Rippling: a heuristic for guiding inductive proofs
Artificial Intelligence
Handbook of logic in artificial intelligence and logic programming
On proving inductive properties of abstract data types
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Generalization Discovery for Proofs by Induction in Conditional Theories
Proceedings of the Twelfth International Florida Artificial Intelligence Research Society Conference
A Mechanizable Induction Principle for Equational Specifications
Proceedings of the 9th International Conference on Automated Deduction
Lemma Discovery in Automated Induction
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Inductive Theorem Proving by Consistency for First-Order Clauses
CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems
Automata-driven automated induction
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
A divergence critic for inductive proof
Journal of Artificial Intelligence Research
Strategic Issues, Problems and Challenges in Inductive Theorem Proving
Electronic Notes in Theoretical Computer Science (ENTCS)
| Hi-index | 5.23 |
Many proofs by induction diverge without a suitable generalization of the goal to be proved.The aim of the present paper is to propose a method that automatically finds a generalized form of the goal before the induction sub-goals are generated and failure begins. The method works in the case of monomorphic theories (see Section 1). However, in contrast to all heuristic-based methods, our generalization method is sound: A goal is an inductive theorem if and only if its generalization is an inductive theorem. As far as we know this is the first approach that proposes sound generalizations for mathematical induction.