Proof Systems for Effectively Propositional Logic

  • Authors:
  • Juan Antonio Navarro;Andrei Voronkov

  • Affiliations:
  • Max Planck Institute for Software Systems,;The University of Manchester,

  • Venue:
  • IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
  • Year:
  • 2008

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Abstract

We consider proof systems for effectively propositional logic. First, we show that propositional resolution for effectively propositional logic may have exponentially longer refutations than resolution for this logic. This shows that methods based on ground instantiation may be weaker than non-ground methods. Second, we introduce a generalisation rule for effectively propositional logic and show that resolution for this logic may have exponentially longer proofs than resolution with generalisation. We also discuss some related questions, such as sort assignments for generalisation.