On the idea of a general proof theory

Synthese ◽  
1974 ◽  
Vol 27 (1-2) ◽  
pp. 63-77 ◽  
Author(s):  
Dag Prawitz
Keyword(s):  
Proof Theory ◽  
General Proof

scholarly journals A more general general proof theory

2017 ◽  
Vol 25 ◽  
pp. 23-46 ◽  
Author(s):  
Heinrich Wansing
Keyword(s):  
Proof Theory ◽  
General Proof

scholarly journals FACETS OF INTENSIONALITY

ARHE ◽  
2021 ◽  
Vol 27 (34) ◽  
pp. 61-83
Author(s):  
KATARINA MAKSIMOVIĆ
Keyword(s):  
Proof Theory ◽  
Essential Role ◽  
Common Belief ◽  
Rule Based ◽  
General Proof ◽  
The Common

The goal of this paper is to introduce the reader to the distinction between intensional and extensional as a distinction between different approaches to meaning. We will argue that despite the common belief, intensional aspects of mathematical notions can be, and in fact have been successfully described in mathematics. One that is for us particularly interesting is the notion of deduction as depicted in general proof theory. Our considerations result in defending a) the importance of a rule-based semantical approach and b) the position according to which non-reductive and somewhat circular explanations play an essential role in describing intensionality in mathematics.

scholarly journals The Fundamental Problem of General Proof Theory

Studia Logica ◽  
2018 ◽  
Vol 107 (1) ◽  
pp. 11-29 ◽  
Author(s):  
Dag Prawitz
Keyword(s):  
Proof Theory ◽  
Fundamental Problem ◽  
General Proof

scholarly journals Reprint of: A more general general proof theory

2017 ◽  
Vol 25 ◽  
pp. S25-S47 ◽  
Author(s):  
Heinrich Wansing
Keyword(s):  
Proof Theory ◽  
General Proof

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

2002 ◽  
Vol 8 (2) ◽  
pp. 246-265 ◽  
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.

scholarly journals GÖDEL’S NOTRE DAME COURSE

2016 ◽  
Vol 22 (4) ◽  
pp. 469-481 ◽  
Author(s):  
MILOŠ ADŽIĆ ◽  
KOSTA DOŠEN
Keyword(s):  
Proof Theory ◽  
Natural Deduction ◽  
Deduction System ◽  
General Proof ◽  
Natural Deduction System ◽  
University Of Notre Dame ◽  
Proper Perspective ◽  
The University

AbstractThis is a companion to a paper by the authors entitled “Gödel’s natural deduction,” which presented and made comments about the natural deduction system in Gödel’s unpublished notes for the elementary logic course he gave at the University of Notre Dame in 1939. In that earlier paper, which was itself a companion to a paper that examined the links between some philosophical views ascribed to Gödel and general proof theory, one can find a brief summary of Gödel’s notes for the Notre Dame course. In order to put the earlier paper in proper perspective, a more complete summary of these interesting notes, with comments concerning them, is given here.

scholarly journals General Proof Theory: Introduction

Studia Logica ◽  
2018 ◽  
Vol 107 (1) ◽  
pp. 1-5 ◽  
Author(s):  
Thomas Piecha ◽  
Peter Schroeder-Heister
Keyword(s):  
Proof Theory ◽  
General Proof
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