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IANDC
2010
141views more  IANDC 2010»
8 years 9 months ago
Regaining cut admissibility in deduction modulo using abstract completion
stract Completion Guillaume Burel a,c,∗ Claude Kirchner b,c aNancy-Universit´e, Universit´e Henri Poincar´e bINRIA Bordeaux - Sud-Ouest cLORIA, ´Equipe Pareo, Bˆatiment B, C...
Guillaume Burel, Claude Kirchner
CORR
2008
Springer
148views Education» more  CORR 2008»
8 years 9 months ago
Efficiently Simulating Higher-Order Arithmetic by a First-Order Theory Modulo
In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems--such as for ...
Guillaume Burel
TYPES
1998
Springer
9 years 2 months ago
Proof Normalization Modulo
We define a generic notion of cut that applies to many first-order theories. We prove a generic cut elimination theorem showing that the cut elimination property holds for all theo...
Gilles Dowek, Benjamin Werner
RTA
2005
Springer
9 years 3 months ago
Arithmetic as a Theory Modulo
We present constructive arithmetic in Deduction modulo with rewrite rules only. In natural deduction and in sequent calculus, the cut elimination theorem and the analysis of the st...
Gilles Dowek, Benjamin Werner
TLCA
2007
Springer
9 years 4 months ago
Embedding Pure Type Systems in the Lambda-Pi-Calculus Modulo
The lambda-Pi-calculus allows to express proofs of minimal predicate logic. It can be extended, in a very simple way, by adding computation rules. This leads to the lambda-Pi-calcu...
Denis Cousineau 0002, Gilles Dowek
LFCS
2007
Springer
9 years 4 months ago
Cut Elimination in Deduction Modulo by Abstract Completion
act Completion (Full Version) Guillaume Burel Claude Kirchner August 6, 2007 Deduction Modulo implements Poincar´e’s principle by identifying deduction and computation as diff...
Guillaume Burel, Claude Kirchner
LICS
2007
IEEE
9 years 4 months ago
Principles of Superdeduction
In predicate logic, the proof that a theorem P holds in a theory Th is typically conducted in natural deduction or in the sequent calculus using all the information contained in t...
Paul Brauner, Clément Houtmann, Claude Kirc...
FROCOS
2009
Springer
9 years 4 months ago
Automating Theories in Intuitionistic Logic
Deduction modulo consists in applying the inference rules of a deductive system modulo a rewrite system over terms and formulæ. This is equivalent to proving within a so-called co...
Guillaume Burel
CADE
2004
Springer
9 years 10 months ago
TaMeD: A Tableau Method for Deduction Modulo
Deduction modulo is a theoretical framework for reasoning modulo a congruence on propositions. Computational steps are thus removed from proofs, thus allowing a clean separatation...
Richard Bonichon
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