Negation in logic and in natural language

Linguistics and Philosophy 25 (5-6):585-600 (2002)
Abstract
In game-theoretical semantics, perfectlyclassical rules yield a strong negation thatviolates tertium non datur when informationalindependence is allowed. Contradictorynegation can be introduced only by a metalogicalstipulation, not by game rules. Accordingly, it mayoccur (without further stipulations) onlysentence-initially. The resulting logic (extendedindependence-friendly logic) explains several regularitiesin natural languages, e.g., why contradictory negation is abarrier to anaphase. In natural language, contradictory negationsometimes occurs nevertheless witin the scope of aquantifier. Such sentences require a secondary interpretationresembling the so-called substitutionalinterpretation of quantifiers.This interpretation is sometimes impossible,and it means a step beyond thenormal first-order semantics, not an alternative to it.
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    Jaakko Hintikka (2004). Independence-Friendly Logic and Axiomatic Set Theory. Annals of Pure and Applied Logic 126 (1-3):313-333.
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