Negation on the Australian plan. (English) Zbl 1457.03007
Summary: 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.
MSC:
| 03A05 | Philosophical and critical aspects of logic and foundations |
| 03B45 | Modal logic (including the logic of norms) |
| 03B50 | Many-valued logic |
| 03B47 | Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) |
Keywords:
negation; compatibility semantics; Kripke semantics; non-classical logics; many-valued logics; modal logicsReferences:
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