Cut-Simulation and Impredicativity
نویسندگان
چکیده
منابع مشابه
Cut-Simulation and Impredicativity
We investigate cut-elimination and cut-simulation in impredicative (higherorder) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic — in our case a sequent calculus for classical type theory — is like adding cut. The phenomenon equally applies to prominent axioms like Booleanand functional extensionality, induction, choice, and des...
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Pure, or type-free, Linear Logic proof nets are Turing complete once cut-elimination is considered as computation. We introduce modal impredicativity as a new form of impredicativity causing the complexity of cut-elimination to be problematic from a complexity point of view. Modal impredicativity occurs when, during reduction, the conclusion of a residual of a box b interacts with a node that b...
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We investigate cut-elimination and cut-simulation in impredicative (higher-order) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic — in our case a sequent calculus for classical type theory — is like adding cut. The phenomenon equally applies to prominent axioms like Booleanand functional extensionality, induction, choice, and de...
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ژورنال
عنوان ژورنال: Logical Methods in Computer Science
سال: 2009
ISSN: 1860-5974
DOI: 10.2168/lmcs-5(1:6)2009