1. A more general general proof theory.
- Author
-
Wansing, Heinrich
- Subjects
PROOF theory ,DERIVATIVES (Mathematics) ,INTUITIONISTIC mathematics ,MATHEMATICAL proofs ,METADATA mapping - Abstract
In this paper it is suggested to generalize our understanding of general (structural) proof theory and to consider it as a general theory of two kinds of derivations, namely proofs and dual proofs. The proposal is substantiated by (i) considerations on assertion, denial, and bi-lateralism, (ii) remarks on compositionality in proof-theoretic semantics, and (iii) comments on falsification and co-implication. The main formal result of the paper is a normal form theorem for the natural deduction proof system N2Int of the bi-intuitionistic logic 2Int. The proof makes use of the faithful embedding of 2Int into intuitionistic logic with respect to validity and shows that conversions of dual proofs can be sidestepped. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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