Extensions of CERES
In Chapter 6 the CERES method was defined as a cut-elimination method for LK-proofs. But the method is potentially much more general and can be extended to a wide range of first-order cacluli. First of all CERES is a semantic method, in the sense that it works for all sound sequent calculi with a definable ancestor relation and a semantically complete clausal calculus. In this chapter we first show that a CERES method can be defined for virtually any sound sequent calculus. Second, we define extensions of LK by equality and definitions rules which are useful for formalizing mathematical theorems and show how to adapt CERES to these extensions of LK. The extension LKDe defined in Section 7.3 will then be used for the analysis of mathematical proofs in Section 8.5.
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