Publication

A Free Variable Sequent Calculus with Uniform Variable Splitting

Arild Waaler and Roger Antonsen
In Automated Reasoning with Analytic Tableaux and Related Methods: International Conference, TABLEAUX, Rome, Italy, Lecture Notes in Computer Science, volume 2796, pages 214–229, Springer-Verlag, 2003.
@InProceedings{WaalerAntonsen03,
  author =    {Arild Waaler and Roger Antonsen},
  title =     {A {F}ree {V}ariable {S}equent {C}alculus with {U}niform {V}ariable {S}plitting},
  booktitle = {Automated Reasoning with Analytic Tableaux and Related Methods: International Conference, TABLEAUX, Rome, Italy},
  year =      2003,
  pages =     {214–229},
  series =    {Lecture Notes in Computer Science},
  number =    2796,
  publisher = {Springer-Verlag},
  ee        = {http://dx.doi.org/10.1007/978-3-540-45206-5_17}
}	  

Abstract

A system with variable splitting is introduced for a sequent calculus with free variables and run-time Skolemization. Derivations in the system are invariant under permutation, so that the order in which rules are applied has no effect on the leaves. Technically this is achieved by means of a simple indexing system for formulae, variables and Skolem functions. Moreover, the way in which variables are split enables us to restrict the term universe branchwise.