Introducing Substitution in Proof Theory
نویسنده
چکیده
We obtain two results about the proof complexity of deep inference: 1) deep-inference proof systems are as powerful as Frege ones, even when both are extended with the Tseitin extension rule or with the substitution rule; 2) there are analytic deepinference proof systems that exhibit an exponential speedup over analytic Gentzen proof systems that they polynomially simulate.
منابع مشابه
π-calculus in (Co)Inductive Type Theory
We present a large and we think also significant case-study in computer assisted formal reasoning. We start by giving a higher order abstract syntax encoding of π-calculus in the higher-order inductive/coinductive type theories CIC and CC. This encoding gives rise to a full-fledged proof editor/proof assistant for the π-calculus, once we embed it in Coq, an interactive proof-development environ...
متن کاملApplication of queuing theory in inventory systems with substitution flexibility
Considering the competition in today’s business environment, tactical planning of a supply chain becomes more complex than before. In many multi-product inventory systems, substitution flexibility can improve profits. This paper aims to prepare a comprehensive substitution inventory model, where an inventory system with two substitute products with ignorable lead time has been considered, and e...
متن کاملMechanization of Analytic Reasoning About Sets
Resolution reasoners, when applied to set theory problems, typically suffer from “lack of focus.” MARS is a program that attempts to rectify this difficulty by exploiting the definition-like character of the set theory axioms. As in the case of its predecessor, SLIM, it employs a tableau proof procedure based on binary resolution, but MARS IS enhanced by an equality substitution rule and a devi...
متن کاملEpsilon Substitution for ID1
Hilbert’s epsilon substitution method provides a technique for showing that a theory is consistent by producing progressively more accurate computable approximations to the non-computable components of a proof. If it can be shown that this process eventually halts with a sufficiently good approximation, the theory is consistent. Here we produce a new formulation of the method for the theory ID1...
متن کاملExtended Abstract: Reconsidering Intuitionistic Duality
This paper proposes a new syntax and proof system called Dualized Intuitionistic Logic (DIL), for intuitionistic propositional logic with the subtraction operator. Our goal is a conservative extension of standard propositional intuitionistic logic with perfect duality (symmetry) between positive and negative connectives. The proof system should satisfy the following metatheoretic properties: so...
متن کامل