Core Concepts
The author explores the integration of induction into saturation-based first-order theorem proving, presenting new inference rules and heuristics to enhance inductive reasoning within the framework.
Abstract
The content discusses the automation of inductive reasoning in theorem proving, focusing on integrating induction into saturation-based proof search. It covers various aspects such as structural induction, relation to state-of-the-art methods, and extensions for integers.
The author introduces different types of induction schemata for term algebras and integers, showcasing how they can be applied within a saturation-based proof search algorithm. They emphasize the importance of finding suitable induction rules and developing efficient strategies for automating inductive reasoning.
Key points include introducing induction inference rules for term algebras and integers, discussing the application of these rules within a saturation-based proof search algorithm, and highlighting the challenges and solutions related to automating inductive reasoning.
The content provides detailed examples illustrating the application of different types of induction rules in verifying program properties and mathematical conjectures. It also emphasizes the significance of combining theory reasoning with superposition techniques to facilitate efficient proof generation.
Overall, the content delves into the complexities of automating inductive reasoning within theorem proving systems, offering insights into novel approaches that enhance the efficiency and effectiveness of this process.
Stats
Induction is integrated directly into saturation-based first-order provers.
New inference rules are introduced to enhance inductive reasoning.
Experimental results demonstrate practical impact within Vampire.
Induction schema instances are generated for term algebras and integers.
Various types of induction rules are presented for different scenarios.
Quotes
"The combination of saturation with induction is very powerful."
"Our work automates induction by integrating it directly into the saturation-based approach."