Reduction and unification in (typed) natural language ontology
Kristina Liefke
Natural language semantics uses many different kinds of objects, incl. individuals, prop- ositions, properties, situations, events, and kinds. Simple type theories tame this ‘zoo’ [1] by assuming only a small number of primitive objects (e.g. individuals, situations), and obtaining all other objects via constructions out of these primitives. By distinguishing subtypes (or sorts), these theories straightforwardly obtain more finely-grained types (e.g. concrete vs. abstract individuals), allowing them to explain selectional restrictions (e.g. eat \(\{^{\checkmark}\) an apple, \(^{\#}\)an opinion\(\}\)) (i). However, this strategy blocks an easy account of selectional flexibility (i.e. why some predicates accept different-type arguments; e.g. remember \(\{\)the girl, that she was dancing\(\}\)) (ii) and of semantic relations bet- ween such arguments (e.g. why remember that she \(\ldots\) entails remember the girl) (iii).
My talk answers this challenge by unifying intuitively distinct types in a single higher-rank type, whose objects code the lower-type objects (see [2-4]). This unification allows the same-type interpretation of expressions from different grammatical categories, immediately explaining (ii) and – through the internal structure of the new objects – (iii). Selectional restrictions (see (i)) are explained through the particular lexical semantics of the embedding predicate and its interaction with the new, higher-type object.
Bibliography
- Emmon Bach, Natural language metaphysics, Logic, Methodology and Philosophy of Science VII (Ruth Barcan Marcus, editor), Elsevier, 1986, pp. 573–593.
- Kristina Liefke, Modelling selectional super-flexibility, Semantics and Linguistic Theory, vol. 31 (2021), pp. 324–344.
- Kristina Liefke and Markus Werning, Evidence for single-type semantics, Journal of Semantics, vol. 35 (2018), no. 4, pp. 639–685.
- Nadine Theiler, Floris Roelofsen, and Maria Aloni, A uniform semantics for declarative and interrogative complements, Journal of Semantics, vol. 35 (2018), no. 3, pp. 409–466.