Introduction to mathematical logic (3rd ed.)
Introduction to mathematical logic (3rd ed.)
Simple second-order languages for which unification is undecidable
Theoretical Computer Science
Handbook of Automated Reasoning: Volume 1
Handbook of Automated Reasoning: Volume 1
Referential Data Structures and Labeled Modal Logic
LFCS '94 Proceedings of the Third International Symposium on Logical Foundations of Computer Science
Operational Logic of Proofs with Functionality Condition on Proof Predicate
LFCS '97 Proceedings of the 4th International Symposium on Logical Foundations of Computer Science
Unification of Terms with Term-Indexed Variables
LFCS '97 Proceedings of the 4th International Symposium on Logical Foundations of Computer Science
Theoretical Computer Science - Clifford lectures and the mathematical foundations of programming semantics
Pillars of computer science
A complexity question in justification logic
WoLLIC'11 Proceedings of the 18th international conference on Logic, language, information and computation
Symbolic models for single-conclusion proof logics
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
| Hi-index | 0.00 |
We introduce an extension of the propositional logic of single-conclusion proofs by the second-order variables denoting the reference constructors of the type "the formula which is proved by x." The resulting Logic of Proofs with References, FLPref, is shown to be decidable, and to enjoy soundness and completeness with respect to the intended provability semantics. We show that FLPref provides a complete test of admissibility of inference rules in a sound extension of arithmetic. This paper may be regarded as a contribution to the theory of automated reasoning systems.