On Thursday, Nicholas Asher started his two-part invited talk (which could also be considered a short course) on “Types, Semantics and Ontology”.

Part 1

Nicholas started with an overview of lexical semantics, describing it as the basic building blocks of meaning, which is a good motivation for our community to study/use it. He talked about the current state of lexical semantics (things that can be done, things that are still challenges), mentioning some specific paradigms/approaches that have been proposed by members of this community (analyzing the meaning of a word by its companies, representing the truth of a sentence with FOL, making inferences based on the choice of words in a sentence, etc.).

He then focused on a particular tool for lexical semantics and composition (i.e., computing the meaning of sentences): Lambda calculus. In this tool, there are functions that map entities to truth values (E -> T, e.g., cat(x)) but, as Guarino had already said, not all predications are equal. Take, for instance, co-predication: you can say “John swept the kitchen” or “John swept the dust”, but you cannot combine them into “John swept the kitchen and the dust”. To understand (formalize) why, we need to know that kitchen and dust are not of the same type in the sentence. This is where ontology comes in.

Nicholas then presented the subtyping relation between types and used it to discuss how to formalize the use of types in linguistics. He presented a couple of ways and the problems associated with them, to finally present his own formalization of the matter and detailed a bit the proof conception of sub typing. This discussion was very technical and frankly I wasn’t able to follow it. Again, enlightening comments are welcome. 🙂

Slides for the first part were made available at the summer school’s website.

Part 2

Nicholas continued the discussion where he left off previously, discussing how people identify types of terms in sentences and how to formalize that (so machines can do it). He then presented some aspects of his proposal — TCL. Again, the lecture was too technical for me to follow.

He then went on to talk about dual aspect expression (e.g., book as the physical object and as the contents written in it) and how it requires a special type structure. He presented dot types (dot objects) as a possible structure for these expressions.