Structural Proof Theory

The genesis of this special issue was in a meeting that took place at Université Paris Diderot on December 15 and 16, 2016. Dale Miller, Professor at École polytechnique, had turned 60 a few days earlier. In a career spanning over three decades and in work conducted in collaboration with several students and colleagues, Dale had had a significant influence in an area that can be described as structural proof theory and its application to computation and reasoning. In recognition of this fact, several of his collaborators thought it appropriate to celebrate the occasion by organizing a symposium on topics broadly connected to his areas of interest and achievements. The meeting was a success in several senses: it was attended by over 35 people, there were 15 technical presentations describing new results, and, quite gratifyingly, we managed to spring the event as a complete surprise to Dale.

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The Church–Fitch knowability paradox in the light of structural proof theory

Synthese ◽

10.1007/s11229-012-0061-7 ◽

2012 ◽

Vol 190 (14) ◽

pp. 2677-2716 ◽

Cited By ~ 12

Author(s):

Paolo Maffezioli ◽

Alberto Naibo ◽

Sara Negri

Keyword(s):

Proof Theory ◽

Knowability Paradox ◽

Structural Proof Theory ◽

The Church

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Resolution and the Origins of Structural Reasoning: Early Proof-Theoretic Ideas of Hertz and Gentzen

Bulletin of Symbolic Logic ◽

10.2178/bsl/1182353872 ◽

2002 ◽

Vol 8 (2) ◽

pp. 246-265 ◽

Cited By ~ 20

Author(s):

Peter Schroeder-Heister

Keyword(s):

Normal Form ◽

Logic Programming ◽

Proof Theory ◽

Structural Rules ◽

General Proof ◽

Early Proof ◽

Sld Resolution ◽

Structural Reasoning ◽

Structural Proof Theory

AbstractIn the 1920s, Paul Hertz (1881–1940) developed certain calculi based on structural rules only and established normal form results for proofs. It is shown that he anticipated important techniques and results of general proof theory as well as of resolution theory, if the latter is regarded as a part of structural proof theory. Furthermore, it is shown that Gentzen, in his first paper of 1933, which heavily draws on Hertz, proves a normal form result which corresponds to the completeness of propositional SLD-resolution in logic programming.

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