Journal of Philosophical Logic

, Volume 48, Issue 6, pp 1119–1144 | Cite as

Negation on the Australian Plan

  • Francesco BertoEmail author
  • Greg Restall
Open Access


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.


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



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Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of St AndrewsSt AndrewsUK
  2. 2.Institute for Logic, Language and Computation (ILLC)University of AmsterdamAmsterdamThe Netherlands
  3. 3.Department of PhilosophyUniversity of MelbourneMelbourneAustralia

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