Artificial Intelligence
System Description: Twelf - A Meta-Logical Framework for Deductive Systems
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
The design and implementation of VAMPIRE
AI Communications - CASC
TPTP, CASC and the development of a semantically guided theorem prover
AI Communications - CASC
The ILTP Problem Library for Intuitionistic Logic
Journal of Automated Reasoning
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
The TPTP Problem Library and Associated Infrastructure
Journal of Automated Reasoning
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
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In intuitionistic sequent calculi, detecting that a sequent is unprovable is often used to direct proof search. This is for instance seen in backward chaining, where an unprovable subgoal means that the proof search must backtrack. In undecidable logics, however, proof search may continue indefinitely, finding neither a proof nor a disproof of a given subgoal. In this paper we characterize a family of truth-preserving abstractions from intuitionistic first-order logic to the monadic fragment of classical first-order logic. Because they are truthful, these abstractions can be used to disprove sequents in intuitionistic first-order logic.