Term Indexing
A Resolution Theorem Prover for Intuitonistic Logic
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
System Description: Twelf - A Meta-Logical Framework for Deductive Systems
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
Games Semantics for Full Propositional Linear Logic
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
The ILTP Problem Library for Intuitionistic Logic
Journal of Automated Reasoning
The focused inverse method for linear logic
The focused inverse method for linear logic
Focusing and higher-order abstract syntax
Proceedings of the 35th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A Logical Characterization of Forward and Backward Chaining in the Inverse Method
Journal of Automated Reasoning
Imogen: Focusing the Polarized Inverse Method for Intuitionistic Propositional Logic
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Focusing the inverse method for linear logic
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Focusing and polarization in intuitionistic logic
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Complete completion using types and weights
Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation
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The inverse method is a generic proof search procedure applicable to non-classical logics satisfying cut elimination and the subformula property. In this paper we describe a general architecture and several high-level optimizations that enable its efficient implementation. Some of these rely on logic-specific properties, such as polarization and focusing, which have been shown to hold in a wide range of non-classical logics. Others, such as rule subsumption and recursive backward subsumption apply in general. We empirically evaluate our techniques on first-order intuitionistic logic with our implementation Imogen and demonstrate a substantial improvement over all other existing intuitionistic theorem provers on problems from the ILTP problem library.