The resolution calculus
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Cut-elimination and redundancy-elimination by resolution
Journal of Symbolic Computation - Special issue on advances in first-order theorem proving
On Skolemization And Proof Complexity
Fundamenta Informaticae
CERES: An analysis of Fürstenberg's proof of the infinity of primes
Theoretical Computer Science
Cut Elimination for First Order Gödel Logic by Hyperclause Resolution
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
A Clausal Approach to Proof Analysis in Second-Order Logic
LFCS '09 Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
Proof transformations and structural invariance
Algebraic and proof-theoretic aspects of non-classical logics
MKM'06 Proceedings of the 5th international conference on Mathematical Knowledge Management
System description: the proof transformation system CERES
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
| Hi-index | 0.00 |
In this paper we show that a large class of cut-elimination methods can be analysed by clause terms representing sets of characteristic clauses extractable from the original proof. Every reduction step of a cut-elimination procedure defines an operation on the corresponding clause term. Using this formal framework we prove that the methods of Gentzen and Tait and, more generally, every method based on a specific set of cut-reduction rules R, yield a resolution proof which is subsumed by a resolution proof of the characteristic clause set. As a consequence we obtain that CERES (a resolution-based method of cut-elimination) is never inferior to any method based on R. On the other hand we show that CERES is not optimal in general; instead there exist cut-reduction rules which efficiently simplify the set of characteristic clauses and thus produce much shorter proofs. Further improvements and pruning methods could thus be obtained by a structural (syntactic) analysis of the characteristic clause terms.