PPs formed by Head Spec

Below is a parse result for a sentence from a pseudo language which has VSO order, noun-determiner order, and optional determiners.

Am I right in thinking that the tree on the left should be suppressed? It is licensed currently by the head specifier rule.

49%20PM

Does this mean, in case adpositions are used in a grammar, the Head Spec rule should constrain its SPEC daughter’s HEAD? To just noun? There is a comment saying:

; Rules for building NPs.  Note that the Matrix uses SPR for
; the specifier of nouns and SUBJ for the subject (specifier) of verbs.

head-spec-phrase := basic-head-spec-phrase & head-initial.
  • but I am not sure what it means; there is a separate Head Subject rule always…

Yes – [PP [PP D]] is a weird structure. Either the P has an underconstrained SPR value or the D has an underconstrained MOD value.

(What I said about nouns above does not make any sense).

I created the structure for P such that it does specify an empty SPR list for the complement.

As for determiners, they are non-mod-lex-items

;;; Determiners
;;; SPEC is non-empty, and already specified by basic-determiner-lex.

determiner-lex := basic-determiner-lex & norm-zero-arg & non-mod-lex-item &
  [ SYNSEM.LOCAL.CAT.VAL [ SPR < >,
                           COMPS < >,
                           SUBJ < > ] ].

def-determiner-lex := determiner-lex & no-icons-lex-item.

In the left tree above, the is a def-determiner-lex.

Here’s basic-determiner-lex, for completeness:

; Note the use of the feature SPEC in basic-determiner-lex.
; This is important semantically to allow the determiner to grab
; onto the INDEX and LTOP of the N' it combines with.  Elsewhere
; in the lexical types we have avoided mentioning the valence features,
; believing the mapping from ARG-ST to valence features to be somewhat
; language-specific.  In this case, however, it does not concern
; a mapping to ARG-ST.

basic-determiner-lex := no-ltop-lex-item &
  [ SYNSEM [ LOCAL [ CAT [ HEAD det,
			   VAL.SPEC.FIRST.LOCAL.CONT.HOOK [ INDEX #ind,
							    LTOP #larg ]],
		     CONT [ HCONS <! qeq &
				   [ HARG #harg,
				     LARG #larg ] !>,
			    RELS <! relation !> ] ],
	     LKEYS.KEYREL quant-relation &
		   [ ARG0 #ind,
		     RSTR #harg ] ] ].

What rule is responsible for the [PP [PP D]] constituent?

Head Specifier rule.

So the SPR value of your P is underconstrained.

Oh, right, of the P itself! Gotcha. Thanks! And should it also be SUBJ < > ?

Take a look at the 567 instructions for non-verbal predicates to see if we ever use non-empty SUBJ values there.