Paper Info
Title
Classical Negation and Game-Theoretical Semantics.
Abstract
Typical applications of Hintikka's game-theoretical semantics (GTS) give rise to semantic attributes-truth, falsity-expressible in the Sigma(1)(1)-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, L-1 and L-2, in both of which two negation signs are available: -> and similar to. The latter is the usual GTS negation which transposes the players' roles, while the former will be interpreted via the notion of mode. Logic L-1 extends independence-friendly (IF) logic; -> behaves as classical negation in L-1. Logic L-2 extends L-1, and it is shown to capture the Sigma(2)(1)-fragment of third-order logic. Consequently the classical negation remains inexpressible in L-2.
Year
DOI
Venue
2014
10.1215/00294527-2798709
NOTRE DAME JOURNAL OF FORMAL LOGIC
Keywords
Field
DocType
game-theoretical semantics,higher-order logic,independence-friendly logic,negation
Discrete mathematics,Negation normal form,Negation,Algorithm,Negation introduction,Negation as failure,Classical logic,Stable model semantics,Game semantics,Well-founded semantics,Mathematics
Journal
Volume
Issue
ISSN
55
4
0029-4527
Citations 
PageRank 
References 
0
0.34
5
Authors
1
Name
Order
Citations
PageRank
Tero Tulenheimo1165.19