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1 results

  • 7 - Formal Properties of Linear Logic Focused Proofs

  • Dale Miller, INRIA Saclay-Île-de-France
  • Book:
    Proof Theory and Logic Programming
    Published online:
    01 December 2025
    Print publication:
    18 December 2025, pp 143-171

  • Summary

    This chapter delves into the formal proof theory of linear logic focused proofs. It defines paths in linear logic formulas, using them to describe right-introduction and left-introduction phases. The chapter proves the admissibility of the non-atomic initial rule and demonstrates the elimination of cut rules in the focused system for linear logic. Finally, it establishes the completeness of the focused proof system with respect to the unfocused proof system for linear logic. Readers primarily interested in the applications of linear logic programming can skip this chapter.