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CORR
2008
Springer

Efficiently Simulating Higher-Order Arithmetic by a First-Order Theory Modulo

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Efficiently Simulating Higher-Order Arithmetic by a First-Order Theory Modulo
In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems--such as for instance natural deduction--are applied. Therefore, the reasoning that is intrinsic of the theory does not appear in the length of proofs. In general, the congruence is defined through a rewrite system over terms and propositions. We define a rigorous framework to study proof lengths in deduction modulo, where the congruence must be computed in polynomial time. We show that even very simple rewrite systems lead to arbitrary proof-length speed-ups in deduction modulo compared to using axioms. As higher-order logic can be encoded as a first-order theory in deduction modulo, we also study how to reinterpret, thanks to deduction modulo, the speed-ups between higherorder and first-order arithmetics that were stated by G
Guillaume Burel
Added 24 Jan 2011
Updated 24 Jan 2011
Type Journal
Year 2008
Where CORR
Authors Guillaume Burel
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