Intro

Semantic modification must satisfy a few constraints:

• must be no cycles in graph (a.)
• must be language-independent (b.)
• must allow modifiers to contrain the objects they refer to (c.)
• must be direction-independent (works for either generation or parsing) (d.)
• must compose solely through consing, so that unification works. (e.)

Below we describe a proposed solution that meets these requirements.

Summary

• The :ref feature is used to avoid cycles (a. above). This :ref is used by [:mod :arg] to refer to what is being modified.

• Three new ug meta-rules:

  • nest-mod:
    • the :sem of the :head and the :sem of the parent are distinct: [:head :sem] != [:sem].
    • the :mod of the head is moved inside the parent's :sem: [:head :mod] = [:sem :mod].
  • cons-mod:
    • the :sem of the :head and the :sem of the parent are identical: [:head :sem] = [:sem].
    • the :mod of the parent is equal to the cons of:
      • :sem of the comp: [:head :mod :first] = [:comp :sem]
      • :mod of the head. [:head :mod :rest] = [:comp :mod].
  • cons-and-nest-mod:
    • the :sem of the :head and the :sem of the parent are identical: [:head :sem] = [:sem].
    • this [:sem :mod] is a list with one member: [:comp :mod].

• English rules' use of these meta rules:

  • nest-mod: np,vp.
  • cons-mod: nmod (a.k.a. nbar),..
  • no-mod: s,s/, cp,..
  • cons-and-nest-mod: vmod.

Lexical entries

Nouns

{:cat :noun
 :sem {:pred :dog
       :ref {:spatial true}
       :mod []}}

Adjectives

{:cat :adj
 :sem {:pred :orange
       :arg {:spatial true}}}

Adverbs

{:cat :adv
 :sem {:pred :stealth
       :arg {:activity true}}}

Verbs

{:cat :verb
 :sem {:pred :sleep
       :activity true
       :subj {:animate true (c.)
	          :ref [1]}}
 :subcat {:1 {:cat :noun
              :sem {:ref [1]}}
	      :2 []}}

Rules

nmod is a rule where :sem and :mod are siblings (cons-mod):

{:rule "nmod"
 :comp [1]
 :sem [2] {:ref [3]}
 :mod <[4]{:arg [3]} [5]>
 :head {:sem [2]
        :mod [5]
        :subcat {:1 [1]
                 :2 []}}}
 :comp {:sem [4]}}

np, by contrast, is a rule where :mod is within :sem (nest-mod):

{:rule "np"
 :sem {:mod [1]
       :pred [2]
	   :ref [3]}
 :head {:sem {:pred [2]
              :ref [3]}
        :mod [1]}}

Example Expression Representations

Here we'll use the example sentence "the small orange cat that you see hunts a grey mouse stealthily" and its constituent phrases:

[s [np the [nmod [nmod small [nmod orange cat]] [cp that [s/ you see]]]] [vmod [vp hunts a mouse] stealthily]]

s is neither nest-mod, cons-mod, nor :cons-and-nest-mod: neither child should have a :mod feature. This is enforced with :mod :unspec as shown below:

Input to generation

{:cat :verb
 :sem {:pred :hunts
       :obj {:pred :mouse
             :mod <{:pred :grey}>}
       :subj {:pred :cat
              :mod <{:pred :see
                     :subj {:pred :you}},
                    {:pred :small},
                    {:pred :orange}>
       :mod <{:pred :stealth>}>}}

Output of generation

{:cat :verb
 :sem {:pred :hunts
       :obj {:ref [3]
             :pred :mouse
             :mod [4] <{:ref [3]
                        :pred :grey}>}
       :ref [2]
       :subj {:pred [5] :cat
              :ref [1]}
              :mod <{:pred :see
                     :obj {:ref [1]
					       :pred [5]}
                     :subj {:pred :you}},
                    {:pred :small
                     :arg [1]},
                    {:pred :orange
                     :arg [1]}>}
       :mod <{:pred :stealth
              :arg [2]}>}
 :mod :unspec}
 :head {:mod :unspec}
 :comp {:mod :unspec}}

[np the [nmod [nmod small [nmod orange cat]] [cp that [s/ you see]]]]

np is nest-mod and so [:sem :mod] = [:head :mod].

Input to generation

{:cat :noun
 :sem {:pred :cat
       :mod <{:pred :see
              :subj {:pred :you}},
             {:pred :small},
             {:pred :orange}>}}

Output of generation

{:cat :noun
 :sem {:pred [5] :cat
       :ref [1]}
       :mod <{:pred :see
              :obj {:ref [1]
                    :pred [5]}
              :subj {:pred :you}}>}
             {:pred :small
              :arg [1]}
             {:pred :orange
              :arg [1]}>
 :mod :unspec}
 :head {:mod :unspec}
 :comp {:mod :unspec}}

[nmod [nmod small [nmod orange cat]] [cp that [s/ you see]]]

nmod is cons-mod; as such, the outer nmod: :sem and :mod are siblings:

Input to generation

{:cat :noun
 :sem {:pred :cat
 :mod <{:pred :see
        :subj {:pred :you}},
       {:pred :small},
       {:pred :orange}>}}

Output of generation

{:cat :noun
 :sem {:pred :cat
       :ref [1]}
 :mod <{:pred :see
        :obj {:ref [1]}
        :subj {:pred :you}}>},
       {:pred :small
        :arg [1]},
       {:pred :orange
        :arg [1]}>}

[nmod [nmod small [nmod orange cat]]]

The middle nmod: :sem and :mod are also siblings:

Output of generation

{:cat :noun
 :sem {:pred :cat
       :ref [1]}
 :mod <{:pred :small
        :arg [1]},
       {:pred :orange
        :arg [1]}>}

[nmod orange cat]

The inner nmod: :sem and :mod are, as in the parent, siblings:

{:cat :noun
 :sem {:pred :cat
       :ref [1]}
 :mod <{:pred :orange
        :arg [1]}>}

[cp that [s/ you see]]

Like s. cp is neither nest-mod, cons-mod, nor cons-and-nest-mod: neither child should have a :mod feature. This is enforced with :mod :unspec on the rule.

Input to generation

{:cat :comp
 :sem {:pred :see
       :subj {:pred :you}}>}

Output of generation

{:cat :comp
 :subcat {:1 {:sem {:ref [1]}}}
 :sem {:pred :see
       :obj {:ref [1]}
       :subj {:pred :you}}>}
 :mod :unspec
 :head {:mod :unspec}
 :comp {:mod :unspec}}

[vmod [vp hunts a grey mouse] stealthily]

Input to generation:

Since vmod is cons-and-nest-mod, the [:sem :mod] is a list with one member: the sem of "stealthily".

{:cat :verb
 :subcat {:1 {:top :top}
          :2 []}
 :sem {:pred :hunts
	   :obj {:pred :mouse
	         :mod <{:pred :grey}>}
	   :mod <{:pred :stealth}>

Output of generation:

{:cat :verb
 :subcat {:1 {:cat :noun
              :sem {:ref [1]}}
          :2 []}}
 :sem {:pred :hunts
       :subj {:ref [1]
	   :obj {:ref [3]
             :pred :mouse
	         :mod <{:ref [3]
			        :pred :grey}>}
	   :ref [2]
	   :mod <{:pred :stealth
	          :arg [2]}>}}
 :mod :unspec
 :head {:mod :unspec}
 :comp {:mod :unspec}}

[vp hunts a grey mouse]

Like s and cp, vp is neither nest-mod, cons-mod nor cons-and-nest-mod: neither child should have a :mod feature. This is enforced with :mod :unspec.

Input to generation

{:subcat {:1 {:top :top}
          :2 []}
 :sem {:pred :hunts
	   :obj {:pred :mouse
	         :mod <{:pred :grey}>}}}

Output of generation

{:subcat {:1 {:cat :noun}
          :2 []}}
 :sem {:pred :hunts
       :subj [1]
	   :obj {:ref [3]
             :pred :mouse
	         :mod <{:ref [3]
			        :pred :grey}>}
	   :ref [2]
 :mod :unspec
 :head {:mod :unspec}
 :comp {:mod :unspec}}