Tech Report CS-90-37

CI2 --- A Logic for Plural Representation

Felix Yen

December 1990


The problem we address is the representation of plurals. The solution we present is CI2, a first-order logic named after the {\em calculus of individuals}. (If one thinks of individuals as being sets, then CI2 is just the calculus of individuals with numbers added.) In CI2, plurals are represented with terms denoting sets. (Singulars are represented with terms denoting unit sets.)

We are primarily concerned with the problem of representing ambiguous sentences and making inferences from them. Our solution involves using a "new" but simple ontology as well as special classes of functions which we describe. The result is a theory that enables us to disambiguate sentences incrementally. We also describe a CI2-specific theorem prover (fully implemented) that uses several techniques that may be of use to those interested in developing systems that can reason about sets.

We demonstrate the viability of our theory by presenting representations for twelve ambiguous, plural sentences. We show how each sentence can be disambiguated and how the desired inferences were computed by our theorem prover. Our dissertation concludes by addressing the problem of modifying existing programs so that they can manipulate plural entities. This is not trivial modification as it entails solving the closure problem, i.e. making closure assumptions. We present a promising approach in which closure assumptions are made only when needed.

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