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The PPI-A construction
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The following is an example of the PPI-A construction:

1
Soe hy dat dien kinnen ha?
would he that done could.PfP have
Could he have done that?

PPI is an abbreviation of the Latin phrase Participium pro Infinitivo (PPI). The term is used to refer to a construction in which two perfect participles show up, where just one participle and an infinitive are expected. In the A-construction, the auxiliary of the perfect selects the perfect participle realised as the modal auxiliary.

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The PPI-A construction displays the presence of two participles while there is only one instance of ha have. Furthermore, the participle dien done is not adjacent to ha have, since the participle kinnen could intervenes. Normally the participle is adjacent to the auxiliary of the perfect, if we abstract away from the disruptive effect of Verb-Second. Hence we conclude that the participle that is not adjacent to ha have is the parasitic participle, whereas the adjacent participle is the true participle.

The PPI-A construction is reminiscent of the A-construction. Consider a normal A-construction (2a), followed by a PPI-A construction (2b):

2
a. Hie hy dat dwaan kinnen?
had he that do could.PfP
Could he have done that?
b. Soe hy dat dien kinnen ha?
would he that done could.PfP have
Could he have done that?

Impressionistically, it seems that the irrealis perfect verb of the ordinary A-construction hie had has been broken into two elements: the irrealis verb soe should and the perfect infinitive hawwe have.

Unlike the PPI-B construction, the PPI-A construction is not restricted to main clauses, but can also be found in embedded clauses. An example is given in (3):

3
Omdat er dat net dien kinnen ha soe
would he that not done could.PfP have should
Because he could not have done that

Of course, it is also grammatical to replace the parasitic participle by an infinitive:

4
Omdat er dat net dwaan kinnen ha soe
would he that not do.OI could.PfP have should
Because he could not have done that

The real participle cannot be replaced by an infinitive:

5
*Omdat er dat net dien kinne ha soe
would he that not done could.OI have should
Because he could not have done that

It might also be questioned whether the word order in the verbal cluster reflects the hierarchical selection relation between the verbs. That is, it might be questioned whether the verb cluster is consequently head-final. It can be shown that the cluster is consistently head-final by applying an idiom test. The idiom útstean kinne can stand does not allow any other verb to intervene, not even the auxiliary of the perfect, as shown in (6):

6
a. Nimmen hie it útstean kinnen
nobody had it stand could.PfP
Nobody could have stood it
b. *Nimmen koe it dus útstien ha
nobody could it so stood have
So, nobody could have stood it

So, the idiom cannot be found in the logical B-construction, as shown above, which is still current in Modern Frisian (see a different B-construction: the logical B-construction). The ungrammaticality is due to the strict character of this idiom. If we replace the idiomatic verb by another verb, the sentence is fine:

7
Nimmen koe it dus ferneard ha
nobody could it so stood have
So, nobody could have stood it

The idiom will help us to determine the structure of the verb cluster. If the linear order reflects the hierarchical order, then the idiom will be able to occur in the PPI-A construction, because the auxiliary of the perfect does not structurally intervene in the idiomatic cluster. This is in fact the case, as the following sentence makes clear:

8
Soe hy dat útstien kinnen ha?
would he that stood could.PfP have
Could he have stood that?

The sentence in (8) is grammatical because the auxiliary of the perfect does not structurally intervene in the idiom. Hence the order reflects the underlying hierarchical relation, whereas the morphological ending may be misleading, as happens to be the case with the parasitic participles.

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