Re: quadrivalent verb

This is my fifth post for today, so it is my final one, and I'll have to combine
answers to other posts without quoting them -- sorry.

First; as many people have said, there's no reason a clause can't be an
argument.  In any language with subordination, in fact, it is likely that some
subordinate clauses are complement clauses; complement clauses are always
arguments.  In fact, one well-known way of classifying verbs classifies them
into those which cannot take a complement clause as an argument, those
which must take a complement clause as an argument, and those which may
or may not take a complement clause as an argument; see this list for a book
by Dixon, Aikhenvald, and Onishi(? Sorry I'm not certain of the last author's
name).

Possibly, though, languages without subordination may nevertheless have
complement clauses, especially in quotation.  Verbs of saying and thinking
usually have "embedded clauses" as one argument.

As far as I know (the wannabe-amateur is speaking here! So there's no
citations to back this up) every language has both embedded clauses and
dependent clauses (where some of its verb's semantics depend on those of
some other clause's verb).  But some languages never have embedded
dependent clauses, that is, clauses that are both embedded in and dependent
on another clause; those are the languages that don't have subordinate
clauses in the strict sense.

As far as I know, subordinate clauses can either be used as if nouns
(complement clauses), as if adjectives (relative clauses), or as if adverbs
(adjunct clauses).  In English, "that" is a complementizer and a relativizer; not
an adposition.  (Of course it's also a demonstrative; in many languages,
complementizers and/or relativizers are similar to demonstratives and/or
question-words.)

Second: About testing whether or not a participant is an argument or an
adjunct, and whether an argument is a core argument or an oblique argument.

Yes, there probably is a test.  No, I don't know where to find one.

There's a test for a Subject, and a test for an Absolutive; look on Chris D.
Bates's (the maths student from Nottinghamshire) wiki for one (more-or-less
cursory) discussion of them.
< http://chrisdb.me.uk/wiki/doku.php?id=grammatical_relations >

Not all professionals "believe in" arguments vs adjuncts; not all "believe in"
core vs oblique.  So odds are that any test is not universally accepted.

The same applies to the Subject test and to the Absolutive test, but in their
cases most linguists who have an alternative test present it as a modification
of those tests, and most linguists who criticize all tests choose those tests as
the main examples to criticize.

Some conlangers also have doubts about argument vs. adjunct; even more
have doubts about the "definition(s)" of argument.
The description of "argument" most often seen is something like;
"A participant which is semantically necessary in order for the verb to mean
anything".  But some don't think that's a definition, that it's merely a
description; others don't think it's any good as a description either, because,
for instance, some of them think that phrases like "semantically necessary" are
pretty useless.

Nevertheless many pros do in fact use the ideas of "argument" and "adjunct".

Then there's the question of "what's a core argument" vs "what's an oblique".
The best (IMO) description of a "core" argument is "an argument that occupies
a grammatical relation".  Obviously that one's going to be no good to you in
finding a test to see whether an argument is a core argument or an oblique
argument, if you're trying to discover how many and what grammatical
relations a language has; you need a definition that doesn't prerequire knowing
what the GRs are.

A theory known as RRG (Role and Reference Grammar, a completely different
thing from RG (which is "Relational Grammar")) has an idea known as "core";
you should look up their definition and see whether it helps.

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A related question is whether or not valency means anything, and if it does,
what is its definition.

Lots of theories "believe in" some idea of valency; some don't.

Just looking at verbs (there's good reason to believe many words that aren't
verbs nevertheless have valency, at least in many theories), if we believe they
have "valency", there may be several different ideas as to what its "valency" is.

If the verb is just sitting in the lexicon available for use:
Maybe you count the number of arguments it can "specifically license"
(whatever that means), including those that are omissible.
Or;
Maybe you count the number of obligatory, mandatory arguments it requires.

If the verb is actually used in a clause;
Maybe you count the number of arguments it actually has explicitly specified in
the clause.
Or, maybe you count also those arguments which are implicitly assumed.

And, either way;
Maybe you count only "core arguments"; or maybe you count "oblique
arguments" as well.

(Some verbs in some languages have mandatory oblique arguments, such as
the locative required by "put" in English.)

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I hope that helps.