Proof Normalization Modulo

Authors:
Gilles Dowek;Benjamin Werner
Affiliations:
-;-
Venue:
TYPES '98 Selected papers from the International Workshop on Types for Proofs and Programs
Year:
1998

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Abstract

We consider a class of logical formalisms, in which first-order logic is extended by identifying propositions modulo a given congruence. We particularly focus on the case where this congruence is induced by a confluent and terminating rewrite system over the propositions. We show that this extension enhances the power of first-order logic and that various formalisms, including Church's higher-order logic (HOL) can be described in our framework. We conjecture that proof normalization and logical consistency always hold over this class of formalisms, provided some minimal conditions over the rewrite system are fulfilled. We prove this conjecture for some subcases, including HOL.