منابع مشابه
Structural Cut Elimination
We present new proofs of cut elimination for intuitionistic, classical, and linear sequent calculi. In all cases the proofs proceed by three nested structural inductions, avoiding the explicit use of multi-sets and termination measures on sequent derivations. This makes them amenable to elegant and concise implementations in Elf, a constraint logic programming language based on the LF logical f...
متن کاملWhich structural rules admit cut elimination? An algebraic criterion
Consider a general class of structural inference rules such as exchange, weakening, contraction and their generalizations. Among them, some are harmless but others do harm to cut elimination. Hence it is natural to ask under which condition cut elimination is preserved when a set of structural rules is added to a structurefree logic. The aim of this work is to give such a condition by using alg...
متن کاملStructural Cut Elimination: I. Intuitionistic and Classical Logic
We present new variants of known proofs of cut elimination for intui-tionistic and classical sequent calculi. In both cases the proofs proceed by three nested structural inductions, avoiding the explicit use of multi-sets and termination measures on sequent derivations. This makes them amenable to elegant and concise representations in LF, which are given in full detail.
متن کاملProof Fragments, Cut-Elimination and Cut-Introduction
Cut-elimination is usually presented as a set of local proof reduction steps together with a terminating strategy thus showing the existence of cut-free proofs for all provable sequents. Viewing cut-elimination as a transformation of mathematical proofs, not only the existence but also the structure and content of the cut-free proofs deserves investigation. In this paper we use proof skeletons ...
متن کاملCut-elimination and Redundancy-elimination by Resolution
Cut-elimination is one of the most important techniques in proof theory. Roughly speaking, eliminating cuts from a proof generates a new proof without lemmas, which essentially consists of the syntactic material of the proven theorem. Traditionally cutelimination served the purpose to show consistency of calculi and thus played a central role in metamathematics. In this traditional context the ...
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ژورنال
عنوان ژورنال: Information and Computation
سال: 2000
ISSN: 0890-5401
DOI: 10.1006/inco.1999.2832