If knowledge representation formalisms are to be suitable for semantic interpretation of natural language, they must be more adept with representations of existence and non-existence than they presently are. Quantifiers must sometimes range over non-existent entities. I review the philosophical background, including Anselm and Kant, and exhibit some ontological problems that natural language sentences pose for knowledge representation. The paraphrase methods of Russell and Quine are unable to deal with many of the problems.
Unfortunately, the shortcomings of the Russell--Quine ontology are reflected in most current knowledge representation formalisms in AI. Several alternatives are considered, including some intensional formalisms and the work of Hobbs, but all have problems. Free logics and possible worlds don't help either. But useful insights are found in the Meinongian theory of Parsons, in which a distinction between nuclear and extranuclear kinds of predicates is made and used to define a universe over which quantification ranges. If this is combined with a naive ontology, with about eight distinct kinds of existence, a better approach to the representation of non-existence can be developed within Hobbs's basic formalism.
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