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Proof Schemata for Theories equivalent to : on the Benefit of Conservative Reflection Principles
Induction is typically formalized as a rule or axiom extension of the
LK-calculus. While this extension of the sequent calculus is simple and
elegant, proof transformation and analysis can be quite difficult. Theories
with an induction rule, for example Peano arithmetic do not have a {\em
Herbrand} theorem. In this work we extend an existing meta-theoretic formalism,
so called proof schemata, a recursive formulation of induction particularly
suited for proof analysis, to Peano arithmetic. This relationship provides a
meaningful conservative reflection principle between \PA and an alternative
proof formalism. Proof schemata have been shown to have a variant of Herbrand's
theorem for classical logic which can be lifted to the subsystem of our new
formalism equivalent to primitive recursive arithmetic.Comment: This is a preprint of an articl