On the Herbrand content of LK
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چکیده
We present a structural representation of the Herbrand content of LK-proofs with cuts of complexity prenex Π2/Σ2. The representation takes the form of a typed non-deterministic tree grammar G of order 2 which generates a finite language, L(G ), of first-order terms that appear in the Herbrand expansions obtained through cut-elimination. In particular, for every Gentzen-style reduction π π ′ between LK-proofs we study the induced grammars, respectively G and G ′, and classify the cases in which language equality, L(G ) = L(G ′), and language inclusion, L(G )⊇ L(G ′), hold.
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تاریخ انتشار 2016