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2014 Classical Negation and Game-Theoretical Semantics
Tero Tulenheimo
Notre Dame J. Formal Logic 55(4): 469-498 (2014). DOI: 10.1215/00294527-2798709

Abstract

Typical applications of Hintikka’s game-theoretical semantics (GTS) give rise to semantic attributes—truth, falsity—expressible in the Σ11-fragment of second-order logic. Actually a much more general notion of semantic attribute is motivated by strategic considerations. When identifying such a generalization, the notion of classical negation plays a crucial role. We study two languages, L1 and L2, in both of which two negation signs are available: and . The latter is the usual GTS negation which transposes the players’ roles, while the former will be interpreted via the notion of mode. Logic L1 extends independence-friendly (IF) logic; behaves as classical negation in L1. Logic L2 extends L1, and it is shown to capture the Σ12-fragment of third-order logic. Consequently the classical negation remains inexpressible in L2.

Citation

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Tero Tulenheimo. "Classical Negation and Game-Theoretical Semantics." Notre Dame J. Formal Logic 55 (4) 469 - 498, 2014. https://doi.org/10.1215/00294527-2798709

Information

Published: 2014
First available in Project Euclid: 7 November 2014

zbMATH: 1342.03030
MathSciNet: MR3276408
Digital Object Identifier: 10.1215/00294527-2798709

Subjects:
Primary: 03B60, 03C80
Secondary: 03B15

Rights: Copyright © 2014 University of Notre Dame

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Vol.55 • No. 4 • 2014
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