Logic for computer science: foundations of automatic theorem proving
Logic for computer science: foundations of automatic theorem proving
Completion for rewriting modulo a congruence
on Rewriting techniques and applications
Proofs and types
Term rewriting and all that
A short introduction to intuitionistic logic
A short introduction to intuitionistic logic
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Journal of Automated Reasoning
HOL-λσ: an intentional first-order expression of higher-order logic
Mathematical Structures in Computer Science
The ILTP Problem Library for Intuitionistic Logic
Journal of Automated Reasoning
A First-Order Representation of Pure Type Systems Using Superdeduction
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
Confluence as a cut elimination property
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
On constructive cut admissibility in deduction modulo
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
A finite first-order theory of classes
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Semantic cut elimination in the intuitionistic sequent calculus
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
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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 compatible theory. Conversely, given a first-order theory, one may want to internalize it into a rewrite system that can be used in deduction modulo, in order to get an analytic deductive system for that theory. In a recent paper, we have shown how this can be done in classical logic. In intuitionistic logic, however, we show here not only that this may be impossible, but also that the set of theories that can be transformed into a rewrite system with an analytic sequent calculus modulo is not co-recursively enumerable. We nonetheless propose a procedure to transform a large class of theories into compatible rewrite systems. We then extend this class by working in conservative extensions, in particular using Skolemization.