About effective versions of game theoretical semantics for first-order logic
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 618-637
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In the article we compare two approaches to effectivisation of game theoretical semantics for first-order logic. One of the approaches was provided by Sergey P. Odintsov, Stanislav O. Speranski, Igor Yu. Shevchenko in the previous article, and it is based on a game-theoretical reconstruction of strategy conception. In this article we provide the other approach — we consider a strategy as a function determined on a set of histories and then we set an equivalence between these two approaches.
Keywords:
game theoretical semantics, Nelson's realizability, computability.
@article{SEMR_2019_16_a9,
author = {I. Yu. Shevchenko},
title = {About effective versions of game theoretical semantics for first-order logic},
journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
pages = {618--637},
year = {2019},
volume = {16},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a9/}
}
I. Yu. Shevchenko. About effective versions of game theoretical semantics for first-order logic. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 618-637. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a9/
[1] J. Hintikka, The Principles of Mathematics Revisited, Cambridge University Press, Cambridge, 1996 | MR | Zbl
[2] D. Nelson, “Constructible falsity”, Journal of Symbolic Logic, 14:1 (1949), 16–26 | DOI | MR | Zbl
[3] S. P. Odintsov, S. O. Speranski, I. Yu. Shevchenko, “Hintikka's independence-friendly logic meets Nelson's realizability”, Studia Logica (First Online: 14.10.2017) | MR
[4] M. J. Osborne, A. Rubinstein, A Course in Game Theory, MIT Press, Cambridge, Massachusetts, 1994 | MR | Zbl
[5] A. L. Mann, G. Sandu, M. Sevenster, Independence-Friendly Logic. A game-theoretic approach, Cambridge University Press, Cambridge, 2011 | MR | Zbl