IKT! and Łukasiewicz-models

Andreas Fjellstad, Jan Fredrik Olsen

Research output: Contribution to journalArticlepeer-review

2 Citations (SciVal)

Abstract

In this note, we show that the first-order logic IK! is sound with regard to the models obtained from continuum-valued Łukasiewicz-models for first-order languages by treating the quantifiers as infinitary strong disjunction/conjunction rather than infinitary weak disjunction/conjunction. Moreover, we show that these models cannot be used to provide a new consistency proof for the theory of truth IKT! obtained by expanding IK! with transparent truth, because the models are inconsistent with transparent truth. Finally, we show that whether or not this inconsistency can be reproduced in the sequent calculus for IKT! depends on how vacuous quantification is treated.

Original languageEnglish
Pages (from-to)247-256
Number of pages10
JournalNotre Dame Journal of Formal Logic
Volume62
Issue number2
DOIs
Publication statusPublished - 2021 May

Subject classification (UKÄ)

  • Probability Theory and Statistics

Keywords

  • !-inconsistency
  • Inconsistency
  • Infinitary sequents
  • Multiplicative quantifiers
  • Non-contractive truth
  • Soundness
  • Vacuous quantification

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