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<?xml version="1.0" standalone="yes"?> <Paper uid="P06-2091"> <Title>Translating HPSG-style Outputs of a Robust Parser into Typed Dynamic Logic</Title> <Section position="4" start_page="707" end_page="710" type="intro"> <SectionTitle> 2 Background </SectionTitle> <Paragraph position="0"/> <Section position="1" start_page="707" end_page="708" type="sub_section"> <SectionTitle> 2.1 Typed Dynamic Logic </SectionTitle> <Paragraph position="0"> Figure 1 shows a number of propositions defined in (Bekki, 2005), including atomic predicate, negation, conjunction, and anaphoric expression. Typed Dynamic Logic is described in typed lambda calculus (Godel's System T) with four ground types: e(entity), i(index), n(natural number), and t(truth). While assignment functions in static logic are functions in meta-language from type e variables (in the case of first-order logic) to objects in the domain D</Paragraph> <Paragraph position="2"> assignment functions in TDL are functions in object-language from indices to entities. Typed Dynamic Logic defines the notion context as a set of assignment functions (an object of type (i 7- e) 7- t) and a proposition as a function from context to context (an object of type ((i 7- e) 7- t) 7- (i 7- e) 7- t). The conjunctions of two propositions are then defined as composite functions thereof. This setting conforms to the view of &quot;propositions as information flow&quot;, which is widely accepted in dynamic semantics.</Paragraph> <Paragraph position="3"> Since all of these higher-order notions are described in lambda terms, the path for compositional type-theoretic semantics based on functional application, functional composition and type raising is clarified. The derivations of TDL semantic representations for the sentences &quot;A boy ran. He tumbled.&quot; are exemplified in Figure 2 and Figure 3. With some instantiation of variables, the semantic representations of these two sentences are simply conjoined and yield a single representation, as shown in &quot;, respectively.</Paragraph> <Paragraph position="4"> The former part of (1) that corresponds to the first sentence, filtering and testing the input context, returns the updated context schematized in (2). The updated context is then passed to the latter part, which corresponds to the second sentence as its input.</Paragraph> <Paragraph position="6"> (2) This mechanism makes anaphoric expressions, such as &quot;He&quot; in &quot;He tumbles&quot;, accessible to its preceding context; namely, the descriptions of their presuppositions can refer to the preceding context compositionally. Moreover, the referents of the anaphoric expressions are correctly calculated as a result of previous filtering and testing.</Paragraph> <Paragraph position="8"/> <Paragraph position="10"> Although the antecedent for x is not determined in this structure, the possible candidates can be enumerated: x linguistic notions such as &quot;entity&quot;, &quot;event&quot; and &quot;situation&quot;, by indices, the anaphoric expressions, such as &quot;the event&quot; and &quot;that case&quot;, can be treated in the same manner.</Paragraph> </Section> <Section position="2" start_page="708" end_page="708" type="sub_section"> <SectionTitle> 2.2 Head-driven Phrase Structure Grammar Head-driven Phrase Structure Grammar (Pollard </SectionTitle> <Paragraph position="0"> and Sag, 1994) is a kind of lexicalized grammar that consists of lexical items and a small number of composition rules called schema.</Paragraph> <Paragraph position="1"> Schemata and lexical items are all described in typed feature structures and the unification operation defined thereon.</Paragraph> <Paragraph position="2"> where the feature structures marked with the same boxed numbers have a shared structure. In the first stage of the derivation of this tree, lexical items are assigned to each of the strings, &quot;John&quot; and &quot;runs.&quot; Next, the mother node, which dominates the two items, is generated by the application of Subject-Head Schema. The recursive application of these operations derives the entire tree.</Paragraph> </Section> <Section position="3" start_page="708" end_page="709" type="sub_section"> <SectionTitle> 3Method </SectionTitle> <Paragraph position="0"> In this section, we present a method to derive TDL semantic representations from HPSG parse trees, adopting, in part, a previous method (Bos et al., 2004). Basically, we first assign TDL representations to lexical items that are terminal nodes of a parse tree, and then compose the TDL representation for the entire tree according to the tree structure (Figure 5). One problematic aspect of this approach is that the composition process of TDL semantic representations and that of HPSG parse trees are not identical. For example, in the HPSG In order to overcome these differences and realize a straightforward composition of TDL representations according to the HPSG parse tree, we defined two extended composition rules, word formation rule and non-local application rule, and redefined TDL unary derivation rules for the use in the HPSG parser. At each step of the composition, one composition rule is chosen from the set of rules,basedontheinformationoftheschemata applied to the HPSG tree and TDL representations of the constituents. In addition, we defined extended TDL semantic representations, referred to as TDL Extended Structures (TD-LESs), to be paired with the extended composition rules.</Paragraph> <Paragraph position="1"> In summary, the proposed method is comprised of TDLESs, assignment rules, composition rules, and unary derivation rules, as will be elucidated in subsequent sections.</Paragraph> </Section> <Section position="4" start_page="709" end_page="709" type="sub_section"> <SectionTitle> 3.1 Data Structure </SectionTitle> <Paragraph position="0"> A TDLES is a tuple hT, p,ni,whereT is an extended TDL term, which can be either a TDL term or a special value o. Here, o is a value used by the word formation rule, which indicates that the word is a word modifier (See Section 3.3). In addition, p and n are the necessary information for extended composition rules, where p is a matrix predicate in T andisusedbytheword formation rule,and n is a nonlocal argument, which takes either a variable occurring in T or an empty value.</Paragraph> <Paragraph position="1"> This element corresponds to the SLASH feature in HPSG and is used by the nonlocal application rule.</Paragraph> <Paragraph position="2"> The TDLES of the common noun &quot;boy&quot; is given in (4). The contents of the structure are T, p and n, beginning at the top. In (4), T corresponds to the TDL term of &quot;boy&quot; in Figure 2, p is the predicate boy,whichis identical to a predicate in the TDL term (the identity relation between the two is indicated by &quot;[?]&quot;). If either T or p is changed, the other will be changed accordingly. This mechanism is a part of the word formation rule,which offers advantages in creating a new predicate from multiple words. Finally, n is an empty value.</Paragraph> </Section> <Section position="5" start_page="709" end_page="710" type="sub_section"> <SectionTitle> 3.2 Assignment Rules </SectionTitle> <Paragraph position="0"> We define assignment rules to associate HPSG lexical items with corresponding TDLESs. For closed class words, such as &quot;a&quot;, &quot;the&quot; or &quot;not&quot;, assignment rules are given in the form of a template for each word as exemplified Shown in (5) is an assignment rule for the indefinite determiner &quot;a&quot;. The upper half of (5) shows a template of an HPSG lexical item that specifies its phonetic form as &quot;a&quot;, where POS is a determiner and specifies a noun. A TDLES is shown in the lower half of the figure. The TDL term slot of this structure is identical to that of &quot;a&quot; in Figure 2, while slots for the matrix predicate and nonlocal argument are empty.</Paragraph> <Paragraph position="1"> For open class words, such as nouns, verbs, adjectives, adverbs and others, assignment rules are defined for each syntactic category.</Paragraph> <Paragraph position="2"> The assignment rule (6) is for common nouns.</Paragraph> <Paragraph position="3"> The HPSG lexical item in the upper half of (6) specifies that the phonetic form of this item is avariable,P, that takes no arguments, does not modify other words and takes a specifier.</Paragraph> <Paragraph position="4"> Here, POS is a noun. In the TDLES assigned to this item, an actual input word will be substituted for the variable P, from which the matrix predicate P is produced. Note that we can obtain the TDLES (4) by applying the rule of (6) to the HPSG lexical item of (3).</Paragraph> <Paragraph position="5"> As for verbs, a base TDL semantic representation is first assigned to a verb root, and the representation is then modified by lexical rules to reflect an inflected form of the verb. This process corresponds to HPSG lexical rules for verbs. Details are not presented herein due to space limitations.</Paragraph> </Section> <Section position="6" start_page="710" end_page="710" type="sub_section"> <SectionTitle> 3.3 Composition Rules </SectionTitle> <Paragraph position="0"> We define three composition rules: the function application rule, the word formation rule,andthe nonlocal application rule.</Paragraph> <Paragraph position="1"> Hereinafter, let S</Paragraph> <Paragraph position="3"> i be TDLESs of the left and the right daughter nodes, respectively. In addition,</Paragraph> <Paragraph position="5"> be TDLESs of the mother node.</Paragraph> <Paragraph position="6"> Function application rule: The composition of TDL terms in the TDLESs is performed by function application, in the same manner as in the original TDL, as explained in Section 2.1. Definition 3.1 (function application rule). If This function corresponds to the behavior of the union of SLASH in HPSG. The composition in the right-hand side of Figure 5 is an example of the application of this rule.</Paragraph> <Paragraph position="7"> Word formation rule: In natural language, it is often the case that a new word is created by combining multiple words, for example, &quot;orange juice&quot;. This phenomenon is called word formation. Typed Dynamic Logic and the HPSG parser handle this phenomenon in different ways. Typed Dynamic Logic does not have any rule for word formation and regards &quot;orange juice&quot; as a single word, whereas most parsers treat &quot;orange juice&quot; as the separate words &quot;orange&quot; and &quot;juice&quot;. This requires a special composition rule for word formation to be defined. Among the constituent words of a compound word, we consider those that are not HPSG heads as word modifiers and define their value for T as o. In addition, we apply the word formation rule defined below.</Paragraph> <Paragraph position="8"> Definition 3.2 (word formation rule). If ) in Definition 3.2 is a function that returns a concatenation of p</Paragraph> <Paragraph position="10"> For example, the composition of a word modifier &quot;orange&quot; (7) and and a common noun &quot;juice&quot; (8) will generate the TDLES (9).</Paragraph> <Paragraph position="11"> Nonlocal application rule: Typed Dynamic Logic and HPSG also handle the phenomenon of wh-movement differently. In HPSG, a wh-phrase is treated as a value of SLASH,and the value is kept until the Filler-Head Schema are applied. In TDL, however, wh-movement is handled by the functional composition rule. In order to resolve the difference between these two approaches, we define the nonlocal application rule, a special rule that introduces a slot relating to HPSG SLASH to TDLESs.</Paragraph> <Paragraph position="12"> This slot becomes the third element of TD-LESs. This rule is applied when the Filler-Head Schema are applied in HPSG parse trees.</Paragraph> </Section> <Section position="7" start_page="710" end_page="710" type="sub_section"> <SectionTitle> 3.4 Unary Derivation Rules </SectionTitle> <Paragraph position="0"> In TDL, type-shifting of a word or a phrase is performed by composition with an empty category (a category that has no phonetic form, but has syntactic/semantic functions). For example, the phrase &quot;this year&quot; is a noun phrase at the first stage and can be changed into a verb modifier when combined with an empty category. Since many of the type-shifting rules are not available in HPSG, we defined unary derivation rules in order to provide an equivalent function to the type-shifting rules of TDL. These unary rules are applied independently with HPSG parse trees. (10) and (11) illus-</Paragraph> </Section> </Section> class="xml-element"></Paper>