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Automating Theories in Intuitionistic Logic
 in "7th International Symposium on Frontiers of Combining Systems FroCoS’09, Italie
"... Abstract. 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 socalled compatible theory. Conversely, given a firstorder theory, one may want to internalize it into a rewrite system t ..."
Abstract

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Abstract. 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 socalled compatible theory. Conversely, given a firstorder 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 corecursively 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. 1