Model: ‘Procedural’ Description

This section describes in detail how the graph is constructed from an input tree. Readers interested in only the general structure of the system should feel free to proceed to the next section.

Variables (nodes)

Factors (edges)

Figure 4.2: Key for explanatory figures for graph creation. Boxes represent variables and circles represent factors.

qAl/OBJ null (NP *) (WH mA) qAl/SBJ null (NP *) (WH mA) (WH mA) qAl/SBJ qAl/OBJ

Figure 4.3: A slot factor is added for each slot variable, and a subcategorization factor is added joining all slots of the same verb. In each box, the name of the variable is in bold at the top and its possible values are listed in italics below it. A value ofnull indicates that a slot is left empty.

qAl/OBJ null (NP *) (WH mA) qAl/SBJ null (NP *) (WH mA) (WH mA) qAl/SBJ qAl/OBJ

Figure 4.4: Wh-path factors are added between the wh-variable and each slot vari- able. In each box, the name of the variable is in bold at the top and its possible values are listed in italics below it. A value ofnull indicates that a slot is left empty.

stp A$xAS byn hm vlAv nsA’

six people among pronoun three women (NP-OBJ (NP (CD stp) (NP (NN A$xAS))) (SBAR (WHNP-0 (-NONE- *0*)) (S (NP-PRD (NN byn) (NP (NP (PRP hm)) (NP-0 (-NONE- *T*)))) (NP-SBJ (CD vlAv) (NP (NN nsA’))))))

follows:

• At each node t of the tree, insert a null complementizer (0) below it if: – t is an SBAR.

– t does not immediately dominate a WHNP, a WHADJP, a WHADVP, a WHPP or anIN.

– t does immediately dominate an S or a FRAG.

The 0 should be marked as a WHNP if t is not the child the of PP.

• The tree is processed by pre-order traversal depth-first search. At each nodet: – If t is a VP whose immediate head is a verb or a modal which lacks a

verbal sister,

∗ Create two sets sbjvals and objvals to represent the possible values of the verb’s subject and object slot variables, respectively. Add to each null (indicating that the slot should be empty) and(NP *). ∗ Add candidate topicalization traces to sbjvals by adding any c-

commanding NP which is marked as an argument and has at most one SBARintervening between it and the verb.

∗ Search recursively from parent to parent up the tree fromt. Whenever you come across an S, SBAR, or SBARQ which dominates a WHNP, add that wh-node to sbjvals and objvals. As you go along, also note any WHADVPs you encounter in the set whadvps, which will contain the possible values of the adverbial slot variable associated with the verb. Break off the search after you have seen two SBARs.

∗ Create a slot variable for the subject slot with possible valuessbjvals. ∗ Create a slot variable for the object slot with possible values objvals. ∗ if the setwhadvps is non-empty, create an adverbial slot variable with

possible values whadvps.

– otherwise, iftbears the function tag-PRD,5_{thas no overt, non-resumptive-} pronoun sister nodes, and t is not an argument of a VP, create a set vals and add (NP *) and null to it. Search for and add wh-word possibili- ties as done above for verbs. Create a new predicative slot variable with possible values vals.

Sometimes the -PRD can itself contain a trace attached to a resumptive pronoun (as in figure 4.5). Handling this is slightly complicated: ift is a -PRD but has an overt, non-resumptive-pronoun sister node, we check if the -PRDconstituent itself is a resumptive pronoun or contains one in an immediately dominatedPP orADJP. If this is the case, we create the-PRD variable as above. During inference, if a trace is assigned to this variable, it is inserted as attached to the-PRD internal resumptive pronoun.

– iftis a prepositional phrase with no overt, non-resumptive pronoun object and noSBARintervenes between the PPand the closestWHNP , create a set vals and add null and (NP *) to it. Gather and add wh-word values as above. Create a new prepositional slot variable with possible values vals.

• Do a depth-first search by pre-order traversal over the tree. Whenever you encounter a WHNP or WHADVP node, attempt to create a wh-variable. The pro- cedure for creating awh-variable from a wh-node t is as follows:

– for each slot variable, if the wh-word c-commands it with at most one intervening SBAR node, then

∗ If the wh-variable is not adverbial, add the slot variable as a possible value for it.

∗ If thewh-variable is adverbial or of unknown type and the slot variable is adverbial, add the slot variable as a possible value for it.

5_{That is, a predicative phrase, such as anNPorADJPwhich would typically be use together with}

– If no possible values are found, abort creation of thewh-variable.

• For each slot variable, create a slot factor of the correct type (verbal, predica- tive, prepositional).

• For each wh-variable, for each of its values, create a wh-factor for the pair.

• For every verb with associated slot variables, create a subcategorization factor containing all those variables.