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Negation on the Australian Plan


We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities between such points. We defuse a number of objections to this Plan, raised by supporters of the American Plan for negation, in which negation is handled via a many-valued semantics. We show that the Australian Plan has substantial advantages over the American Plan.


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Correspondence to Francesco Berto.

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Berto, F., Restall, G. Negation on the Australian Plan. J Philos Logic 48, 1119–1144 (2019).

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  • Negation
  • Compatibility semantics
  • Kripke semantics
  • Non-classical logics
  • Many-valued logics
  • Modal logics