The Deduction Theorem for Strong Propositional Proof Systems [chapter]

Olaf Beyersdorff
2007 Lecture Notes in Computer Science  
This paper focuses on the deduction theorem for propositional logic. We define and investigate different deduction properties and show that the presence of these deduction properties for strong proof systems is powerful enough to characterize the existence of optimal and even polynomially bounded proof systems. We also exhibit a similar, but apparently weaker condition that implies the existence of complete disjoint NP-pairs. In particular, this yields a sufficient condition for the
more » ... of the canonical pair of Frege systems and provides a general framework for the search for complete NP-pairs.
doi:10.1007/978-3-540-77050-3_20 fatcat:2b7dlniphnfv3ofvduq62i3tce