Notre Dame Journal of Formal Logic

Classical Negation and Game-Theoretical Semantics

Tero Tulenheimo

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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.

Article information

Source
Notre Dame J. Formal Logic, Volume 55, Number 4 (2014), 469-498.

Dates
First available in Project Euclid: 7 November 2014

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1415382952

Digital Object Identifier
doi:10.1215/00294527-2798709

Mathematical Reviews number (MathSciNet)
MR3276408

Zentralblatt MATH identifier
1342.03030

Subjects
Primary: 03B60: Other nonclassical logic 03C80: Logic with extra quantifiers and operators [See also 03B42, 03B44, 03B45, 03B48]
Secondary: 03B15: Higher-order logic and type theory

Keywords
game-theoretical semantics higher-order logic independence-friendly logic negation

Citation

Tulenheimo, Tero. Classical Negation and Game-Theoretical Semantics. Notre Dame J. Formal Logic 55 (2014), no. 4, 469--498. doi:10.1215/00294527-2798709. https://projecteuclid.org/euclid.ndjfl/1415382952


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