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<Paper uid="P85-1022">
  <Title>A Computational Semantics for Natural Language</Title>
  <Section position="2" start_page="172" end_page="172" type="metho">
    <SectionTitle>
2. Ontological Assumptions
</SectionTitle>
    <Paragraph position="0"> To get started, we make the following assumptions about what categories of things are in the world.</Paragraph>
    <Paragraph position="1"> a. There are individuals. These include objects of the usual kind (such as Ron and Nancy) as well as situations.</Paragraph>
    <Paragraph position="2"> Situations comprise states (such as Ron's being tall) and events (such as Ron giving his inaugural address on January 21, 1985).</Paragraph>
    <Paragraph position="3"> b. There are relations (subsuming properties). Examples are COOKIE (= the property of being a cookie) and BUY (= the relation which Nancy has to the cookies she buys). Associated with each relation is a characteristic set of roles appropriate to that relation (such as AGENT, PATIENT, LO-CATION, etc.) which can be filled by individuals. Simple situations consist of individuals playing roles in relations. Unlike properties and relations in situation semantics \[Barwise &amp; Perry 1983\[, our relations do not have fixed arity (number of arguments). This is made possible by taking explicit account of roles, and has important linguistic consequences. Also there is no distinguished ontological category of locations~ instead, the location of an event is just the individual that fills the LOCATION role.</Paragraph>
    <Paragraph position="4"> c. Some relations are sortal relations, or sorts. Associated with each sort {but not with any non-sortal relation) is a criterion of identity for individuals of that sort \[Cocchiarella 1977, Gupta 1980 I. Predicates denoting sorts occur in the restrictor-clanses of quantifiers (see section 4.2 below), and the associated criteria of identity are essential to determining the truth values of quantified assertions.</Paragraph>
    <Paragraph position="5"> Two important sorts of situations are states and events.</Paragraph>
    <Paragraph position="6"> One can characterize a wide range of subsorts of these (which we shall call situation types) by specifying a particular configuration of relation, individuals, and roles. For example, one might consider the sort of event in which Ron kisses Nancy in the Oval Office, i.e. in which the relation is KISS, Ron plays the AGENT role, Nancy plays the PATIENT role, and the Oval Office plays the LOCATION role. One might also consider the sort of state in which Ron is a person, i.e. in which the relation is PERSON, and Ron plays the INSTANCE role. We assume that the INSTANCE role is appropriate only for sortal relations.</Paragraph>
    <Paragraph position="7"> d. There are concepts, both subjective and objective.</Paragraph>
    <Paragraph position="8"> Some individuals are information-processing organisms that use complex symbolic objects (subjective concepts) as computational media for information storage and retrieval, inference, planning, etc. An example is Ron's internal representation of the property COOKIE. This representation in turn is a token of a certain abstract type ~'COOKIE, an objective concept which is shared by the vast majority of speakers of English. t Note that the objective concept ~COOKIE, the property COOKIE, and the extension of that property (i.e. the set ofall cookies) are three distinct things that play three different roles in the semantics of the English noun cookie.</Paragraph>
    <Paragraph position="9"> e. There are computational processes in organisms for manipulating concepts e.g. methods for constructing complex concepts from simpler ones, inferencing nmchanisms, etc. Concepts of situations are called propositions; organisms use inferencing mechanisms to derive new propositions from old. To the extent that concepts are accurate representations of existing things and the relations in which they stand, organisms can contain information. We call the system of objective concepts and concept-manipulating mechanisms instantiated in an organism its conceptual ~ystem.</Paragraph>
    <Paragraph position="10"> Communities of organisms can share the same conceptual system.</Paragraph>
    <Paragraph position="11"> f. Communities of organisms whose common conceptual system contains a subsystem of a certain kind called a grammar can cornnmnicate with each other. Roughly, grammars are conceptual subsystems that mediate between events of a specific type (calh:d utterances) and other aspects of reality. Grammars enable organisms to use utterances to give and receive information about the world. This is the subject of sections 4-6.</Paragraph>
  </Section>
  <Section position="3" start_page="172" end_page="175" type="metho">
    <SectionTitle>
3. The Internal
Representation Language: NFLT
</SectionTitle>
    <Paragraph position="0"> The translation of input sentences into a logical formalism of some kind is a fairly standard feature of computer systems for natural-language understanding, and one which is shared by the HPSG system. A distinctive feature of this system, however, is the particular logical formalism involved, which is called NFLT (Neo-Fregean Language of Thought). 2 This is a new logical language that is being developed to serve as the internal representation medium in computer agents with natural language capabilities. The language is the result of augmenting and partially reinterpreting the standard predicate calculus formalism in several ways, some of which will be described very briefly in this section. Historically, the predicate calculus was deve|oped by mathematical logicians as an explication of the logic of mathematical proofs, in order to throw light on the nature of purely mathematical concepts and knowledge.</Paragraph>
    <Paragraph position="1"> Since many basic concepts that are commonplace in natural language (including concepts of belief, desire, intention, temporal change, causality, subjunctive conditionality, etc.) play no role in pure mathematics, we should not be especially surprised to find that the predicate calculus requires supplementation in order to represent adequately and naturally information involving these concepts. The belief that such supplementation is needed has led to the design of NFLT, While NFLT is much closer semantically to natural language than is the standard predicate calculus, and is to some extent inspired by psycho\[ogistic considerations, it is nevertheless a formal logic admitting of a mathematically precise semantics. The intended semantics incorporates a Fregean distinction between sense and denotation, associated principles of compositionality, and a somewhat non-Fregean theory of situations or situation-types as the denotations of sentential formulas.</Paragraph>
    <Section position="1" start_page="172" end_page="172" type="sub_section">
      <SectionTitle>
3.1. Predicates of Variable Arity
</SectionTitle>
      <Paragraph position="0"> Atomic formulas in NFLT have an explicit ro\[e-marker for each argument; in this respect NFLT resembles semantic network formalisms and differs from standard predicate t We regard this notion of obiective concept as the appropriate basis on which to reconstruct, ia terms of information processing, Saussure's notions of ~ignifiant (signifier) and #ignifig (signified) \[1916!, as well an Frege's notion of Sinn (sense, connotation) \[1892 I.</Paragraph>
      <Paragraph position="1"> ~&amp;quot; The formalism is called ~neo-Fregean&amp;quot; because it incorporates many of the semantic ideas of Gottlob Frege, though it also departs from Frege's ideas in several significant ways. It is called a &amp;quot;language of thought&amp;quot; because unlike English, which is first and foremost a medium of communication, NFLT is designed to serve as a medium of reasoning in computer problem-solving systems, which we regard for theoretical purposes as thinking organisms, (Frege referred to his own logical formalism, Begriffsschrift, an a &amp;quot;formula language for pure thought&amp;quot; \[Frege 1879, title and p. 6 (translation)\]).</Paragraph>
      <Paragraph position="2">  calculus, in which the roles are order-coded. This explicit representation of roles permits each predicate-symbol in NFLT to take a variable number of arguments, which in turn makes it possible to represent occurrences of the same verb with the same predicate-symbol, despite differences in valence (i.e. number and identity of attached complements and adjuncts). This clears up a host of problems that arise in theoretical frameworks (such an Montague semantics and situation semantics) that depend on fixed-arity relations (see \[Carlson forthcoming\] and \[Dowry 1982\] for discussion). In particular, new roles (corresponding to adjuncts or optional complements in natural language) can be added as required, and there is no need for explicit existential quantification over ~missing arguments&amp;quot;.</Paragraph>
      <Paragraph position="3"> Atomic formulas in NFLT are compounded of a base-predicate and a set of rolemark-argument pairs, as in the following example:  (la) English: Ron kissed Nancy in the Oval Office on April 1, 1985.</Paragraph>
      <Paragraph position="4"> (lb) NFLT Internal Syntax: (kiss (agent . con) (patient . nancy) (location . oval-office) (time . 4-i-85) ) (lc) NFLT Display Syntax: ( KISS agt: RON p~:nt: NANCY loc: OVAL-OFFICE art: 4-i-8S)  The base-predicate 'KISS' takes a variable number of arguments, depending on the needs of a particular context. \[n ,iLe display syntax, the arguments are explicitly introduced by abbreviated lowercase role markers.</Paragraph>
    </Section>
    <Section position="2" start_page="172" end_page="172" type="sub_section">
      <SectionTitle>
3.2. Sortal Quantification
</SectionTitle>
      <Paragraph position="0"> Quantificational expressi..s in NFLT differ from those in predicate calculus by alway~ rontaining a restrictor-clause consisting of a sortal predication, in addition to the u, sual scope-clause, as in the following example:  Note that we always quantify over instances of a sort, i.e. the quantified variable fills the instance role in the restrictorclause. null This style of quantifier is superior in several ways to that of the predicate calcuhls for the purposes of representing commonsense knowledge. It is intuitively more natural, since it follows the quantificational pattern of English. More importantly, it is more general, being sufficient to handle a number of natural language determiners such as many, most, few, etc., that cannot be represented using only the unrestricted quantification of standard predicate calculus (see \[Wallace 1965\], {Barwise &amp; Cooper 1981\]). Finally, information carried by the sortal predicates in quantifiers (namely, criteria of identity for things of the various sorts in question) provides a sound semantic basis for counting the members of extensions of such predicates (see section 2, assumption c above).</Paragraph>
      <Paragraph position="1"> Any internal structure which a variable may have is irrelevant to its function as a uniquely identifiable place-holder in a formula, in particular, a quantified formula can itself serve as its own ~bound variable&amp;quot;. This is how quantitiers are actually implemented in the HPSG system; in the internal (i.e. implementation) syntax for quantified NFLTformulas, bound variables of the usual sort are dispensed with in favor of pointers to the relevant quantified formulas. Thus, of the three occurrences of X5 in the displayformula (2b), the first has no counterpart in the internal syntax, while the last two correspond internally to LISP pointers back to the data structure that implements (2b).</Paragraph>
      <Paragraph position="2"> This method of implementing quantification has some important advantages. First, it eliminates the technical problems of variable clash that arise in conventional treatments. There are no ~alphabetic variants&amp;quot;, just structurally equivalent concept tokens. Secondly, each occurrence of a quantified ~bound variable&amp;quot; provides direct computational access to the determiner, restrictor-clause, and scope-clause with which it is associated.</Paragraph>
      <Paragraph position="3"> A special class of quantificational expressions, called quantifier expressions, have no scope-clause. An example  is: (3) NFLT Display Syntax:  (SOME gl (COOKIE inst: xl) ) Such expressions translate quantified noun phrases in English, e.g. a cookie.</Paragraph>
    </Section>
    <Section position="3" start_page="172" end_page="174" type="sub_section">
      <SectionTitle>
3.3. Causal Relations and
Non-Extensionality
</SectionTitle>
      <Paragraph position="0"> According to the standard semantics for the predicate calculus, predicate symbols denote the extensions of relations (i.e. sets of ordered n-tuples) and sentential formulas denote truth values. By contrast, we propose a noneztensional semantics for NFLT: we take predicate symbols to denote relations themselves (rather than their extensions), and sentential formulas to denote situations or situation types (rather than the corresponding truth values). 3 The motivation for this is to provide for the expression of propositions involving causal relations among situations, as in the following example: a The distinction between situations and situation types corresponds roughly to the fnite/infinitive distinction in natural language. For discussion of this within the framework of situation semantics, see \[Cooper 1984\].</Paragraph>
      <Paragraph position="1">  Now, the predicate calculus is an extensional language in the sense that the replacement of categorical subparts within an expression by new subparts having the same extension must preserve the extension of the original expression. Such replacements within a sentential expression must preserve the truth-value of the expression, since the extension of a sentence is a truth-value. NFLT is not extensional in this sense. \[n particular, some of its predicatesymbols may denote causal relations among situations, and extension-preserving substitutions within causal contexts do not generally preserve the causal relations. Suppose, for example, that the formula (4b) is true. While the extension of the NFLT-predicate 'GENOTYPE-XYZW' is the set of animals of genotype XYZW, its denotation is not this set, but rather what Putnam I1969\] would call a &amp;quot;physical property&amp;quot;, the property of having the genotype XYZW. As noted above (section 2, assumption d) a property is to be distinguished both from the set of objects of which it holds and from any concept of it. Now even if this property were to happen by coincidence to have the same extension as the property of being a citizen of Polo Alto born precisely at noon on I April \].956, the substitution of a predicate-symbol denoting this latter property for 'GENOTYPE-XYZW' in the formula (4b) would produce a falsehood.</Paragraph>
      <Paragraph position="2"> However, NFLT's lack of extensionality does not involve any departure from compositional semantics. The denotation of an NFLT-predicate-symbol is a property; thus, although the substitution discussed earlier preserves the extension of 'GENOTYPE-XYZW', it does not preserve the denotation of that predicate-symbol. Similarly, the denotation of an NFLT-sentence is a situation or ~ttuation-type, as distinguished both from a mere truth-val,e and from a propositionJ Then, although NFLT is not at~ extensional language in the standard sense, a Fregean a.alogue of the principle of extensionality does hold for it: The replacement of subparts within an expression by new subparts having the same denotation must preserve the denotation of the original expression (see \[Frege 18921). Moreover, such replacements within an NFLT-sentence must preserve tile truth-value of that sentence, since the truth-value is determined by the denotation.</Paragraph>
    </Section>
    <Section position="4" start_page="174" end_page="175" type="sub_section">
      <SectionTitle>
3.4. Intentionality and
Conceptual Raising
</SectionTitle>
      <Paragraph position="0"> The NFLT notation for representing information about propositional attitudes is an improved version of the neo-Fregean scheme described in \[Creary 1979 I, section 2, which is itself an extension and improvement of that found in \[McCarthy 1979\]. The basic idea underlying this scheme is that propositional attitudes are relations between people (or other intelligent organisms) and propositions; both ternm of such relations are taken as members of the domain of discourse. Objective propositions and their component objective concepts are regarded a.s abstract entities, roughly on a par with numbers, sets, etc. They are person-independent components of situations involving belief, knowledge, desire, and the like. More specifically, objective concepts are abstract types which may have as token~ the subjective concepts of individual organisms, which in turn are configurations of information and associated procedures in various individual memories (cf. section 2, assurnption d above).</Paragraph>
      <Paragraph position="1"> Unlike Montague semantics \[Montague 19731, the semantic theory underlying NFLT does not imply that an organism necessarily believes all the logical equivalents of a proposition it believes. This is because distinct propositions have as tokens distinct subjective concepts, even if they necessarily have the same truth-value.</Paragraph>
      <Paragraph position="2"> Here is an example of the use of NFLT to represent information concerning propositional attitudes:  (5a) English: Nancy wants to tickle Ron.</Paragraph>
      <Paragraph position="3"> (5b) NFLT Display Syntax: (WANT appr: NANCY prop: t(TICKLE agt:I ptnt:RON)) \[n a Fregean spirit, we assign to each categorematic expression of NFLT both a sense and a denotation. For ex- null ample, the denotation of the predicate-constant 'COOKIE' is the property COOKIE, while the sense of that constant is a certain objective concept - the ~standard public&amp;quot; concept of a cookie. We say that ~COOKIE' expresses its sense and denotes its denotation. The result of appending the &amp;quot;conceptual raising&amp;quot; symbol ' l&amp;quot; to the constant &amp;quot;COOKIE' is a new constant, ' TCOOKIE', that denotes the concept that 'COOKTE' expresses (i.e. ' 1&amp;quot;' applies to a constant and forms a standard name of the sense of that constant). By appending multiple occurrences of ' T' to constants, we obtain new constants that denote concepts of concepts, concepts of concepts of concepts, etc. 5 \[n expression (5b), ' 1&amp;quot; is not explicitly appended to a constant, but instead is prefxed to a compound expression. When used in this way, &amp;quot; 1&amp;quot; functions as a syncategorematic operator that &amp;quot;conceptually raises&amp;quot; each categorematic constant within its scope and forms a term incorporating the raised constants and denoting a proposition. 4 Thus, something similar to what Barwise and Perry call &amp;quot;situation semantics&amp;quot; 119831 is to be provided for NFLTexpressions, insofar as those expressions involve no ascription of propositional attitudes (the Barwise-Perry semantics for ascriptions of propositional attitudes takes a quite different approach from that to be described for NFLT in the next section): s For further details concerning this Fregean conceptual hierarchy, see \[Creary 1979 I, sections 2.2 and 2.3.1. Capitalization, '$'-postfixing, and braces are used there to do the work done here by the symbol ' t'.</Paragraph>
      <Paragraph position="4">  Thus, the subformula ' T (TICKLE aqt:I ptnt:RON) ' is the name of a proposition whose component concepts are the relation-concept TTICKLE and the individual concepts TI and I'RON. This proposition is the sense of the unraised subformula ' (TICKLE agt: I pint: RON) '.</Paragraph>
      <Paragraph position="5"> The individual concept TI, the minimal concept of self, is an especially interesting objective concept. We assume that for each sufficiently self-conscious and active organism X, X's minimal internal representation of itself is g token of TI. This concept is the sense of the indexical pronoun I, and is itself indexical in the sense that what it is a concept of is determined not by its content (which is the same for each token), but rather by the context of its use. The content of this concept is partly descriptive but mostly procedural, consisting mainly of the unique and important role that it plays in the information-processing of the organisms that have it.</Paragraph>
    </Section>
  </Section>
  <Section position="4" start_page="175" end_page="175" type="metho">
    <SectionTitle>
4. Lexicon
</SectionTitle>
    <Paragraph position="0"> HPSG's head grammar takes as its point of departure Saussure's \[1916 t notion of a sign. A sign is a conceptual object, shared by a group of organisms, which consist,~ of two associated concepts that we call (by a conventional abuse of language) a phonolooical representation and a semantic representation. For example, members of the English-speaking community share a sign which consists of an internal representation of the utterance-type /kUki/ together with an internal representation of the property of being a cookie.</Paragraph>
    <Paragraph position="1"> In a computer implementation, we model such a conceptual object with a data object of this form: (6) (cookie ;COOKIE} Here the symbol 'cookie' is a surrogate for a phonological representation (in fact we ignore phonology altogether and deal only with typewritten English input). The symbol 'COOKIE' (a basic constant of NFLT denoting the prop-erty COOKIE) models the corresponding semantic representation. We call a data object such as (6) a lezical entry. Of course there must be more to a language than simple signs like (6). Words and phrases of certain kinds can characteristically combine with certain other kinds of phrases to form longer expressions that can convey :,nformation about the world. Correspondingly, we assume that a grammar contains in addition to a lexicon a set of grammatical rules (see next section) for combining simple signs to produce new signs which pair longer English expressions with more complex NFLT translations. For rules to work, each sign must contain information about how it figures in the rules.</Paragraph>
    <Paragraph position="2"> We call this information the (syntactic) category of the sign. Following established practice, we encode categories as specifications of values for a finite set of features. Augmented with such information, lexical signs assume forms such as these:</Paragraph>
    <Paragraph position="4"> Such features as MAJOR (major category), AGR (agreement), and VFORM (verb form) encode inherent syntactic properties of signs.</Paragraph>
    <Paragraph position="5"> Still more information is required, however. Certain expressions (heads) characteristically combine with other expressions of specified categories (complements) to form larger expressions. (For the time being we ignore optional elements, called adjuncts.) This is the linguistic notion of subcategoeization. For example, the English verb touches subcategorizes for two NP's, of which one must be thirdperson-singular. We encode subcategorization information as the value of a feature called SUBCAT. Thus the value of the SUBCAT feature is a sequence of categories. (Such features, called stack-valued features, play a central role in the HG account of binding. See \[Pollard forthcomingi. ) Augmented with its SUBCAT feature, the \[exical sign (2b) takes the form: (8) {kisses ; KZflS; \[MAJOR: V; VFORM: FIN 1 SUBCAT: NP, NP-3RDSG} (Symbols like 'NP' and 'NP-3RDSG' are shorthand for certain sets of feature specifications). For ease of reference, we use traditional grammatical relation names for complements. Modifying the usage of Dowry \[1982\], we designate them (in reverse of the order that they appear in SUBCAT) as subject, direct object, indirect object, and oblique objects. (Under this definition, determiners count as subjects of the nouns they combine with.) Complements that themselves subcategorize for a complement fall outside this hierarchy and are called controlled complements. The complement next in sequence after a controlled complement is called its controller.</Paragraph>
    <Paragraph position="6"> For the sign (8) to play a communicative role, one additional kind of information is needed. Typically, heads give information about relation.~, while complements give information about the roles that individuals play in those relations. Thus lexical signs must assign roles to their complements. Augmented with role-assignment information, the lexical sign (8) takes the form: (9) (kisses ; KISS; IMAJOR: V: VFORM: FIN i SUBCAT: ~NP, patient), (NP-3RDSG, agent? } Thu~ (9) assign,, the roles AGENT and PATIENT to the sub-ject and direct object respectively. (Note: we assume that nouns subcategorize for a determiner complement and assign it the instance role. See section 6 below.)</Paragraph>
  </Section>
  <Section position="5" start_page="175" end_page="178" type="metho">
    <SectionTitle>
5. Grammatical Rules
</SectionTitle>
    <Paragraph position="0"> \[n addition to the lexicon, the grammar must contain mechanisms for constructing more complex signs that mediate between longer English expressions and more complex NFLT translations. Such mechanisms are called grammatical rules. From a purely syntactic point of view, rules can be regarded as ordering principles. For example, English grammar has a rule something like this: (lO) If X is a sign whose SUBCAT value contains just one category Y, and Z is a sign whose category is consistent with Y, then X and Z can be combined to form a new sign W whose expression is got by  concatenating the expressions of X and Z.</Paragraph>
    <Paragraph position="1"> That is, put the final complement (subject} to the left of the head. We write this rule in the abbreviated form: (11) -&gt; C H \[Condition: length of SUBCAT of H = 11 The form of (11) is analogous to conventional phrase structure rules such as NP - &gt; DET N or S - &gt; NP VP; in fact (11) subsumes both of these. However, (11) has no left-hand side. This is because the category of the constructed sign (mother) can be computed from the constituent signs (daughters) by general principles, as we shall presently show.</Paragraph>
    <Paragraph position="2"> Two more rules of English are:  (12) -&gt; H C \[Condition: length of SUBCAT of H = 2 I (13) -&gt; I-I C2 C1 \[Condition: length of SUBCAT of H = 31 (12) says: put a direct object or subject-controlled complement after the head. And (13) says: put an indirect object  or object-controlled complement after the direct object. As in (11), the complement signs have to be consistent with the subcategorization specifications on the head. In (13), the indices on the complement symbols correspond to the order of the complement categories in the SUBCAT of the head.</Paragraph>
    <Paragraph position="3"> The category and translation of a mother need not be specified by the rule used to construct it. Instead, they are computed from information on the daughters by universal principles that govern rule application. Two such principles are the Head Feature Principle (HFP) (14) and the Subcategorization Principle (15): (14) Head Feature Principle: Unless otherwise specified, the head features on a mother coincide with the head features on the head daughter.</Paragraph>
    <Paragraph position="4"> (For present purposes, assume the head features are all features except SUBCAT.) (15) Subcategorization Principle: The SUBCAT value on the mother is got by deleting from the SUBCAT value on the head daughter those categories corresponding to complement daughters.</Paragraph>
    <Paragraph position="5"> (Additional principles not discussed here govern control and binding.} The basic idea is that we start with the head daughter and then process the complement daughters in the order given by the indices on the complement symbols in the rule. So far, we have said nothing about the determination of the mother's translation. We turn to this question in the next section.</Paragraph>
  </Section>
  <Section position="6" start_page="178" end_page="178" type="metho">
    <SectionTitle>
6. The Semantic Interpretation Principle
</SectionTitle>
    <Paragraph position="0"> Now we can explain how the NFLT-translation of a phrase is computed from the translations of its constituents. The basic idea is that every time we apply a grammar rule, we process the head first and then the complements in the order indicated by the rule (see \[Proudian &amp; Pollard 1985i). As each complement is processed, the corresponding category-role pair is popped off the SUBCAT stack of the head; the category information is merged (unified) with the category of the complement, and the role information is used to combine the complement translation with the head translation. We state this formally as:  (16) Semantic Interpretation Principle (SIP):  The translation of the mother is computed by the following program: a. Initialize the mother's translation to be the head daughter's translation.</Paragraph>
    <Paragraph position="1"> b. Cycle through the complement daughters, setting the mother's translation to the result of combining the complement's translation with the mother's translation.</Paragraph>
    <Paragraph position="2"> c. Return the mother's translation.</Paragraph>
    <Paragraph position="3"> The program given in (16) calls a function whose arguments are a sign (the complement), a rolemark (gotten from the top of the bead's SUBCAT stack), and an NFLT expression (the value of the mother translation computed thus far). This function is given in (17). There are two cases to consider, according as the translation of the complement is a determiner or not.</Paragraph>
    <Paragraph position="4"> (17) Function for Combining Complements: a. If the MAJOR feature value of the complement is DET, form the quantifier-expression whose determiner is the complement translation and whose restriction is the mother translation. Then add to the restriction a role link with the indicated rolemark (viz. instance} whose argument is a pointer back to that quantifier-expression, and return the resulting quantifier-expression. null b. Otherwise, add to the mother translation a role link with the indicated rolemark whose argument is a pointer to the complement translation (a quantifier-expression or individual constant). \[f the complement translation is a quantifier-expression, return the quantificational expression formed from that quantifier-expression by letting its scope-clause be the mother translation; if not, return the mother translation.</Paragraph>
    <Paragraph position="5"> The first case arises when the head daughter is a noun and the complement is a determiner. Then (17) simply returns a complement like (3). In the second case, there are two subcases according as the complement transiation is a quantifier-expression or something else (individual constant, sentential expression, propositional term, etc.) For example, suppose the head is this: (18) {jogs ; JOG; \[MAJOR: V; VFORM: FIN I SUBCAT: &lt;NP-3RDSG, agent) } If the (subject) complement translation is 'RON' (not a quantifier-expression), the mother translation is just:</Paragraph>
  </Section>
  <Section position="7" start_page="178" end_page="178" type="metho">
    <SectionTitle>
(19) {JOG aqt:RON);
</SectionTitle>
    <Paragraph position="0"> but if the complement translation is '{I~LL P3 (PERSON inst:P3)}' (a quantifier-expresslon), the mother translation is:  concatenating the expressions of X and Z. That is, put the final complement (subject) to the left of the head. We write this rule in the abbreviated form: (11) -&gt; C H \[Condition: length of SUBCAT of H = 11 The form of (11) is analogous to conventional phrase structure rules such as NP - &gt; DET N or S - &gt; NP VP; in fact (U) subsumes both of these. However, (11) has no left-hand side. This is because the category of the constructed sign (mother) can be computed from the constituent signs (daughter8) by general principles, as we shall presently show.</Paragraph>
    <Paragraph position="1"> Two more rules of English are:</Paragraph>
    <Paragraph position="3"> \[Condition: length of SUBCAT of H = 3\] (12) says: put a direct object or subject-controlled complement after the head. And (13) says: put an indirect object or object-controlled complement after the direct object. As in (11), the complement signs have to be consistent with the subcategorization specifications on the head. In (13), the indices on the complement symbols correspond so the order of the complement categories in the SUBCAT of the head.</Paragraph>
    <Paragraph position="4"> The category and translation of a mother need not be specified by the rule used to construct it. instead, they are computed from information on the daughters by universal principles that govern rule application. Two such principles are the Head Feature Principle (HFP) (14) and the  The SUBCAT value on the mother is got by deleting from the SUBCAT value on the head daughter those categories corresponding to complement daughters.</Paragraph>
    <Paragraph position="5"> (Additional principles not discussed here govern control and binding.) The basic idea is that we start with the head daughter and then process the complement daughters in the order given by the indices on the complement symbols in the rule. So far, we have said nothing about the determination of the mother's translation. We turn to this question in the next section.</Paragraph>
  </Section>
  <Section position="8" start_page="178" end_page="178" type="metho">
    <SectionTitle>
6. The Semantic Interpretation Principle
</SectionTitle>
    <Paragraph position="0"> Now we can explain how the NFLT-translation of a phrase is computed from the translations of its constituents. The basic idea is that every time we apply a grammar rule, we process the head first and then the complements in the order indicated by the rule (see !Proudiaa &amp; Pollard 19851). As each complement is processed, the corresponding category-role pair is popped off the SUBCAT stack of the head; the category information is merged (unified) with the category of the complement, and the role information is used to combine the complement translation with the head translation. We state this formally as:  (16) Semantic Interpretation Principle (SIP):  The translation of the mother is computed by the following program: a. Initialize the mother's translation to be the head daughter's translation.</Paragraph>
    <Paragraph position="1"> b. Cycle through the complement daughters, setting the mother's translation to the result of combining the complement's translation with the mother's translation.</Paragraph>
    <Paragraph position="2"> c. Return the mother's translation.</Paragraph>
    <Paragraph position="3"> The program given in (16) calls a function whose arguments are a sign (the complement), a rolemark (gotten from the top of the head's SUBCAT stack), and an NFLT expression (the value of the mother translation computed thus far). This function is given in (17). There are two cases to consider, according as the translation of the complement is a determiner or not.</Paragraph>
    <Paragraph position="4"> (17) Function for Combining Complements: a. If the MAJOR feature value of the complement is DET, form the quantifier-expression whose determiner is the complement translation and whose restriction is the mother translation. Then add to the restriction a role link with the indicated rolemark (viz. instance) whose argument is a pointer back to that quantifier-expression, and return the resulting quantifier-expression. null b. Otherwise, add to the mother translation a role link with the indicated rolemark whose argument is a pointer to the complement translation (a quantifier-expression or individual constant). If the complement translation is a quantifier-expression, return tile quantificational expression formed from that quantifier-expression by letting its scope-clause be the mother translatio,; if not, return the mother translation.</Paragraph>
    <Paragraph position="5"> The first case arises when the head daughter is a noun and the complement is a determiner. Then (17) simply returns a complement like (3). In the second c,~e. there are two subcases according as the complement translation is a quantifier-expression or something else (individual constant, sentential expression, propositional term, etc.) For example, suppose the head is this: (18) {jogs ; JOG; \[MAJOR: V; VFORM: FIN I SUBCAT: &lt;NP-3RDSG, agent.&gt;} If the (subject) complement translation is 'RON' (not a quantifier-expression), the mother translation is just:</Paragraph>
  </Section>
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