A proof environment for arithmetic with the omega rule

  • Siani Baker
  • Alan Smaill
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 958)


An important technique for investigating derivability in formal systems of arithmetic has been to embed such systems into semiformal systems with the Ω-rule. This paper exploits this notion within the domain of automated theorem-proving and discusses the implementation of such a proof environment, namely the CORE system which implements a version of the primitive recursive Ω-rule. This involves providing an appropriate representation for infinite proofs, and a means of verifying properties of such objects. By means of the CORE system, from a finite number of instances a conjecture for a proof of the universally quantified formula is automatically derived by an inductive inference algorithm, and checked for correctness. In addition, candidates for cut formulae may be generated by an explanation-based learning algorithm. This is an alternative approach to reasoning about inductively defined domains from traditional structural induction, which may sometimes be more intuitive.


Proof Theory Rule Application Proof Tree Peano Arithmetic Automate Deduction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Siani Baker
    • 1
  • Alan Smaill
    • 2
  1. 1.Cambridge UniversityCambridgeUK
  2. 2.Edinburgh UniversityEdinburghUK

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