Consistency of Variable Splitting in Free Variable Systems of First-Order Logic

Roger Antonsen and Arild Waaler

In Bernhard Beckert, editor, Automated Reasoning with Analytic Tableaux and Related Methods: 14th International Conference, TABLEAUX, Koblenz, Germany, volume 3702 of Lecture Notes in Computer Science, pages 33-47, Springer-Verlag, 2005.

http://dx.doi.org/10.1007/11554554_5

@InProceedings{AntonsenWaaler05,
  author =    {Roger Antonsen and Arild Waaler},
  title =     {Consistency of {V}ariable {S}plitting in {F}ree {V}ariable {S}ystems of {F}irst-{O}rder {L}ogic},
  booktitle = {Automated Reasoning with Analytic Tableaux and Related Methods: 14th International Conference, TABLEAUX, Koblenz, Germany},
  year =      2005,
  pages =     {33–47},
  series =    {Lecture Notes in Computer Science},
  editor =    {Bernhard Beckert},
  volume =    3702,
  isbn =      {3-540-28931-3},
  publisher = {Springer-Verlag},
  ee        = {http://dx.doi.org/10.1007/11554554_5}
}

Abstract

We prove consistency of a sequent calculus for classical logic with explicit splitting of free variables by means of a semantical soundness argument. The free variable system is a mature formulation of the system proposed at TABLEAUX 2003 [1]. We also identify some challenging and interesting open research problems.