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Advances in Proof Theory

Philology, 2016
The aim of this volume is to collect original contributions by the best specialists from the area of proof theory, constructivity, and computation and discuss recent trends and results in these areas.
Kahle, Reinhard, Studer, Thomas, Strahm, Thomas   +2 more
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Proof Theory: Sequent Calculi and Related Formalisms

, 2014
K. Bimbó
semanticscholar   +2 more sources

A theory of classes: proofs and models

Mathematical Structures in Computer Science, 1997
We investigate the proof structure and models of theories of classes, where classes are ‘collections’ of entities. The theories are weaker than set theories and arise from a study of type classes in programming languages, as well as from comprehension schemata in categories. We introduce two languages of proofs: one a simple type theory and the
Hilken, Barney P, Rydeheard, David E
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Theories and Ordinals in Proof Theory

Synthese, 2006
The author gives a very good survey on the aims and techniques of ordinal analysis. It includes not only the classical topics of subsystems of second-order arithmetic and of set theory, but also newer developments in relation to model-theoretic characterizations (partial models and patterns of resemblance; Sec.~4), characterizations via \(E\)-recursion
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Proof Theories for Semilattice Logics

Mathematical Logic Quarterly, 1987
This paper presents original results which unify much of the research on the semilattice relevant logics \({}^ uT_ +\), \({}^ uR_ +\), \({}^ uTW_ +\), \({}^ uRW_ +\) introduced by \textit{A. Urquhart} [The semantics of entailment (University of Pittsburgh Doctoral Dissertation) (1973); J. Symb.
Steve Giambrone, Alasdair Urquhart
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Proof Theory of Constructive Systems: Inductive Types and Univalence

, 2016
In Feferman’s work, explicit mathematics and theories of generalized inductive definitions play a central role. One objective of this article is to describe the connections with Martin–Lof type theory and constructive Zermelo–Fraenkel set theory.
M. Rathjen
semanticscholar   +1 more source

The Knowledge Complexity of Interactive Proof Systems

SIAM journal on computing (Print), 1989
Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the ...
S. Goldwasser, S. Micali, C. Rackoff
semanticscholar   +1 more source

Proof Theory

, 1989
Although this is an introductory text on proof theory, most of its contents is not found in a unified form elsewhere in the literature, except at a very advanced level.
Pohlers, Wolfram
core   +3 more sources

A survey of proof theory

Journal of Symbolic Logic, 1968
One might fairly say that the very meaning of our subject has changed since Hilbert introduced it under the name Beweistheorie (it was meant to be the principal tool for formulating Hubert's general conception of how to analyze mathematical reasoning).
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Basic Proof Theory

2000
This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category ...
Troelstra, A.S., Schwichtenberg, H.
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