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PreprintCC BY 4.0arXiv

A Kleene-inspired sequent system for a minimal logic of evidence and truth

  • Nino Grandinetti
  • Abilio Rodrigues
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Abstract

This paper investigates the proof theory of the logic of evidence and truth LETFm, with the aim of obtaining a sequent calculus consisting only of logical rules, suitable for a simple bottom-up decision procedure. We begin with G1f, a sequent system containing structural rules, which makes explicit the main difficulties in obtaining a fully logical and decidable calculus for LETFm. We then introduce G3f, a G3-style system obtained from by applying Kleene's trick, which absorbs contraction into the logical rules by adding the principal formula of the rule to its premises.

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Cite

BibTeXRIS
BibTeX
@misc{grandinetti2026kleeneinspired,
  title = {{A Kleene-inspired sequent system for a minimal logic of evidence and truth}},
  author = {Nino Grandinetti and Abilio Rodrigues},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24203},
  eprint = {2610.24203},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24203},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Kleene-inspired sequent system for a minimal logic of evidence and truth
AU  - Nino Grandinetti
AU  - Abilio Rodrigues
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.24203
UR  - https://arxiv.org/abs/2610.24203
AB  - This paper investigates the proof theory of the logic of evidence and truth LETFm, with the aim of obtaining a sequent calculus consisting only of logical rules, suitable for a simple bottom-up decision procedure. We begin with G1f, a sequent system containing structural rules, which makes explicit the main difficulties in obtaining a fully logical and decidable calculus for LETFm. We then introduce G3f, a G3-style system obtained from by applying Kleene's trick, which absorbs contraction into the logical rules by adding the principal formula of the rule to its premises.
ER  -