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On 11 September 2015 at 07:22, Patrik Austin <[log in to unmask]> wrote:
> It's still quite difficult to follow without examples :(

I shall endeavor to provide some. :)

> On second thought I think logical expressions can also be useful, but I wish they were more closely linked to the(/an) actual language. Sometimes a mixed technique is the best. The standard method of linguistics with an original example sentence followed by an intermediate formulation and a final translation (into English) is of course something that most people could understand... ;)
>
> Anyway apposition is not completely trivial with names if we think of titles such as Mister Blake, Professor Blake or painter Blake. You can't really put it all in the dictionary; while having apposition at hand allows you to deal with titles, full names (Blake, William) as well as determiners (every man, some woman etc.) with one strategy.

Apposition is defined as the relationship between phrases that are
next to each other and have the same referent, but describe it in
different ways.
That is exactly what the phrase-level semantics for my monocategorial
language formalize: each phrase binds a new argument variable, which
is shared among all the words in that phrase, the lexical semantics of
which provide constraints on the identity of the referent for that
phrase.

As And noted, it's not clear that multipart names like "William Blake"
actually are appositive; and "for realsies" it makes more sense to me
to treat names as single units which incidentally happen to have their
own, unrelated, internal grammar. But with appropriate definitions for
"William" and "Blake", the appositive interpretation can be made to
work.

"William Blake" is the entity which is a member of the set of things
named "William" *and* is a member of the family "Blake". "Mister
Blake" is the entity which is a member of the set of people properly
addressed as "Mister", and is also a member of the family "Blake".
Similar for "professor", "painter", and so on.

> I think Alex's Davidsonian paaS passes the test with a minor precision. If I remember correctly, Alex told us one of the a's is a Davidsonian argument, but here it might be that none of them is; or that to make the grammar work properly, it has to be a monocategorial (all-noun) language, so eventually there's no difference between Davidsonian and ordinary arguments, and we'd be looking for a semantic formula instead.
>
> AGENT dance William, AGENT dance Blake
> [apposition]
>
> vs.
>
> AGENT dance William, COMPANION William Blake
> [semantic embedding]
>
> With the grammar xyzS if the semantic formula is "X of Y is Z":
>
> ==> [apposition]: "Agent of dance is William, agent of dance is Blake" (i.e. William Blake, or: Blake, William).
> ==> [semantic embedding]: "Agent of dance is William, companion of William is Blake".
>
> Actually the latter means "William, accompanied by Blake, is dancing."

My monocategorial version of "William Blake is dancing" would come out
like this:

"William Blake agent, dance event." (or even just "William Blake,
dance", if you trust pragmatics to recover the correct argument
positions in this case, which you probably can.)
Ignoring the complexities of handling quantification and
non-intersectivity, since neither of those arise in this example, the
interpretation goes something like this:

Parse: (S (C (P (n "William") (P (n "Blake") (P (n "agent")))) (C (P
(n "dance") (P (n "event"))))))

[|(S (C (P (n "William") (P (n "Blake") (P (n "agent")))) (C (P (n
"dance") (P (n "event"))))))|] =
∃x.[|(C (P (n "William") (P (n "Blake") (P (n "agent")))) (C (P (n
"dance") (P (n "event")))))|](x) =
∃x.(λx. ∃y. [|(P (n "William") (P (n "Blake") (P (n
"agent"))))|](x)(y) & [|(C (P (n "dance") (P (n "event"))))|](x))(x) =
∃x.∃y. [|(P (n "William") (P (n "Blake") (P (n "agent"))))|](x)(y) &
[|(C (P (n "dance") (P (n "event"))))|](x) =
∃x.∃y. (λx.λy.[|(n "William")|](x)(y) & [|(P (n "Blake") (P (n
"agent")))|](x)(y))(x)(y) & (λx. ∃y. [|(P (n "dance") (P (n
"event")))|](x)(y))(x) =
∃x.∃y. [|(n "William")|](x)(y) & [|(P (n "Blake") (P (n
"agent")))|](x)(y) & ∃y. [|(P (n "dance") (P (n "event")))|](x)(y) =
∃x.∃y. [|(n "William")|](x)(y) & [|(P (n "Blake") (P (n
"agent")))|](x)(y) & ∃y. [|(P (n "dance") (P (n "event")))|](x)(y)

and skipping a few steps....

∃x.∃y. [|(n "William")|](x)(y) & [|(n "Blake")|](x)(y) & ∃r. r(x,y) &
[|(n "agent")|](x)(y) & ∃y. [|(n "dance")|](x)(y) & [|(n
"event")|](x)(y) =
∃x.∃y. (λx.λy. William(y))(x)(y) & (λx.λy. Blake(y))(x)(y) & ∃r.
r(x,y) & (λx.λy. ag(x, y))(x)(y) & ∃y. (λx.λy. dance(y))(x)(y) &
(λx.λy. x = y)(x)(y) =
∃x.∃y. William(y) & Blake(y) & ∃r. r(x,y) & ag(x, y) & ∃y. dance(y) &
x = y & ∃r. r(x,y)

Now we can simplify a little bit to get

∃x.∃y. William(y) & Blake(y) & ag(x, y) & dance(x)

In contrast, "William and Blake are dancing" (or "William accompanied
by Blake is dancing") would be rendered as

"William agent, Blake agent, dance event"

Which goes through a similar interpretation process to produce the logical form

∃x.∃y. William(y) & ag(x, y) & ∃y. Blake(y) & ag(x, y) & dance(x)

Renaming shadowed variables for better readability, this is equivalent to

∃x.∃y. William(y) & ag(x, y) & ∃z. Blake(z) & ag(x, z) & dance(x)

-l.