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# THEORY: Valency-Reducing Operations on High-Valency Predicates

From: Eldin Raigmore Saturday, May 20, 2006, 20:01
```Topics in this post:

(Topics that were covered recently on this list -- probably within the past
year, certainly within the past two years -- are marked with *.
If you wish you should skip those topics marked with *, referring back to
them only when necesssary.)

[VALENCY-REDUCING OPERATIONS ON MONOVALENT PREDICATES]

*[VALENCY-REDUCING OPERATIONS ON BIVALENT PREDICATES]
*-Examples

-Pragmatics (new -- don't skip)

*Questions

*[VALENCY-REDUCING OPERATIONS ON TRIVALENT PREDICATES]

*-Examples (I _think_ it's been mentioned before...)

-Pragmatics (new, I _think_)

Questions (if these have been covered before, I can't find the answers)

--Further reducing the valency (new -- don't skip)

[VALENCY-REDUCING OPERATIONS ON TETRAVALENT PREDICATES]

-Pragmatics

Questions

--Further reducing the valency (incomplete)

[MORPHOSYNTACTI ALIGNMENT] (Questions only)

----------

[VALENCY-REDUCING OPERATIONS ON MONOVALENT PREDICATES]

(Should it be "monovalent" or "univalent"?)

There is only one valency-reducing operation on a monovalent predicate that
creates an avalent predicate derived from it.

The only argument can be rendered implicit and non-referential.

It's not that interesting by itself.

----------

[VALENCY-REDUCING OPERATIONS ON BIVALENT PREDICATES]

Consider a bivalent predicate P(x,y).

There are four fundamentally different valency-reducing operations on
bivalent predicates that derive monovalent predicates from them.

(Should that be monovalent or univalent?)

Summarizing;

We can render either argument implicit and non-referential:
Pa(x) = "for some y, P(x,y)"
Pb(y) = "for some x, P(x,y)"

We can fill two places with the same thing, that is, make the two arguments
identical to each other:
Pc(x) = "P(x,x)"

We can have the two arguments "reciprocate" with each other:
Pd(x&y) = "P(x,y) and P(y,x)"

Operation "a" might be called "object-deletion" or "impersonal anti-
passive".
Operation "b" might be called "subject-deletion" or "impersonal passive".
Operation "c" might be called "reflexivization".
Operation "d" might be called "reciprocation".

--
-Examples

Examples of "a" and "b" might be;
if P = "ate", x = "John", y = "sandwich",
then
P(x,y) = "John ate a sandwich",
so
Pa(x) = "John ate"
and
Pb(y) = "The sandwich was eaten".

Examples of "c" and "d" might be;
If P = "hit", x = "Jill", and y = "Jack",
P(x,y) = "Jill hit Jack",
Pc(x) = "Jill hit herself",
Pd(x&y) = "Jill and Jack hit each other".

--
-Pragmatics

Pragmatically, if I state:
"Pa(x) and Pb(y)",
my addressee is likely to assume the "defeasible implicature" that this
means
"P(x,y)".

That is, if I say
"John ate, and the sandwich was eaten",
then, unless the language allows me to say explicitly that
"John ate the sandwich",
my hearers are probably going to assume that that's what I meant.

But I am not aware of any languages wherein that kind of thing happens for
any clause that has a monotransitive bivalent version in any other language.

I believe there are languages where you can't say in just one clause
whether it was Jill who hit Jack or Jack who hit Jill; that is, if P
= "hit", the language contains a P' such that
P'(x,y) = "P(x,y) or P(y,x)"
and contains either Pa or Pb; but doesn't contain P itself.
So you have to say
"Jill hit-or-was-hit-by Jack, and Jill hit someone"
or
"Jill hit-or-was-hit-by Jack, and Jack got hit"
if you want to communicate the fact that Jill hit Jack.

But I am not aware of any natlangs in which this "hit" verb doesn't have a
bivalent and monotransitive gloss.

--
Questions
Does anyone else know of any such natlangs?
Does anyone know of any conlangs like that?

----------

[VALENCY-REDUCING OPERATIONS ON TRIVALENT PREDICATES]

Consider a trivalent predicate Q(x,y,z).

There are nine fundamentally different valency-reducing operations on
trivalent predicates that derive bivalent predicates from them.

Summarizing;

We can render any one of the three arguments implicit and non-referential:
Qe(x,y) = "for some z, Q(x,y,z)"
Qf(x,z) = "for some y, Q(x,y,z)"
Qg(y,z) = "for some x, Q(x,y,z)"

We can fill any two of the three places with the same thing, that is, make
any pair of arguments identical to each other:
Qh(x,y) = "Q(x,x,y)"
Qi(x,y) = "Q(x,y,x)"
Qj(x,y) = "Q(x,y,y)"

We can have any two of the three arguments "reciprocate" with each other:
Qk(x&y,z) = "Q(x,y,z) and Q(y,x,z)"
Ql(x,y&z) = "Q(x,y,z) and Q(x,z,y)"
Qm(x&z,y) = "Q(x,y,z) and Q(z,y,x)"

Operation "e" might be called "direct-object-deletion".
Operation "f" might be called "indirect-object-deletion".
Operation "g" might be called "subject-deletion".
Operations "h", "i", and "j" are three kinds of "reflexivization".
Operations "k", "l", and "m" are three kinds of "reciprocation".

--
-Examples

Examples of "e", "f", "g" might be;
if Q = "gave", x = "Jill", y = "Jack", z = "bike",
Q(x,y,z) = "Jill gave Jack a bike",
Qe(x,y) = "Jill gave Jack (something)",
Qf(x,z) = "Jill gave her bike away",
Qg(y,z) = "Jack got a bike as a gift".

Examples of "h", "i", and "j" might be,
if Q = "show",
then
Qh(I, invoice) = "I showed myself the invoice" (by opening the envelope,
perhaps)
Qi(flasher, me) = "The flasher showed himself to me"
Qj(psychiatrist, me) = "The psychiatrist showed me to myself".

Examples of "k", "l", and "m":
For Q = "gave", x = "Jill", y = "Jack", z = "rings",
Qk(x&y,z) =
Qk(Jill & Jack, rings) = "Jill and Jack gave each other rings";

for Q = "married", x = "Parson Brown", y = "Jill", z = "Jack",
Ql(x, y&z) = Ql(Parson Brown, Jill & Jack) =
= "Parson Brown married Jill and Jack to each other";

for Q = "betrayed", x = "Winston", y = "police", z = "Julia",
Qm(x&z, y) = Qm(Winston & Julia, police) =
= "Winston and Julia betrayed each other to the police".

--
-Pragmatics

Pragmatically, if I state:
"Qe(x,y) and Qf(x,z)",
or
"Qe(x,y) and Qg(y,z)",
or
"Qf(x,z) and Qg(y,z)",
my addressee is likely to assume the "defeasible implicature" that this
means
"Q(x,y,z)".

That is, if I say
"Jill gifted Jack, and Jill gave away her bike",
or
or
"Jill gave away her bike, and Jack got a bike as a gift",
then, unless the language allows me to say explicitly that
"Jill gave Jack her bike",
my hearers are probably going to assume that that's what I meant.

Most languages do have ditransitive verbs; and in most of them these verbs
form a minority, significantly smaller than the classes of monotransitive
and intransitive verbs.

But some languages do not have any ditransitive verbs; and, even those that
do, might lack a ditransitive that some other language has.

So there are some languages where even "give" clauses and/or "show" clauses
will have to be glossed as two monotransitive clauses, or at least as two
bivalent clauses; just as above.

--
Questions
Does anyone else know of any such natlangs?
Does anyone know of any conlangs like that?

---
--Further reducing the valency

After each of operations e, f, g, h, i, or j, any of operations a, b, c, or
d may be applied:
Qea(x) = "for some y, Qe(x,y)" =
= "for some y for some z, Q(x,y,z)"

Qfa(x) = "for some z, Qf(x,z)" =
= "for some z for some y, Q(x,y,z)"

Note that semantically
Qea(x) = Qfa(x).

Qga(y) = "for some z, Qg(y,z)" =
= "for some z for some x, Q(x,y,z)"

Note that semantically
Qeb(y) = Qga(y).

Qha(x) = "for some y, Qh(x,y)" =
= "for some y Q(x,x,y)"

Qia(x) = "for some y, Qi(x,y)" =
= "for some y Q(x,y,x)"

Qja(x) = "for some y, Qj(x,y)" =
= "for some y Q(x,y,y)"

Qeb(y) = "for some x, Qe(x,y)" =
= "for some x for some z, Q(x,y,z)"

Note that semantically
Qeb(y) = Qga(y).

Qfb(z) = "for some x, Qf(x,z)" =
= "for some x for some y, Q(x,y,z)"

Qgb(z) = "for some y, Qg(y,z)" =
= "for some y for some x, Q(x,y,z)"

Note that semantically
Qfb(z) = Qgb(z).

Qhb(y) = "for some x, Qh(x,y)" =
= "for some x Q(x,x,y)"

Qib(y) = "for some x, Qi(x,y)" =
= "for some x Q(x,y,x)"

Qjb(y) = "for some x, Qj(x,y)" =
= "for some x Q(x,y,y)"

Qec(x) = "Qe(x,x)" =
= "for some z, Q(x,x,z)"

Qfc(x) = "Qf(x,x)" =
= "for some z, Q(x,z,x)"

Qgc(x) = "Qg(x,x)" =
= "for some z, Q(z,x,x)"

Qhc(x) = "Qh(x,x)" =
= "Q(x,x,x)"

Qic(x) = "Qi(x,x)" =
= "Q(x,x,x)"

Qjc(x) = "Qj(x,x)" =
= "Q(x,x,x)"

Qed(x&y) = "Qe(x,y) and Qe(y,x)" =
= "for some z, Q(x,y,z) and for some z, Q(y,x,z)"

Qfd(x&z) = "Qf(x,z) and Qf(z,x)" =
= "for some y, Q(x,y,z) and for some y, Q(z,y,x)"

Qgd(y&z) = "Qg(y,z) and Qg(z,y)" =
= "for some x, Q(x,y,z) and for some x, Q(x,z,y)"

Qhd(x&y) = "Qh(x,y) and Qh(y,x)" =
= "Q(x,x,y) and Q(y,y,x)"

Qid(x&y) = "Qi(x,y) and Qi(y,x)" =
= "Q(x,y,x) and Q(y,x,y"

Qjd(x&y) = "Qj(x,y) and Qj(y,x)" =
= "Q(x,y,y) and Q(y,x,x)"

--
After each of the operations k, l, and m, it might be possible to follow
with operations a or b; but not with operation d.
It may be possible to follow them with operation c.
Not all of the operations obtained by following up one of the operations k
or l or m with one of a or b or c are likely to be independently meaningful.

Qka(x&y) = "for some z, Qk(x&y,z)" =
= "for some z, Q(x,y,z) and Q(y,x,z)"
Note that, semantically, Qka(x&y) implies, but is not necessarily implied
by, Qed(x&y).

Qla(x) = "for some y & z, Ql(x,y&z)" =
= "for some y & z, Q(x,y,z) and Q(x,z,y)".
This is one of the ones I suspect might not be independently meaningful.

Qma(x&z) = "for some y, Qm(x&z,y)" =
= "for some y, Q(x,y,z) and Q(z,y,x)".
Note that, semantically, Qma(x&z) implies, but is not necessarily implied
by, Qfd(x&z).

Qkb(z) = "for some x&y, Qk(x&y,z)" =
= "for some x&y, Q(x,y,z) and Q(y,x,z)"
This is one of the ones I suspect might not be independently meaningful.

Qlb(y&z) = "for some x, Ql(x,y&z)" =
= "for some x, Q(x,y,z) and Q(x,z,y)".
Note that, semantically, Qlb(y&z) implies, but is not necessarily implied
by, Qgd(y&z).

Qmb(y) = "for some x&z, Qm(x&z,y)" =
= "for some x&z, Q(x,y,z) and Q(z,y,x)".
This is one of the ones I suspect might not be independently meaningful.

--
What happens when we follow one of k or l or m with c?
Qkc(x&y) = "Qk(x&y,x&y)" =
= "Q(x,y,x&y) and Q(y,x,x&y)"

Qlc(y&z) = "Ql(y&z,y&z)" =
= "Q(y&z,y,z) and Q(y&z,z,y)"

Qmc(x&z) = "Qm(x&z,x&z)" =
= "Q(x,x&z,z) and Q(z,x&z,x)"

But are these likely to be independently meaningful?

----------

[VALENCY-REDUCING OPERATIONS ON TETRAVALENT PREDICATES]

Consider a tetravalent predicate R(w,x,y,z).

There are sixteen fundamentally different valency-reducing operations on
tetravalent predicates that derive trivalent predicates from them.

Summarizing;

We can render any one of the four arguments implicit and non-referential:
Rn(w,x,y) = "for some z, R(w,x,y,z)"
Ro(w,x,z) = "for some y, R(w,x,y,z)"
Rp(w,y,z) = "for some x, R(w,x,y,z)"
Rq(x,y,z) = "for some w, R(w,x,y,z)"

We can fill any two of the four places with the same thing, that is, make
any of six pair of arguments identical to each other:
Rr(w,x,y) = "R(w,x,y,w)"
Rs(w,x,y) = "R(w,x,y,x)"
Rt(w,x,y) = "R(w,x,y,y)"
Ru(w,x,z) = "R(w,x,w,z)"
Rv(w,x,z) = "R(w,x,x,z)"
Rw(w,y,z) = "R(w,w,y,z)"

We can have any two of the three arguments "reciprocate" with each other:
Rx(w,x,y&z) = "R(w,x,y,z) and R(w,x,z,y)"
Ry(w,x&z,y) = "R(w,x,y,z) and R(w,z,y,x)"
Rz(w,x&y,z) = "R(w,x,y,z) and R(w,y,x,z)"
R@(w&z,x,y) = "R(w,x,y,z) and R(z,x,y,w)"
R#(w&y,x,z) = "R(w,x,y,z) and R(y,x,w,z)"
R\$(w&x,y,z) = "R(w,x,y,z) and R(x,w,y,z)"

--
-Pragmatics

Pragmatically, if I state:
"Rn(w,x,y) and Ro(w,x,z)",
or
"Rn(w,x,y) and Rp(w,y,z)",
or
"Rn(w,x,y) and Rq(x,y,z)",
or
"Ro(w,x,z) and Rp(w,y,z)",
or
"Ro(w,x,z) and Rq(x,y,z)",
or
"Rp(w,y,z) and Rq(x,y,z)",
my addressee is likely to assume the "defeasible implicature" that this
means
"R(w,x,y,z)".

If one language has a tetravalent verb
R(w,x,y,z), and another doesn't, but does have two trivalent verbs which
gloss as two of
Rn(w,x,y) or Ro(w,x,z) or Rp(w,y,z) or Rq(x,y,z),
then in that second language, the clause R(w,x,y,z) will have to be glossed
as two trivalent clauses; just as above.

--
Questions
Can anyone think of any natlangish examples?

---
--Further reducing the valency

After any of the operations n, o, p, q, r, s, t, u, v, w, it should be
possible to apply any of the operations e, f, g, h, i, j, k, l, or m:

[details to be available later, on request]

--
After each of the operations x, y, z, @, #, and \$, it should be possible to
follow with operations e, f, or g; but which of them can be followed with
operations k, l, or m will be idiosyncratic.

[details to be available later, on request]

It might be possible to follow one of operations x, y, z, @, #, or \$, with
one of operations h, i, or j.

[details to be available later, on request]

Not all of the operations obtained by following up one of the operations x,
y, z, @, #, or \$, with one of e, f, g, h, i, or j, are likely to be
independently meaningful.

[details to be available later, on request]

----------

[MORPHOSYNTACTIC ALIGNMENT]

Does anyone know how the participants of tetravalent clauses line up with
those of trivalent and bivalent and monovalent clauses?

Assuming a scarcity of natlangish examples, how many people, and who, can
come up with an answer for a conlang? And for how many and which conlangs?

----------

eldin
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