Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 55, Number 4 (2014), 469-498.
Classical Negation and Game-Theoretical Semantics
Typical applications of Hintikka’s game-theoretical semantics (GTS) give rise to semantic attributes—truth, falsity—expressible in the -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, and , 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 extends independence-friendly (IF) logic; behaves as classical negation in . Logic extends , and it is shown to capture the -fragment of third-order logic. Consequently the classical negation remains inexpressible in .
Notre Dame J. Formal Logic, Volume 55, Number 4 (2014), 469-498.
First available in Project Euclid: 7 November 2014
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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