Inhabitation in Typed Lambda-Calculi (A Syntactic Approach)
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
Journal of Automated Reasoning
HOL-λσ: an intentional first-order expression of higher-order logic
Mathematical Structures in Computer Science
Eigenvariables, bracketing and the decidability of positive minimal predicate logic
Theoretical Computer Science
Eigenvariables, bracketing and the decidability of positive minimal predicate logic
Theoretical Computer Science
Proof Search and Counter Model of Positive Minimal Predicate Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Decidability of the class e by Maslov's inverse method
Fields of logic and computation
| Hi-index | 5.24 |
We give a new proof of a theorem of Mints that the positive fragment of minimal predicate logic is decidable. The idea of the proof is to replace the eigenvariable condition of sequent calculus by an appropriate scoping mechanism. The algorithm given by this proof seems to be more practical than that given by the original proof. A naive implementation is given at the end of the paper. Another contribution is to show that this result extends to a large class of theories, including simple type theory (higher-order logic) and second-order propositional logic. We obtain this way a new proof of the decidability of the inhabitation problem for positive types in system F.