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Paper detail

On the Herbrand content of LK

We present a structural representation of the Herbrand content of LK-proofs with cuts of complexity prenex Sigma-2/Pi-2. The representation takes the form of a typed non-deterministic tree grammar of order 2 which generates a finite language of first-order terms that appear in the Herbrand expansions obtained through cut-elimination. In particular, for every Gentzen-style reduction between LK-proofs we study the induced grammars and classify the cases in which language equality and inclusion hold.

preprint2016arXivOpen access
Bahareh AfshariStefan HetzlGraham E. Leigh
Logic in Computer Sciencemath.LOFormal Languages and Automata Theory
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Bahareh AfshariStefan HetzlGraham E. Leigh

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