Frege Systems
نویسنده
چکیده
منابع مشابه
The Deduction Rule and Linear and Near-Linear Proof Simulations
We introduce new proof systems for propositional logic, simple deduction Frege systems, general deduction Frege systems and nested deduction Frege systems, which augment Frege systems with variants of the deduction rule. We give upper bounds on the lengths of proofs in Frege proof systems compared to lengths in these new systems. As applications we give near-linear simulations of the propositio...
متن کاملPropositional Consistency Proofs
Partial consistency statements can be expressed as polynomial-size propositional formulas. Frege proof systems have polynomial-size partial self-consistency proofs. Frege proof systems have polynomialsize proofs of partial consistency of extended Frege proof systems if and only if Frege proof systems polynomially simulate extended Frege proof systems. We give a new proof of Reckhow’s theorem th...
متن کاملOn the Deduction Rule and the Number of Proof Lines
We introduce new proof systems for propositional logic, simple deduction Frege systems, general deduction Frege systems and nested deduction Frege systems, which augment Frege systems with variants of the deduction rule. We give upper bounds on the lengths of proofs in these systems compared to lengths in Frege proof systems. As an application we give a near-linear simulation of the proposition...
متن کاملA On the Power of Substitution in the Calculus of Structures
There are two contributions in this paper. First, we give a direct proof of the known fact that Frege systems with substitution can be p-simulated by the calculus of structures extended with the substitution rule. This is done without referring to the p-equivalence of extended Frege systems and Frege systems with substitution. Second, we then show that the cut-free calculus of structures with s...
متن کاملExtension without cut
In proof theory one distinguishes sequent proofs with cut and cut-free sequent proofs, while for proof complexity one distinguishes Frege-systems and extended Frege-systems. In this paper we show how deep inference can provide a uniform treatment for both classifications, such that we can define cut-free systems with extension, which is neither possible with Frege-systems, nor with the sequent ...
متن کاملOn Interpolation and Automatization for Frege Systems
The interpolation method has been one of the main tools for proving lower bounds for propositional proof systems. Loosely speaking, if one can prove that a particular proof system has the feasible interpolation property, then a generic reduction can (usually) be applied to prove lower bounds for the proof system, sometimes assuming a (usually modest) complexity-theoretic assumption. In this pap...
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