A Note on Ontology and Ordinary Language

We argue for a compositional semantics grounded in a strongly typed ontology that reflects our commonsense view of the world and the way we talk about it. Assuming such a structure we show that the semantics of various natural language phenomena may become nearly trivial.

💡 Research Summary

The paper “A Note on Ontology and Ordinary Language” argues that many of the difficulties encountered in natural‑language semantics stem from a mismatch between the impoverished ontological commitments of standard formal semantic frameworks and the rich, commonsense structure of the world that ordinary language presupposes. To bridge this gap the author proposes a compositional semantics that is grounded in a strongly typed ontology—a hierarchy of types (entity, animal, human, artifact, etc.) that mirrors our everyday conceptualization of reality.

The core idea is to annotate every variable in a logical form with a type, using the notation x :: t. Predicates and properties are then restricted to the types they normally apply to (e.g., Articulate(x :: human), Hungry(x :: animal)). Proper names are treated as constants that instantiate an entity of a given type. Equality (Is(x, y)) and identity statements are handled by unifying the types of the two terms involved.

A central technical contribution is the type‑unification operation, denoted s • t. When a single variable is assigned multiple types within the same scope, the system computes the least upper bound (lub) of those types in the subsumption hierarchy. If one type subsumes the other (e.g., human ⊑ entity), the result is the more specific type (human). The operation is associative and commutative, allowing unification in any order. The paper demonstrates this mechanism with simple examples such as “Sheba is hungry” (unifying entity and animal to animal) and “Sheba is a young artist” (unifying entity, human, and the second‑intension concepts Artist and Young). The latter illustrates the distinction between first‑intension ontological concepts (e.g., human) that are essential and second‑intension logical concepts (e.g., Artist, Young) that are accidental, context‑dependent, and definable by logical formulas.

The author then tackles nominal compounds. By embedding ontological sorts into the predicates that represent the compounds, the semantics of phrases such as “book review” and “book proposal” become straightforward. A “book review” is interpreted as an activity (ReviewOf) whose object must be an existing book; a “book proposal” is a ProposalFor a book that may not yet exist. The paper provides template compositional functions for several compound patterns and shows how type unification either succeeds (producing a coherent interpretation) or fails (as in the implausible phrase “artificial car”, where Artificial expects a naturalObj while car is an artifact).

A further contribution is the explicit handling of abstract vs. actual existence. Certain predicates (e.g., Imminent) are only meaningful when applied to events that have not yet occurred; such events are initially assigned an abstract existence type. When additional information (e.g., “the event was lengthy”) is introduced, the event can be “brought down” to actual existence. The paper illustrates this with sentences like “John attended the seminar” (both the human and the seminar are actual entities) versus “John cancelled the seminar” (the seminar may be merely a planned event that never materialized). Similarly, planning verbs (Plan) are shown to permit their event arguments to remain abstract unless contextual cues force them to be concrete.

The treatment of identity statements (e.g., “William H. Bonney is Billy the Kid”) demonstrates that unifying the types of the two names yields a richer semantic contribution than a trivial reflexive identity (“William H. Bonney is William H. Bonney”), because the former links two distinct descriptors to a single underlying entity.

The paper acknowledges that type unification can fail when no ontological relationship exists between the assigned types, and such failures correspond to intuitively odd or nonsensical phrases. These failures can be caught at the logical level, preserving the overall robustness of the approach.

In summary, by integrating a richly structured, strongly typed ontology into the very fabric of logical forms, the author shows that many seemingly complex semantic phenomena—type‑coercion, nominal compounds, abstract existence, and identity—become almost trivial to handle. The framework preserves compositionality, respects commonsense intuitions, and offers a clear path toward computational implementations that can automatically infer the appropriate ontological types and perform the necessary unifications during semantic parsing.