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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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Journal ArticleDOI
Cut normal forms and proof complexity
Matthias Baaz,Alexander Leitsch +1 more
TL;DR: It is proved that the elimination of monotone cuts can be of nonelementary complexity (here generalized disjunctions in the antecedents of sequents play a central role) and a large class of problems where cut-elimination of monOTone cuts is only exponential and this bound is tight.
Journal ArticleDOI
Proof theory for theories of ordinals—I: recursively Mahlo ordinals
TL;DR: This paper is the first published one in which a proof-theoretic analysis a la Gentzen–Takeuti of recursively large ordinals is expounded.
Book
Justification Logic: Reasoning with Reasons
Sergei Artemov,Melvin Fitting +1 more
TL;DR: Justification logic as discussed by the authors is a theory of reasoning that enables the tracking of evidence for statements and therefore provides a logical framework for the reliability of assertions, which is the first systematic account of the subject, progressing from modal logic through to an arithmetic interpretation of intuitionistic logic.
DissertationDOI
A mechanization of sorted higher-order logic based on the resolution principle
TL;DR: This thesis develops a sorted higher-order logic SUM HOL suitable for automatic theorem proving applications, and develops two notions of set-theoretic semantics for SUM HOL, which generalize general SUM-models further to SUM-model structures, which allow full extensionality to fail.
Dissertation
Hoare Logic and VDM: Machine-Checked Soundness and Completeness Proofs
TL;DR: The role of auxiliary variables in Hoare Logic is illuminated and a new structural rule for adjusting auxiliary variables when strengthening preconditions and weakening postconditions is proposed, which is stronger than all previously suggested structural rules, including rules of adaptation.