When are different type-logical semantic definitions defining equivalent meanings?

The paper considers the issue of different type-logical semantic definitions (of some natural language fragment) being “essentially” the same, though expressed using different type-systems. A definition of the equivalence is suggested, and is applied to four definitions of a very simple extensional fragment of English.

► Type-logical grammars specify semantics by using types.
► The paper defines when two specifications, using different types, specify the same meanings.
► Four different typed meanings are shown equivalent.