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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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Computational reverse mathematics and foundational analysis
TL;DR: In this article, the authors give a detailed account of the motivations and methodology of foundational analysis, which have heretofore been largely left implicit in the practice, and show how this account can be fruitfully applied in the evaluation of major foundational approaches by a careful examination of two case studies: a partial realization of Hilbert's program due to Simpson [1988], and predicativism in the extended form due to Feferman and Schutte.
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Infinitary and Cyclic Proof Systems for Transitive Closure Logic
Liron Cohen,Reuben N. S. Rowe +1 more
TL;DR: This paper presents an infinitaryProof system for transitive closure logic which is an infinite descent-style counterpart to the existing (explicit induction) proof system for the logic and shows that it is complete for the standard semantics and subsumes the explicit system.
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An unexpected separation result in Linearly Bounded Arithmetic
Arnold Beckmann,Jan Johannsen +1 more
TL;DR: The theories Si1(α) and Ti1( α) are the analogues of Buss' relativized bounded arithmetic theories in the language where every term is bounded by a polynomial, and thus all definable functions grow linearly in length.
On Natural Deduction in Fixpoint Logics
TL;DR: This paper shows how to obtain complete (but infinitary) proof systems as well as relatively complete (finitistic) ones for first-order fixpoint logics.
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A computational framework for Karl Popper's logic of scientific discovery
Wei Li,Yuefei Sui +1 more
TL;DR: This work develops approximation algorithms for SAT problems to derive a feasible R-calculus based on the relation between deduction and satisfiability and provides a full spectrum of belief revision: from philosophical to feasible revision.