Experiments with proof plans for induction
Journal of Automated Reasoning
Rippling: a heuristic for guiding inductive proofs
Artificial Intelligence
Analogy for Automated Reasoning
Analogy for Automated Reasoning
Proceedings of the 10th International Conference on Automated Deduction
Synthesis of Induction Orderings for Existence Proofs
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Termination Orderings for Rippling
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Internal Analogy in Theorem Proving
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Lemma Discovery in Automated Induction
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Analogy as a means of discovery in problem solving and learning
Analogy as a means of discovery in problem solving and learning
A model of analogy-driven proof-plan construction
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Second-order matching modulo evaluation: a technique for reusing proofs
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Flexibly Interleaving Processes
ICCBR '99 Proceedings of the Third International Conference on Case-Based Reasoning and Development
Changing Data Structures in Type Theory: A Study of Natural Numbers
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
Formal Proof: Reconciling Correctness and Understanding
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
Strategy variations in analogical problem solving
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Measuring the level of transfer learning by an AP physics problem-solver
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
Analogical model formulation for transfer learning in AP Physics
Artificial Intelligence
Verification of object-oriented software: The KeY approach
Verification of object-oriented software: The KeY approach
Domain transfer via cross-domain analogy
Cognitive Systems Research
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In this paper, we investigate analogy-driven proof plan construction in inductive theorem proving. The intention is to produce a plan for a target theorem that is similar to a given source theorem. We identify second-order mappings from the source to the target that preserve induction-specific proof-relevant abstractions dictating whether the source plan can be replayed. We replay the planning decisions taken in the source if the reasons or justifications for these decisions still hold in the target. If the source and target plan differ significantly at some isolated point, additional reformulations are invoked to add, delete, or modify planning steps. These reformulations are not ad hoc but are triggered by peculiarities of the mappings and by failed justifications. Employing analogy on top of the proof planner CLAM has extended the problem-solving horizon of CLAM: With analogy, some theorems could be proved automatically that neither CLAM nor NQTHM could prove automatically.