Linearity and regularity with negation normal form

Proving completeness of NC-resolution under a linear restriction has been elusive; it is proved here for formulas in negation normal form. The proof uses a generalization of the Anderson–Bledsoe excess literal argument, which was developed for resolution. That result is extended to NC-resolution with partial replacement. A simple proof of the completeness of regular, connected tableaux for formulas in conjunctive normal form is also presented. These techniques are then used to establish the completeness of regular, connected tableaux for formulas in negation normal form.

Authors

• Reiner Hähnle
• Neil V. Murray Erik Rosenthal
• Erik Rosenthal

Keywords

• Automated theorem proving
• Negation normal form
• Resolution
• Linear resolution
• Non-clausal resolution
• Tableaux
• Regular tableaux
• Excess literal technique