Hintikka’s Independence-Friendly Logic Meets Nelson’s Realizability

Studia Logica 106 (3):637-670 (2018)
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Abstract

Inspired by Hintikka’s ideas on constructivism, we are going to ‘effectivize’ the game-theoretic semantics for independence-friendly first-order logic, 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.

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Citations of this work

HYPE: A System of Hyperintensional Logic.Hannes Leitgeb - 2019 - Journal of Philosophical Logic 48 (2):305-405.

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References found in this work

Constructible falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.
Compositional semantics for a language of imperfect information.W. Hodges - 1997 - Logic Journal of the IGPL 5 (4):539-563.
Finite partially-ordered quantification.Wilbur John Walkoe Jr - 1970 - Journal of Symbolic Logic 35 (4):535-555.
Finite Partially‐Ordered Quantifiers.Herbert B. Enderton - 1970 - Mathematical Logic Quarterly 16 (8):393-397.
From if to bi.Samson Abramsky & Jouko Väänänen - 2009 - Synthese 167 (2):207 - 230.

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