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# Expansion Tree Proofs and Their Conversion to Natural Deduction Proofs

@inproceedings{Miller1984ExpansionTP, title={Expansion Tree Proofs and Their Conversion to Natural Deduction Proofs}, author={Dale Miller}, booktitle={CADE}, year={1984} }

- Published 1984 in CADE
DOI:10.1007/978-0-387-34768-4_22

We present a new form of Herbrand's theorem which is centered around structures called expansion trees. Such trees contains substitution formulas and selected (critical) variables at various non-terminal nodes. These trees encode a shallow formula and a deep formula the latter containing the formulas which label the terminal nodes of the expansion tree. If a certain relation among the selected variables of an expansion tree is acyclic and if the deep formula of the tree is tautologous, then we… CONTINUE READING

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