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<Paper uid="H89-2006">
  <Title>UNIFICATION-BASED SEMANTIC INTERPRETATION IN THE BBN SPOKEN LANGUAGE SYSTEM</Title>
  <Section position="4" start_page="0" end_page="39" type="metho">
    <SectionTitle>
2 THE GRAMMAR FORMALISM
</SectionTitle>
    <Paragraph position="0"> The BBN grammar formalism, described in detail in (Boisen et al., 1989), is most closely related to Definite Clause Grammar (Pereira and Warren, 1980). Rules consist of a single left-hand term and zero or more right hand terms. Terms can have features, whose values are themselves terms. Variables, indicated by the &amp;quot;:&amp;quot; prefix, indicate identity between different slots in and among terms.</Paragraph>
    <Paragraph position="1"> Here is an example of a simple grammar rule written in this formalism:  This rule says that a VP can derive a transitive verb followed by an object NP. The person, number and mood of the VP -- indicated by the variables :P, :N and :MOOD respectively -- must be the same as the person, number and mood of the verb.</Paragraph>
    <Paragraph position="2"> The distinguishing feature of the BBN formalism, in which it differs from DCG, is its strict system of typing. Each functor that can head a term is associated with a type and a fixed set of argument positions that are also typed. For example, the functor &amp;quot;AGR&amp;quot; has the type AGREEMENT, and the argument types PERSON and NUMBER. Variables are also typed; for example the variable :P has the type PERSON and the variable :N has the type NUMBER. A given grammar written in the formalism, then, has two components: a set of functor type declarations and a set of grammar rules. This typing feature enables the the grammar rules to be statically checked against the type declarations. A large class of errors in the grammar m such as accidentally ommitted features, transpositions or mispellings -- can be caught when the grammar is loaded into the computer instead of through run-time debugging. This capability has proven very useful indeed in the course of creating and modifying a large (~800 rule) grammar.</Paragraph>
  </Section>
  <Section position="5" start_page="39" end_page="40" type="metho">
    <SectionTitle>
3 BASIC EXAMPLES
</SectionTitle>
    <Paragraph position="0"> We now present a very simple example of the use of semantic features in unification, adding semantic features to the VP rule considered earlier. These new features are underlined:</Paragraph>
    <Paragraph position="2"> This rule passes up a formula as the semantics of the VP, indicated by the variable :WFF. The semantics of the subject of the clause, indicated by the variable :SUB J, is passed down to the verb, as is the semantics of the object NP, indicated by the variable :OBJ.</Paragraph>
    <Paragraph position="3"> For the transitive verb &amp;quot;hire&amp;quot;, we have the following lexical rule:</Paragraph>
    <Paragraph position="5"> We can think of this rule in functional terms as taking semantic arguments :SUBJ and :OBJ and returning as a value the wff (HIRE' :SUBJ :OBJ). Note the placement of semantic arguments to the verb inside the subcategorizafion term (headed by the functor &amp;quot;TRANSITIVE&amp;quot;) instead of at the top-level of the &amp;quot;V&amp;quot;. This means that a verb with a differing number of arguments, such as &amp;quot;give&amp;quot;, has a different subcategorization functor with a corresponding number of argument places for the semantic translations of these arguments.</Paragraph>
    <Paragraph position="6"> Like Definite Clause Grammar, the BBN formalism does not require that every term on the right-hand side of the rule derive a non-empty string. This is neccesary to handle traces. But empty-deriving terms are also made use of in some grammar rules as so-called &amp;quot;constraint nodes&amp;quot;. These do not generate a real constituent of the parse tree, but instead stipulate that a particular relationship hold between these constituents. For example, in the rule turning a PP into a (post-copular) VP, we require that the PP semantics be construable as a specifying a predication on the subject of the VP:</Paragraph>
    <Paragraph position="8"> PREDICATIVE-PP is a constraint clause, taldng the semantics of an NP and a PP and returning a wff that is a predication that the PP may be construed as making of the NP. As the rule shows, the wff returned is passed up as the translation of the VP.</Paragraph>
    <Paragraph position="9"> Constraint nodes are used not only to impose a stipulation on the constituents of a rule but also to allow for~ multiple ways to satisfy these constituents. For example, the PP &amp;quot;in the Information Sciences Division&amp;quot; can apply differently to different subjects: to a person, in which case it indicates that the person is an employee of the Information Sciences Division, or to a department, in which it indicates that the department is one of those making up the Information Sciences Division.</Paragraph>
    <Paragraph position="10"> So far we have not indicated how the system would distinguish between these two cases: in other words, how it would tell a person and a department apart. In the next section, we discuss the internal structure of NP semantics where such information is stored.</Paragraph>
  </Section>
  <Section position="6" start_page="40" end_page="40" type="metho">
    <SectionTitle>
4 REPRESENTATION OF PHRASAL SE-
MANTICS
</SectionTitle>
    <Paragraph position="0"> The variables :SUBJ and :OBJ in the previously presented lexical rule for &amp;quot;hire&amp;quot; are typed to range over term structures that represent noun phrase semantics. These structures have the following form:</Paragraph>
  </Section>
  <Section position="7" start_page="40" end_page="40" type="metho">
    <SectionTitle>
(Q-TERM QUANTIFIER VAR NOM-SEM)
</SectionTitle>
    <Paragraph position="0"> The QUANTIFIER is one of the many quanfifiers that correspond to determiners in English: ALl, SOME, THE and various WH determiners. Proper NPs are treated as definite descriptions in our system; they are thus represented using the THE quantifier.</Paragraph>
    <Paragraph position="1"> The VAR denotes a variable of the object language, and is left uninstantiated (being filled in by a unique object-language variable by the quantifier module). The NOM-SEM represents the set that the quantification ranges over, it effectively represents the semantics of the head of the NP after modification by the NP's other constituents.</Paragraph>
    <Paragraph position="2"> NOM-SEMs have a structure of their own. The pnncipal functor of this type is NOM, which has the argument structure:</Paragraph>
  </Section>
  <Section position="8" start_page="40" end_page="40" type="metho">
    <SectionTitle>
(NOM PARAM-LIST SET-EXP SORT)
</SectionTitle>
    <Paragraph position="0"> The PARAM-LIST is a (possibly empty) list of parameters, used to indicate the free argument places in a relational noun. SET-EXP is a logical expression which denotes a set of individuals. SORT is a term structure which represents the semantic class of the elements of SET-EXP.</Paragraph>
    <Paragraph position="1"> Note that this means that the SORT field of the NOM is accesible, via one level of indirection, from the Q-TERM NP representation. It is this feature which provides the means for selectional restriction based on semantic class.</Paragraph>
    <Paragraph position="2"> Semantic classes (arranged in a hierarchy) are represented as complex terms, whose arguments may themselves be complex terms. A translation (described in the next section) is established between semantic classes and these terms such that non-empty overlap between two classes corresponds to unifiability of the corresponding terms, and disjointness between classes corresponds to non-unifiability of the corresponding terms.</Paragraph>
    <Paragraph position="3"> As an example, we give a second version of the rule for &amp;quot;hire&amp;quot;, this time incorporating the selectional restriction that a department hires a person:  The use of the numbers &amp;quot;1&amp;quot; and &amp;quot;2&amp;quot; above is intended to indicate the multiple occurrences of the complex forms they label. (Note that this is simply the Common Lisp (Steele Jr., 1984) convention for re-entrant list structure in the rule above. This is at present only used for notational compactness; the system does not currently attempt to take computational advantage of re-entrancy during unification or other processing.) Adjective phrase semantic representations (ADJ-SEMs) come in two varieties:</Paragraph>
  </Section>
  <Section position="9" start_page="40" end_page="40" type="metho">
    <SectionTitle>
(MODIFYINO-ADJ NOM-SEM NOM-SEM)
and
(PREDICATIVE-ADJ NP-SEMANTICS WFF)
</SectionTitle>
    <Paragraph position="0"> These represent different semantic types of adjective, and will be explained in a later section.</Paragraph>
    <Paragraph position="1"> The last major category whose semantic representation we consider here is the prepositional phrase. PPs in our system are given only partial semantic interpretations consisting of the preposition of the PP and the translation of the PP's NP object. Their representations are thus of the following form:</Paragraph>
  </Section>
  <Section position="10" start_page="40" end_page="41" type="metho">
    <SectionTitle>
(PP-SEM PREP NP-SEMANTICS)
5 ENCODING SEMANTIC CLASSES AS
TERMS
</SectionTitle>
    <Paragraph position="0"> The translation from semantic classes to complex terms can be performed systematically. In this section we present an algorithm for translating semantic classes to terms, designed to work on taxonomies of semantic classes represented in a system such as KL-ONE (Schmolze and Israel, 1983) or NIKL (Moser, 1983).</Paragraph>
    <Paragraph position="1"> It has the advantage, important from the point of view  of such systems, that it correctly handles the distinction between &amp;quot;primitive&amp;quot; and &amp;quot;defined&amp;quot; classes --&amp;quot;defined&amp;quot; meaning that the class is simply an intersection of two or more other classes.</Paragraph>
    <Paragraph position="2"> The algorithm is seen in Figure 1, where the main work is done by the function TRANSLATE. Throughout, the symbol &amp;quot;:ANY&amp;quot; indicates a &amp;quot;don't care&amp;quot; variable, unifying with anything. This is in fact the only use of variables made. The operation REGULARIZI:~ is used to remove non-primitive classes from the taxonomy, and set them aside. It is simple and we do not give it here.</Paragraph>
    <Paragraph position="3"> We now consider the classes PERSON, MALE, FE-MALE, ADULT, CHILD, MAN and PRIEST. MALE and FEMALE are disjoint sub-classes of PERSON, as are ADULT and CHILD. MAN is the class which is the intersection of ADULT and MALE. PRIEST is a sub-class of MAN, but not identical to it. Following are the translations the algorithm in Figure 1 gives to several of these classes:</Paragraph>
    <Paragraph position="5"> Essentially, the algorithm works by mapping each set of mutnzlly disjoint children of the class to an argument place of the term to be associated with that class. The term associated with a class has the same depth as the depth of the class in the laxonomy.</Paragraph>
    <Paragraph position="6"> The Iranslation produces by this algorithm are similar to those produced by the algorithm by Mellish (Mellish, 1988). We claim two advantages for ours. First, and as already pointed out, it takes into account the difference between &amp;quot;if&amp;quot; (primitive) and if-and-only-if (nonprimitive) axiomitizations, where it would seem that the Mellish algorithm does not. Second, it is simpler, not requiring such notions as &amp;quot;paths&amp;quot; and extensions &amp;quot;to&amp;quot; and &amp;quot;beyond&amp;quot; them.</Paragraph>
    <Paragraph position="7"> As a final comment on the issue of encoding semantic classes as terms, we note that there is another encoding method which may have been overlooked: that is, encoding each class as a term which has the same number of arguments as there are classes. It works as follows. In the argument position corresponding to the class being translated put a &amp;quot;1&amp;quot;, and put a &amp;quot;1&amp;quot; in argument positions corresponding to subsuming classes as well. In argument positions corresponding to disjoint classes put a &amp;quot;0&amp;quot;. In all other positions put a &amp;quot;dont-care&amp;quot; variable. While perhaps using space inefficiently, this encoding will have all the desired properties.</Paragraph>
  </Section>
  <Section position="11" start_page="41" end_page="44" type="metho">
    <SectionTitle>
6 ANALYSIS OF NOUN PHRASES AND
NOUN MODIFIERS
</SectionTitle>
    <Paragraph position="0"> The following is a simplified version of the rule for regular count noun phrases:</Paragraph>
    <Paragraph position="2"> This rule generates NPs that have at least a determiner and a head noun, and which have zero or more prenominal superlative or comparative adjectives (&amp;quot;fastest&amp;quot;, &amp;quot;bigger&amp;quot; etc.), prenominal positive adjectives (&amp;quot;red&amp;quot;,&amp;quot;aUeged&amp;quot;) and adjuncts (&amp;quot;in the house&amp;quot;, &amp;quot;that came from Florida&amp;quot;). Its effect is to take the NOM-SEM semantics of the head noun (the N-BAR) and thread it through the various modifications, add a quantifier and a variable for quantification and deliver the resulting pack-&amp;quot; age as the semantics for the whole NP.</Paragraph>
    <Paragraph position="3"> The initial NOM-SEM comes from the N-BAR, and is signified by :NOM1, the variable in that position. It is first of all passed to the DETERMINER. Along with a quantifier, :Q, the DETERMINER passes back a possibly modified NOM-SEM, :NOM2. The reason for this is that the determiner may be possessive, and a possessive determiner effectively functions as a noun modifier which enters into scope relations with other modifiers of the NP. Consider the noun phrase &amp;quot;John's best book&amp;quot;.</Paragraph>
    <Paragraph position="4"> This cannot be analyzed as (SET X (BEST' BOOK') (EQUAL (AUTHOR-OF X) JOHN')) that is, as the subset of the best books in the world that also happen to be written by John. Instead, it must be analyzed as:</Paragraph>
    <Paragraph position="6"> The essential point is that the possessive DETERMINER must carry out its modification before other elements of the NP can, yet must still follow all other modifications in affixing a quantifier to the final result of the NP. If the determiner is conceived of as just a higher-order function returning a single value, as in Montague Grammar, it is difficult to see how this can be done. The virtue of our unification approach is that it allows the determiner to return as separate values both a quantifier and a suitably modified nominal.</Paragraph>
    <Paragraph position="7"> If the determiner is not possessive it simply passes up the same NOM-SEM it was originally given. The NOM-SEM returned by the DETERMINER, whether modified or not, is then passed down to the adjuncts of the NP as :NOM2, which modify it and return :NOM3. This is then passed to the regular (non-superlative) prenominal adjectives for further modification, returning :NOM4. Finally, :NOM4 is passed to the constituent OPTNON-POSADJP, the optional superlative adjectives. The final NOM-SEM, :NOM5, is passed up to become an element of the complete Q-TERM semantics of the NP.</Paragraph>
    <Paragraph position="8"> As an example of the action of the modifying elements in the above rule, consider the following rule for generating an NP adjunct from a PP:</Paragraph>
    <Paragraph position="10"> The NOM-SEM passed in from the containing NP, :NOM1, is in turn passed down to a constraint node, MODIFYING-PP, which takes the semantics of the PP, :PP, and &amp;quot;computes&amp;quot; the modified NOM-SEM, :NOM2, which is then passed back to the NP as the result of the modification.</Paragraph>
    <Paragraph position="11"> MODIFYING-PP is used to encompass different kinds of PP modification. Relational modification, where the PP essentially fills in an argument, is handled by the following solution to MODIFYING-PP:  Since this rule is a constraint node solution, its fight-hand side is empty. It unifies the NP object of the PP with the &amp;quot;parameter NP&amp;quot; of the argument nominal. Of course, it will not be unifiable if the argument nominal does not contain a parameter NP, or if the parameter NP of the argument nominal contains the wrong semantic type.</Paragraph>
    <Paragraph position="12"> The lexical rule for relational noun &amp;quot;salary&amp;quot; is as follows: null  Note that requirement that the filler of the slot be of sort PERSON, and the co-occurence of this filler inside the NOM's set expression.</Paragraph>
    <Paragraph position="13"> Of course PPs can also occur in a predicative sense. For example, a person can be &amp;quot;in&amp;quot; in a department. To handle this we have the following solution to to the constraint node PREDICATWE-PP:</Paragraph>
    <Paragraph position="15"> Note that this constraint solution will only unify if the class of the NP object of the PP unifies with DEPTS, and the class of the NP being predicated of unifies with PERSON.</Paragraph>
    <Paragraph position="16"> When such a PP occurs as an adjunct to an NP, the derivation passes through the following indirect &amp;quot;lifting&amp;quot;  Although the right-hand side of the rule is in this case not empty, it will like all constraint nodes derive the empty string in the end.</Paragraph>
    <Paragraph position="17">  Similar distinctions of modificational power are seen in the case of adjectives, where an adjective like &amp;quot;average&amp;quot; or &amp;quot;previous&amp;quot; has the power to abstract over free parameters of the noun meaning, and an adjective like &amp;quot;female&amp;quot; does not. Consider the rule below:  This rule generates a string of one or more adjectives. Nominal semantics is threaded through the adjectives right to left. Adjectives like &amp;quot;previous&amp;quot;, with the power to modify the whole noun, have a semantic representation headed by the functor &amp;quot;MODIFYING-ADJ&amp;quot;, while adjectives like &amp;quot;female&amp;quot;, which only operate upon individual elements of the noun's extension, have a representation headed by the functor &amp;quot;PREDICATIVE-ADJ&amp;quot;. The constraint node MODIFYING-ADJ-READING accepts the first kind of adjective unchanged and lifts the second kind to the appropriate level. Note that while predicative PPs and adjectives can be &amp;quot;lifted&amp;quot; to the noun modifying level, the converse is not true. That is, the system does not allow &amp;quot;That value is previous&amp;quot; or &amp;quot;That salary is of Clark&amp;quot;.</Paragraph>
  </Section>
  <Section position="12" start_page="44" end_page="44" type="metho">
    <SectionTitle>
7 CONSTRAINT NODES AND THEIR
IMPACT ON PARSING
</SectionTitle>
    <Paragraph position="0"> Constraint nodes are generally useful in that they allow one to give a name to a particular condition and use it in multiple places throughout the grammar. Consider verbs which take PPs and ADJPs as complements. In &amp;quot;John became happy&amp;quot;, it is intended that that the adjective &amp;quot;happy&amp;quot; apply to the subject &amp;quot;John&amp;quot;. It would not make sense to say &amp;quot;The table became happy&amp;quot;. Similarly, in &amp;quot;I put the book on the floor&amp;quot;, the PP &amp;quot;on the floor&amp;quot; is intended to apply to the object NP &amp;quot;the book&amp;quot; and it would not make sense to say &amp;quot;I put the idea on the floor&amp;quot; Semantic type constraints in such cases clearly hold not just between the verb and its various arguments, but between the arguments themselves. A constraint node like PREDICATIVE-PP can be used to express this relationship between arguments where it is needed.</Paragraph>
    <Paragraph position="1"> The HARC system currently employs a bottom-up left-to-right parser. The decision to use a bottom-up parser was made in order to facilitate the eventual handling of fragmentary and ill-formed input.</Paragraph>
    <Paragraph position="2"> The parser is based on the algorithm of Graham, Harrison and Ruzzo (Susan L. Graham, 1980), but has been modified to work with a unification grammar(Haas, to appear). Formally speaking, this algorithm can parse the kind of grammar we have been discussing without any modification, since the constraint nodes and their solutions can simply be incorporated into the algorithm's empty symbols table.</Paragraph>
    <Paragraph position="3"> For a non-toy domain, however, this increases the size of the parse tables intolerably. We have therefore modified the algorithm so that it treats constraint node empty symbols specially, not expanding them when the parse tables are built but instead waiting until parse time where it solves them top-down through a process that might be thought of as a kind of all-paths non-backtracking Prolog. null A problem still appears when constraint nodes receive traces as arguments. Until a trace is bound, it of course contains very little information, and hence unifies with almost any constraint node solution. Since bottom-up parsing often hypothesizes traces, there is a consequent combinatorial explosion which can lead to slow parsing.</Paragraph>
    <Paragraph position="4"> The obvious solution to this problem is simply to defer the attempt to solve constraint nodes until the point in the parse where they have received adequate instantiafion. The definition of &amp;quot;adequate&amp;quot; clearly differs from constraint node to constraint node: in the case of PREDICATIVE-PP it might be that the preposition and class of NP object be known. Until constraint nodes are sufficiently instantiated to bother solving, they can simply be carried as extra riders on chart edges, being passed up as new edges are built. At the time of writing this solution is in the process of being implemented.</Paragraph>
  </Section>
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