Proof Transformation by CERES
نویسندگان
چکیده
Cut-elimination is the most prominent form of proof transformation in logic. The elimination of cuts in formal proofs corresponds to the removal of intermediate statements (lemmas) in mathematical proofs. The cut-elimination method CERES (cut-elimination by resolution) works by constructing a set of clauses from a proof with cuts. Any resolution refutation of this set then serves as a skeleton of an LK-proof with only atomic cuts. In this paper we present an extension of CERES to a calculus LKDe which is stronger than the Gentzen calculus LK (it contains rules for introduction of definitions and equality rules). This extension makes it much easier to formalize mathematical proofs and increases the performance of the cut-elimination method. The system CERES already proved efficient in handling very large proofs.
منابع مشابه
System Description: The Proof Transformation System CERES
Cut-elimination is the most prominent form of proof transformation in logic. The elimination of cuts in formal proofs corresponds to the removal of intermediate statements (lemmas) in mathematical proofs. The cut-elimination method CERES (cut-elimination by resolution) works by extracting a set of clauses from a proof with cuts. Any resolution refutation of this set then serves as a skeleton of...
متن کاملEquational Theories in CERES
Cut-elimination is the most important proof transformation in logic. Equality is a central paradigm in mathematics and plays a key role in automated deduction. Therefore its importance awakes the necessity of integrating equality into existing cut-elimination methods. In this paper we extend the resolution-based method of cut-elimination CERES to CERES-e by adding equality (and paramodulation t...
متن کاملSystem Description : The Cut - Elimination System CERES ∗
Cut-elimination is the most prominent form of proof transformation in logic. The elimination of cuts in formal proofs corresponds to the removal of intermediate statements (lemmas) in mathematical proofs. The cut-elimination method CERES (cut-elimination by resolution) works by constructing a set of clauses from a proof with cuts. Any resolution refutation of this set then serves as a skeleton ...
متن کاملTransforming and Analyzing Proofs in the CERES-System
Cut-elimination is the most prominent form of proof transformation in logic. The elimination of cuts in formal proofs corresponds to the removal of intermediate statements (lemmas) in mathematical proofs. Cut-elimination can be applied to mine real mathematical proofs, i.e. for extracting explicit and algorithmic information. The system CERES (cut-elimination by resolution) is based on automate...
متن کاملCut-Elimination: Experiments with CERES
Cut-elimination is the most prominent form of proof transformation in logic. The elimination of cuts in formal proofs corresponds to the removal of intermediate statements (lemmas) in mathematical proofs. The cut-elimination method CERES (cut-elimination by resolution) works by constructing a set of clauses from a proof with cuts. Any resolution refutation of this set can then serve as a skelet...
متن کامل