Inspired by Hintikka’s ideas on constructivism, we are going to ‘effectivize’ the game-theoretic semantics (abbreviated GTS) for independence-friendly first-order logic (IF-FOL), but in a somewhat different way than he did in the monograph ‘The Principles of Mathematics Revisited’. First we show that Nelson’s realizability interpretation—which extends the famous Kleene’s realizability interpretation by adding ‘strong negation’—restricted to the implication-free first-order formulas can be viewed as an effective version of GTS for FOL. Then we propose a realizability interpretation for IF-FOL, inspired by the so-called ‘trump semantics’ which was discovered by Hodges, and show that this trump realizability interpretation can be viewed as an effective version of GTS for IF-FOL. Finally we prove that the trump realizability interpretation for IF-FOL appropriately generalises Nelson’s restricted realizability interpretation for the implication-free first-order formulas.
Original languageEnglish
Pages (from-to)637–670
Number of pages34
JournalStudia Logica
Volume106
Issue number3
DOIs
StatePublished - 1 Jun 2018

    Scopus subject areas

  • Logic
  • History and Philosophy of Science

    Research areas

  • independence-friendly logic, game-theoretic semantics, trump semantics, constructivism, realizability, strong negation, Strong negation, Game-theoretic semantics, Independence-friendly logic, Trump semantics, Constructivism, Realizability

ID: 10084465