Hintikka’s independence-friendly logic meets Nelson’s realizability

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Hintikka’s independence-friendly logic meets Nelson’s realizability. / Odintsov, Sergei P.; Speranski, Stanislav O.; Shevchenko, Igor Yu.

In: Studia Logica, Vol. 106, No. 3, 01.06.2018, p. 637–670.

Research output: Contribution to journal › Article › peer-review

Author

Odintsov, Sergei P. ; Speranski, Stanislav O. ; Shevchenko, Igor Yu. / Hintikka’s independence-friendly logic meets Nelson’s realizability. In: Studia Logica. 2018 ; Vol. 106, No. 3. pp. 637–670.

BibTeX

@article{e887a0ecd8e64b57afe5bd783b72a8c9,

title = "Hintikka{\textquoteright}s independence-friendly logic meets Nelson{\textquoteright}s realizability",

abstract = "Inspired by Hintikka{\textquoteright}s ideas on constructivism, we are going to {\textquoteleft}effectivize{\textquoteright} 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 {\textquoteleft}The Principles of Mathematics Revisited{\textquoteright}. First we show that Nelson{\textquoteright}s realizability interpretation—which extends the famous Kleene{\textquoteright}s realizability interpretation by adding {\textquoteleft}strong negation{\textquoteright}—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 {\textquoteleft}trump semantics{\textquoteright} 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{\textquoteright}s restricted realizability interpretation for the implication-free first-order formulas.",

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

author = "Odintsov, {Sergei P.} and Speranski, {Stanislav O.} and Shevchenko, {Igor Yu.}",

note = "Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media B.V.",

year = "2018",

month = jun,

day = "1",

doi = "10.1007/s11225-017-9760-x",

language = "English",

volume = "106",

pages = "637–670",

journal = "Studia Logica",

issn = "0039-3215",

publisher = "Springer Nature",

number = "3",

}

RIS

TY - JOUR

T1 - Hintikka’s independence-friendly logic meets Nelson’s realizability

AU - Odintsov, Sergei P.

AU - Speranski, Stanislav O.

AU - Shevchenko, Igor Yu.

PY - 2018/6/1

Y1 - 2018/6/1

N2 - 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.

AB - 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.

KW - independence-friendly logic

KW - game-theoretic semantics

KW - trump semantics

KW - constructivism

KW - realizability

KW - strong negation

KW - Strong negation

KW - Game-theoretic semantics

KW - Independence-friendly logic

KW - Trump semantics

KW - Constructivism

KW - Realizability

UR - http://www.scopus.com/inward/record.url?scp=85031416462&partnerID=8YFLogxK

U2 - 10.1007/s11225-017-9760-x

DO - 10.1007/s11225-017-9760-x

M3 - Article

VL - 106

SP - 637

EP - 670

JO - Studia Logica

JF - Studia Logica

SN - 0039-3215

IS - 3

ER -

ID: 10084465