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Proof Theory
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The article was published on 1975-01-01 and is currently open access. It has received 770 citations till now. The article focuses on the topics: Proof theory & Gentzen's consistency proof.read more
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On the polynomial-space completeness of intuitionistic propositional logic
TL;DR: An alternative, purely semantical and relatively simple, proof of the Statman's result that both intuitionistic propositional logic and its implicational fragment are PSPACE-complete is presented.
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Algorithmic introduction of quantified cuts
TL;DR: A method for inverting Gentzen's cut-elimination in classical first-order logic based on first computing a compressed representation of the terms present in the cut-free proof and then cut-formulas that realize such a compression.
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Mtac: A Monad for Typed Tactic Programming in Coq
TL;DR: Mtac is presented, a lightweight but powerful extension to Coq that supports dependently typed tactic programming, and avoids the need to touch the trusted kernel typechecker of Coq by encapsulating uses of these new tactical primitives in a monad, and instrumenting Coq so that it executes monadic tactics during type inference.
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Semantics and truth relative to a world
TL;DR: It is argued that relativity of truth to a world plays no significant role in empirical semantic theory, even as it is done in the model-theoretic tradition relying on intensional type theory.
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On Go¨del's theorems on lengths of proofs I: number of lines and speedup for arithmetics
TL;DR: This paper gives the first publicly known proof of Godel's claim that there is superrecursive (in fact, unbounded) proof speedup of ( i + l)st-order arithmetic over i th- order arithmetic, where arithmetic is formalized in Hilbert-style calculi with + and • as function symbols or with the language of PRA.