Glossary:Sorts/Types

Warning:
The material on this page has been created as part of a seminar. It is still heavily under construction and we do not guarantee its correctness. If you have comments on this page or suggestions for improvement, please contact Manfred Sailer.
This note will be removed once the page has been carefully checked and integrated into the main part of this wiki.

Types

AE:

• Type: (/taɪp/)

Definition

In logic and semantics a concept of type is often used to distinguish different kinds of expression (and of semantic value). These types are used as syntactic categories for the expressions in the semantic representation language. Each type will correspond to a certain set of possible denotations.
The (minimal) set of basic types is {e, t}:
– e (for entity) is the type of individual terms
– t (for truth value) is the type of formulae
All pairs <ϭ, τ> made up of (basic or complex) types ϭ, τ are types. <ϭ, τ> is the type of functions which map arguments of type ϭ to values of type τ.
In short: The set of types is the smallest set T such that e,tєT, and if ϭ,τ єT, then also <ϭ,τ> єT.

Examples

1) Homer slept. <e,t> - sleep is an intransitive verb that does not require an object
2) Homer choked Bart. <e,<e,t>> - choke is a transitive verb and requires a direct object

Sorts

AE:

• Sort: (/sɔː(r)t/)

Definition

In semantics, there are different sorts of entities. You distinguish between entities which represent a single person or object and entities that represent a group of persons/objects. Additionally, you differentiate between concrete and abstract entities. A concrete entity refers to a specific object, e.g. a particular being (which usually has a name); on the other hand, an abstract entity refers to a non-specific object.

Examples

Example: The election of Mayor Quimby took place on Sunday.

Solution: The election of Mayor Quimby refers to a concrete (single) event.