Integrating Theories into Inference Systems
نویسندگان
چکیده
The axiomatization of arithmetical properties in theorem proving creates many straightforward inference steps. In analyzing mathematical proofs with the CERES (Cut-Elimination by Resolution) system, it is convenient to hide these inferences. The central topic of the thesis is the extension of the CERES method to allow reasoning modulo equational theories. For this, the inference systems of Sequent Calculus modulo and Extended Narrowing and Resolution replace their non-equational counterparts in CERES. The method is illustrated by examples comparing inference modulo the theory of associativity and commutativity with unit element to inference in the empty theory.
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