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1 results

  • 4 - Classical and Intuitionistic Logics

  • Dale Miller, INRIA Saclay-Île-de-France
  • Book:
    Proof Theory and Logic Programming
    Published online:
    01 December 2025
    Print publication:
    18 December 2025, pp 37-60

  • Summary

    This chapter presents sequent calculus proof systems for classical and intuitionistic logics, which are variations of Gentzen’s LK and LJ proof systems. It highlights the differences in their inference rules, particularly regarding the right-hand side of sequents. The chapter discusses the cut-elimination theorem for these logics and its significance. It also explores the increase in proof size that can result from eliminating cuts. Furthermore, the chapter considers the choices involved in proof search within these systems, distinguishing between don’t-know and don’t-care nondeterminism. Bibliographic notes direct the reader to relevant historical and contemporary works.