Processing English with a Generalized Phrase Structure Grammar

Home , Phrase structure grammar, Transformational syntax

PROCESSING ENGLISH WITH A GENERALIZED PHRASE STRUCTURE GRAMMAR

Jean Mark Gawron, Jonathan King, John Lamping, Egon Loebner, Eo Anne Paulson, Geoffrey K. Pullum, Ivan A. Sag, and Thomas Wasow

Computer Research Center Hewlett Packard Company 1501 Page Mill Road Palo Alto, CA 94304

ABSTRACT can be achieved without detailed syntactic analysis. There is, of course, a massive This paper describes a natural language pragmatic component to human linguistic processing system implemented at Hewlett-Packard's interaction. But we hold that pragmatic inference Computer Research Center. The system's main makes use of a logically prior grammatical and components are: a Generalized Phrase Structure semantic analysis. This can be fruitfully modeled Grammar (GPSG); a top-down parser; a logic and exploited even in the complete absence of any transducer that outputs a first-order logical modeling of pragmatic inferencing capability. representation; and a "disambiguator" that uses However, this does not entail an incompatibility sortal information to convert "normal-form" between our work and research on modeling first-order logical expressions into the query discourse organization and conversational language for HIRE, a relational database hosted in interaction directly= Ultimately, a successful the SPHERE system. We argue that theoretical language understanding system wilt require both developments in GPSG syntax and in Montague kinds of research, combining the advantages of semantics have specific advantages to bring to this precise, grammar-driven analysis of utterance domain of computational linguistics. The syntax structure and pragmatic inferencing based on and semantics of the system are totally discourse structures and knowledge of the world. domain-independent, and thus, in principle, We stress, however, that our concerns at this highly portable. We discuss the prospects for stage do not extend beyond the specification of a extending domain-independence to the lexical system that can efficiently extract literal meaning semantics as well, and thus to the logical semantic from isolated sentences of arbitrarily complex representations. grammatical structure. Future systems will exploit the literal meaning thus extracted in more ambitious applications that involve pragmatic I. INTRODUCTION reasoning and discourse manipulation.

This paper is an interim progress report on The system embodies two features that linguistic research carried out at Hewlett-Packard simultaneously promote extensibility, facilitate Laboratories since the summer of 1981. The modification, and increase efficiency. The first is research had three goals: (1) demonstrating the that its grammar is context-free in the informal computational tractability of Generalized Phrase sense sometimes (rather misleadingly) used in Structure Grammar (GPSG), (2) implementing a discussions of the autonomy of grammar and GPSG system covering a large fragment of English, pragmatics: the syntactic rules and the semantic and (3) establishing the feasibility of using GPSG translation rules are independent of the specific for interactions with an inferencing knowledge application domain. Our rules are not devised ad base. hoc with a particular application or type of interaction in mind. Instead, they are motivated Section 2 describes the general architecture by recent theoretical developments in natural of the system. Section 3 discusses the grammar language syntax, and evaluated by the usual and the lexicon. A brief dicussion of the parsing linguistic canons of simplicity and generality. No technique used in found in Section 4. Section 5 changes in the knowledge base or other exigencies discusses the semantics of the system, and Section deriving from a particular context of application 6 presents ~ detailed example of a parse-tree can introduce a problem for the grammar (as complete with semantics. Some typical examples distinct, of course, from the lexicon). that the system can handle are given in the Appendix. The second relevant feature is that the grammar ir the- system is context-free in the sense The system is based on recent developments of formal language theory. This makes the in syntax and semantics, reflecting a modular view extensive mathematical literature on context-free in which grammatical structure an~ abstract logical phrase structure grammars (CF-PSG's) directly structure have independent status. The relevant to the enterprise, and permits utilization understanding of a sentence occurs in a number of of all the well-known techniques for the stages, distinct from each other and governed by computational implementation of context-free different principles of organization. We are grammars. It might seem anachronistic to base a opposed to the idea that language understanding language understanding system on context-free

74 parsing. As Pratt (1975, 423) observes: "It is translation rule. The syntax-semantics match is fashionable these days to want to avoid all realized as follows: each rule is a triple consisting reference to context-free grammars beyond warning of a rule name, a syntactic statement (~ormally a students that they are unfit for computer local condition on node admissibility), and a consumption as far as computational linguistics is semantic translation, specifying how the concerned." Moreover, widely accepted arguments higher-order logic representations of the daughter have been given in the linguistics literature to the nodes combine to yield the correct translation for effect that some human languages are not even the mother. = weakly context-free and thus cannot possibly be described by a CF-PSG. However, Gazdar and The present GPSG system has five Pullum (1982) answer all of these arguments, components : showing that they are either formally invalid or empirically unsupported or both. It seems 1. Grammar appropriate, therefore, to take a renewed interest a. Lexicon in the possibility of CF-PSG description of human b. Rules and Metarules languages, both in computational linguistics and in 2. Parser and Grammar Compiler linguistic research generally. 3. Semantics Handler 4. Disambiguator 5. HIRE database 2. COMPONENTSOF THE SYSTEM 3. GRAMMARAND LEXICON The linguistic basis of the GPSG linguistic system resides in the work reported in Gazdar The grammar that has been implemented thus (1981, 1982) and Gazdar, Pullum, and Sag (1981). 1 far is only a subset of a much larger GPSG These papers argue on empirical and theoretical grammar that we have defined on paper. It grounds that context-freeness is a desirable nevertheless describes a broad sampling of the constraint on grammars. It clearly would not be basic constructions of English, including a variety so desirable, however, if (1) it led to lost of prepositional phrase constructions, noun-noun generalizations or (2) it resulted in an compounds, the auxiliary system, genitives, unmanageable number of rules in the grammar. questions and relative clauses, passives, and Gazdar (1982) proposes a way of simultaneously existential sentences. avoiding these two problems. Linguistic generalizations can be captured in a context-free Each entry in the lexicon contains two kinds grammar with a metagrammor, i.e. a higher-level of information about a lexical item, syntactic and grammar that generates the actual grammar as its semantic. The syntactic part of an entry consists language. The metagrammar has two kinds of of a syntactic feature specification; this includes, statements: inter alia, information about any irregular morphology the item may have, and what is known (1) Rule schemata. These are in the linguistic literature as strict basically like ordinary rules, except that subcategorization information. In our terms the they contain variables ranging over latter is information linking lexical items of a categories and features. particular category to specific environments in which that category is introduced by phrase (2) Metarules. These are implicational structure rules. Presence in the lexical entry for statements, written in the form ===>B, an item I of the feature R (where R is the name which capture relations between rules. A of a rule) indicates that / may appear in metarule ===>t~ is interpreted as saying, structures admitted by R, and absence indicates "for every rule that is an instantiation of that it may not. the schema =, there is a corresponding rule of form [5." Here 13 will be @(~), where 8 The semantic information in a lexical entry is issome mapping specified partly by the sometimes simple, directly linking a lexical item general theory of grammar and partly in with some HIRE predicate or relation. With verbs the metarule formulation. For instance, or prepositions, there is also a specification of it is taken to be part of the theory of what case roles to associate with particular grammar that @ preserves unchanged the arguments (cf. below for discussion of case roles). subcategorization (rule name) features of Expressions that make a complex logical rules (cf. below). contribution to the sentence in which they appear witl in general have complicated translations. Thus every has the translation- The GPSG system also assumes the Rule-to-Rule Hypothesis, first advanced by Richard Montague, which requires that each syntactic rule be associated with a single semantic 2. There is a theoretical issue here about whether semantic translation rules need to be stipulated for each syntactic rule or whether there is a general way of predicting their form. See I. See also Gazdar, Pullum, Sag, and Wasow Klein and Sag (t981) for an attempt to develop the (1982) for some further discussion and comparison latter view, which is not at present implemented with other work in the linguistic literature. in our system.

75 Passive sentences are thus analyzed directly, and not reduced to the form of active sentences in the course of being analyzed, in the way that is (LAMBDA P (LAMBDA Q ((FORALL X (P X)) familiar from work on transformational grammars and on ATN's. However, this does not mean that --> (Q x)))), no relation between passives and their active This indicates that it denotes a function which counterparts is expressed in the system, because takes as argument a set P, and returns the set of the rules for analyzing passives are in a sense properties that are true of all members of that set derivatively defined on the basis of' rules for (cf. below for slightly more detailed discussion). analyzing actives.

A typical rule looks like this: More difficult than treating passives and the like, and often cited as literally impossible within a V N]! N!I2: ((V N!!2) N!!)> context-free grammar'," is treating constructions like questions and relative clauses. The apparent The exclamation marks here are our notation for difficulty resides in the fact that in a question like the bars in an X-bar category system. (See Which employee has Personnel reported that Anne Jackendoff (1977) for a theory of this thinks has performed outstandingly?, the portion type--though one which differs on points of detail beginning with the third word must constitute a from ours.) The rule has the form . string analyzable as a sentence except that at some Here a is the name 'VP109'; b is a condition that point it must lack a third person singular noun will admit a node labeled 'V!' if it has three phrase in a position where such a noun phrase daughter nodes labeled respectively 'V' (verb), could otherwise have occurred. If it lacks no 'Nit' (noun phrase at the second bar level), and noun phrase, we get ungrammatical strings of the 'NI!' (the numeral 2 being merely an index to type *Which employee has Personnel reported that permit reference to a specific symbol in the Anne thinks Montague has performed semantics, the metarules, and the rule compiler, outstandingly?. If it lacks a noun phrase at a and is not a part of the category label); and c is position where the verb agreement indicates a semantic translation rule stating that the V something other than a singular one is required, constituent translates as a function expression we get ungrammaticalities like *Which employee has taking as its argument the translation of the Personnel reported that Anne thinks have second N!!, the result being a function expression performed outstandingly?. The problem is thus to be applied to the translation of the first N!!. one of guaranteeing a grammatical dependency across a context that may be arbitrarily wide, By a general convention in the theory of while keeping the grammar context-free. The grammar, the rule name is one of the feature technique used is introduced into the linguistic values marked on the lexical head of any rule that literature by Gazdar (1981). It involves an introduces a lexical category (as this one augmentation of the nonterminal vocabulary of the introduces V). Only verbs marked with that grammar that permits constituents with "gaps" to feature value satisfy this rule. For example, if we be treated as not belonging to the same category include in the lexicon the word give and assign to as similar constituents without gaps. This would it the feature VPI09, then this rule would generate be an unwelcome and inelegant enlargement of the the verb phrase gave Anne a job. grammar if it had to be done by means of case-by-case stipulation, but again the use of a A typical metarule is the passive metarule, metagrammar avoids this. Gazdar (1981) proposes which looks like this (ignoring semantics): a new set of syntactic categories of the form a/B, where ~ and 15 are categories from the basic nonterminal vocabulary of the grammar. These are V NI! W > => V[PAS] W>> called slash categories. A slash category e/B may W is a string variable ranging over zero or more be thought of as representing a constituent of category symbols. The metarule has the form => >, where N is a name and and We employ a method of introducing slash categories are schemata that have rules as their instantiations that was suggested by Sag (1982): a metarule when appropriate substitutions are made for the stating that for every rule introducing some B free variables. This metarule says that for every under = there is a parallel rule introducing 15/~ rule that expands a verb phrase as verb followed under =/~. In other words, any constituent can by noun phrase followed by anything else have a gap of type ~" if one of its daughter (including nothing else), there is another rule that constituents does too. Wherever this would lead to expands verb phrase as verb with passive a daughter constituent with the label [/~' in some morphology followed by whatever followed the noun phrase in the given rule. The metarule PAS would apply to grammar rule VP109 given above, yielding the rule: 3. ~ regard was given a job not as a passive V[PAS] N{!> verb phrase itself but as a verb phrase containing the verb be plus a passive verb phrase containing As we noted above, the rule number feature is given and a job. preserved here, so we get Anne was given a job, where the passive verb phrase is given a job, but not *Anne was hired a job. 3 4. See Pullum and Gazdar (1982) for references.

76 rule, another metarule allows a parallel rule representations derived at each node are referred without the ~'/;r, and therefore defines rules that to as the Logical Representation (LR). allow for actual gaps--i.e., missing constituents. In this way, complete sets of rules for describing The disambiguator provides the crucial the unbounded dependencies found in interrogative transition from LR to HIRoE queries; the and relative clauses can readily be written. Even disambiguator uses information about the sort, or long-distance agreement facts can be (and are) domoin of definition, of various terms in the logical captured, since the morphosyntactic features representation. One of the most important relevant to a specific case of agreement are functions of the disambiguator is to eliminate present in the feature composition of any given ~'. parses that do not make sense in the conceptual scheme of HIRE.

4. PARSING HIRE is a relational database with a certain amount of inferencin9 capability. It is implemented The system is initialized by expanding out in SPHERE, a database system which is a the grammar. That is, tile metarules are applied descendant of FOL (described in Weyhrauch to the rules to produce the full rule set, which is (1980)). Many of the relation-names output by then compiled and used by the parser. Metarules the disambiguator are derived relations defined by are not consulted during the process of parsing. axioms in SPHERE. The SPHERE environment was One might well wonder about the possible benefits important for this application, since it was of the other alternative: a parser that made the essential to have something that could process metarule-derived rules to order each time they first-order logical output, and SPHERE does just were needed, instead of consulting a precompiled that. A noticeable recent trend in database theory list. This possibility has been explored by Kay has been a move toward an interdisciplinary (1982). Kay draws an analogy between metarules comingling of mathematical logic and relational and phonological rules, modeling both by means of database technology (see especially Gallaire and finite state transducers. We believe that this line Minker (1978) and Gallaire, Minker and Nicolas is worth pursuing; however, the GPSG system (198])). We regard it as an important fact about currently operates off a precompiled set of rules. the GPSG system that links computational linguistics to first-order logical representation Application of ten metarules to forty basic just as the work referred to above has linked rules yielded 283 grammar rules in the 1/1/82 first-order logic to relational database theory. We version of the GPSG system. Since then the believe that SPHERE offers promising prospects for grammar has been expanded somewhat, though the a knowledge representation system that is current version is still undergoing some principled and general in the way that we have debugging, and the number of rules is unstable. tried to exemplify in our syntactic and semantic The size of the grammar-plus-metarules system rule system. Filman, Lamping and Montalvo (]982) grows by a factor of five or six through the rule present details of some capabilities of SPHERE that compilation. The great practical advantage of we have not as yet exploited in our work, using a metarule-induced grammar is, therefore, involving the use of multiple contexts to represent that the work of designing and revising the system viewpoints, beliefs, and modalities, which are of linguistic rules can proceed on a body of generally regarded as insuperable stumbling-blocks statements that is under twenty percent of the size to first-order logic approaches. it would be if it were formulated as a simple list of context-free rules. Thus far the linguistic work we have described has been in keeping with GPSG The system uses a standard type of presented in the papers cited above. However two top-down parser with no Iookahead, augmented semantic innovations have been introduced to slightly to prevent it from looking for a given facilitate the disambiguator's translation from LR to constituent starting in a given spot more than a HIRE query. As a result the linguistic system once. It produces, in parallel, all legal parse version of LR has two new properties: trees for a sentence, with semantic translations associated with each node. (1) The intensional logic of the published work was set aside and LR was designed to be an extensional first-order language. Although 5. SEMANTICS constituent translations built up on the way to a root node may be second-order, the system- The semantics handler uses the translation maintains first-order reducibility. This rule associated with a node to construct its reducibility is illustrated by the following analysis semantics from the semantics of its daughters. of noun phrases as second-order properties This construction makes crucial use of a procedure (essentially the analysis of Montague (]970)). For that we call Cooper storage (after Robin Cooper; example, the proper name Egon and the quantified see below). In the spirit of current research in noun phrase every opplicant are both translated as formal semantics, each syntactic constituent is sets of properties: associated directly with a single logic expression (modulo Cooper Storage), rather than any program or procedure for producing such an expression. Our semantic analysis thus embraces the principle of "surface compositionality." The semantic

77 Egon = LAMBDA P (P EGON) (1968), these mediating relations are called case Every applicant = LAMBDA P (FORALL X roles. ((APPLICANT X) --> (P X))) The disambiguator narrows the case roles Egon is translated as the set of properties down to specific knowledge base relations. To true of Egon, and every applicant, as the set of take a simple example, Anne works for HP has a properties true of all applicants. Since basic logical representation reducible to: predicates in the logic are first-order, neither of the above expressions can be made the direct (EXISTS SIGMA (AND (EMPLOYMENT SIGMA) • argument of any basic predicate; instead the (AG SIGMA ANNE) argument is some unique entity-level variable (LOC SIGMA HP))) which is later bound to the quantifier-expression by quantifying in. This technique is essentially Here SIGMA is a variable over situations or event the storage device proposed in Cooper (1975). instantiations, s The formula may be read, "There One advantage of this method of "deferring" the is an employment-situation whose Agent is Anne introduction into the interpretation process of and whose Location is HP." The lexical entry for phrases with quantifier meanings is that it allows work supplies the information that its subject is an for a natural, nonsyntactic treatment of scope Agent and its complement a Location. The ambiguities. Another is that with a logic limited to disambiguator now needs to further specify the first-order predicates, there is still a natural case roles as HIRE relations. It does this by treatment for coordinated noun phrases of treating each atomic formula in the expression apparently heterogeneous semantics, such as Egon locally, using the fact that Anne is a person in and every applicant. order to interpret AG, and the fact that HP is an organization in order to interpret LOC. In this (2) HIRE represents events as objects. All case, it interprets the AG role as objects in the knowledge base, including events, employment.employee and the LOC role as belong to various sorts. For our purposes, a sort employment.organization. is a set. HIRE relations are declared as properties of entities within particular sorts. For example, The advantages of using the roles in Logical there is an employment sort, consisting of various Representation, rather than going directly to particular employment events, and an predicates in a knowledge base, include (1) the employment.employee relation as well as ability to interpret at least some prepositional employment .organization and employment.manager phrases, those known as adjuncts, without relations. More conventional relations, like subcategorizing verbs specially for them, since the employee.manager are defined as joins of the basic case role may be supplied either by a verb or a event relations. This allows the semantics to make preposition. (2) the option of interpreting some fairly obvious connections between verbs and 'vague' verbs such as have and give using case events (between, say, the verb work and events roles without event types. These verbs, then, of employment), and to represent different become "purely" relational. For example, the relations between a verb and its arguments as representation of Egon gave Montague a job would different first-order relations between an event be: and its participants. Although the lexical treatment sketched here is clearly domain (EXISTS SIGMA (AND ((SO EGON) SIGMA) dependent (the English verb work doesn't ((POS MONTAGUE) SIGMA) necessarily involve employment events), it was (EMPLOYMENT SIGMA))) chosen primarily to simplify the ontology of a first implementation. As an alternative, one might Here SO 'source' will pick out the same consider associating work with events of a sort employment.manager relation it did in the example labor, one of whose subsorts was an employment above; and POS 'possession' is the same relation as event, defining employments as those labors that associated with have. Here the situation-type associated with an organization. is supplied by the translation of the noun job. It is important to realize that this representation is Whichever choice one makes about the basic derived without giving the noun phrase a job any event-types of verbs, the mapping from verbs to special treatment. The lexical entry for give HIRE relations cannot be direct. Consider a contains the information that the subject is the sentence like Anne work5 for Egon. The HIRE source of the direct object, and the direct object representation will predicate the the possession of the indirect object. If there employment.manager relation of a particular were lamps in our knowledge base, the derived employment event and a particular manager, and representation of Egon gave Montague a lamp would the employment.employee relation of that same simply be the above formula with the predicate event and ,~knl,~. Yet where Egon in this example lamp replacing employment. The possession is picked out with the employment .manager relation would hold between Montague and some relation, the sentence Anne worl

78 lamp, and the disambiguator would retrieve such matters. The syntax of a lexical entry is , where Two active research goals of the current L is the spelling of the item, C is its grammatical project are to give all lexical entries domain category and feature specification (if other than independent representations, and to make all the default set) and T is its translation into LR. knowledge base-specific predicates and relations the exclusive province of the disambiguator. One Consider how we assign an LR to a sentence important means to that end is case roles, which like Every applicant is competent. The translation allow us a level of abstract, purely "linguistic" of every supplies most of the structure of the relations to mediate between logical representations universal quantification needed in LR. It and HIRE queries. Another is the use of general represents a function from properties to functions event types such as labor, to replace event-types from properties to truth values, so when applied specific to HIRE, such as employments. The case to applicant it yields a constituent, namely every roles maintain a separation between the domain applicant, which has one of the property slots representation language and LR. Insofar as that filled, and represents a function from properties separation is achieved, then absolute portability to truth-values; it is: of the system, up to and including the lexicon, is an attainable goal. (LAMBDA P (FORALL X ((APPLICANT X) IMPLIES (P X)))) Absolute portability obviously has immediate practical benefits for any system that expects to This function can now be applied to the function handle a large fragment of English, since the denoted by competent, i.e. effort in moving from one application to another will be limited to "tuning" the disambiguator to a ( LAMBDA Y new ontology, and adding "specialized" vocabulary. (EXPERT.LEVEL HIGH Y)) The actual rules governing the production of first-order logical representations make no This yields: reference to the facts of HIRE. The question remains of just how portable the current lexicon (FORALL X is; the answer is that much of it is already domain ((APPLICANT X) independent. Quantifiers like every (as we saw in IMPLIES the discussion of NP semantics) are expressed as (LAMBDA Y logical constants; verbs like give are expressed (EXPERT.LEVEL HIGH Y)) X)) entirely in terms of the case relations that hold among their arguments. Verbs like work can be And after one more lambda-conversion, we abstracted away from the domain by a simple have: extension. The obvious goal is to try to give domain independent representations to a core ( FORALL X vocabulary of English that could be used in a ((APPLICANT X) variety of application domains. IMPLIES (EXPERT.LEVEL HIGH X)))

6. AN EXAMPLE Fig. 1 shows one parse tree that would be generated by the above rules, together with its We shall now give a slightly more detailed logical translation. The sentence is Bill illustration of how the syntax and compositional interviewed every applicant. The complicated semantics rules work. We are still simplifying translation of the VP is necessary because considerably, since we have selected an example INTERVIEW is a one-place predicate that takes an where rote frames are not involved, and we are entity-type argument, not the type of function not employing features on nodes. Here we have that every applicant denotes. We thus defer the grammar of a trivial subset of English: combining the NP translation with the verb by using Cooper storage. A translation with a stored <$1: S -> NP VP: (NP Vp)>" NP is represented above in angle-brackets. Notice DET N: (DET N)> that at the S node the NP every applicant is still V NP: iV NP)> stored, but the subject is not stored. It has V A: A> directly combined with the VP, by taking the VP as an argument. INTERVIEW is itself a two-place Suppose that the lexicon associated with the above predicate, but one of its argument places has been rules is: filled by a place-holding variable, X1. There is th~Js ~ only one slot left. The translation can now the part of the semantics that isn't in storage:

~~79 Fig. 1. A typical parse tree~~

~~S <((LAMBDA P (P BILL))(INTERVIEW X1)), <(LAMBDA P (FORALL X ((APPLICANT X) IMPLIES (P X)))) >>~~

~~NP VP ((LAMBDA P (P BILL))) <(INTERVIEW X1) (LAMBDA P (FORALL X ((APPLICANT X) IMPLIES (P X))))>~~

~~Bill V NP INTERVIEW (LAMBDA P (FORALL X ((APPLICANT X) interviewedI IMPLIES (P X)))) ~i ICANT DET applicant LAMBDA Q (LAMBDA P (FORALL X ((Q X) IMPLIES (P X))))~~

~~every~~

~~7. CONCLUSION~~

((LAMBDA P (P BILL))(INTERVIEW X1)) :> What we have outlined is a natural language ((INTERVIEW Xl) BILL) system that is a direct implementation of a linguistic theory. We have argued that in this The function (LAMBDA P (P BILL)) has been case the linguistic theory has the special appeal of evaluated with P set to the value (INTERVIEW computational tractability (promoted by its X1); this is a. conventional lambda-conversion. context-freeness), and that the system as a whole The rule for storage retrieval is to make a offers the hope of a happy marriage of linguistic one-place predicate of the sentence translation by theory, mathematical logic, and advanced lambda-binding the placeholding variable, and then computer applications. The system's theoretical to apply the NP translation as a function to the underpinnings give it compatibility with current result. The S-node translation above becomes: research in Generalized Phrase Structure Grammar, and its augmented first order logic gives it compatibility with a whole body of ongoing ((LAMBDA P research in the field of model-theoretic semantics. (FORALL X ((APPLICANT X) IMPLIES (P X)))) The work done thus far is only the first (LAMBDA X1 ((INTERVIEW X1) BILL))) step on the road to a robust and practical natural language processor, but the guiding principle [lambda-conversion] ==> throughout has been extensibility, both of the grammar, and of the applicability to various (FORALL X ((APPLICANT X) IMPLIES spheres of computation. ((LAMBDA X1 ((INTERVIEW X1) BILL)) X))) ACKNOWLEDGEMENT [lambda-conversion] ::> Grateful acknowledgement is given to two (FORALL X ((APPLICANT X) IMPLIES brave souls, Steve Gadol and Bob Kanefsky, who (((INTERVIEW X) BILL)))) helped give this system some of its credibility by implementing the actual hook-up with HIRE. This is the desired final result. Thanks are also due Robert Filman and Bert Raphael for helpful comments on an early version of this paper. And a special thanks is due Richard Weyhrauch, for encouragement, wise advice, and comfort in times of debugging.

~~80 APPENDIX REFERENCES~~

This appendix lists some sentences that are Barwise, Jon, and John Perry. 1981. actually translated into HIRE and answered by the "Situations and attitudes." Journal of current system. Declarative sentences presented Philosophy 78, 668-692. to the system are evaluated with respect with Cooper, Robin. 1975. Montague's Semantic their truth value in the usual way, and thus also Theory and Transformational Syntax. function as queries. Doctoral dissertation, University of Massachusetts, Amherst. SIMPLE SENTENCES Fillmore, Charles. 1968. "The Case for Case." In Bach, Emmon and Robert Harms. 1. HP employs Egon. Universals in Linguistic Theory. New 2. Egon works for HP. York: Holt, Rinehart and Winston. 3. HP offered Montague the position. Filman, Robert E., John Lamping, and Fanya 4. HP gave Montague a job. Nlontalvo. 1982. "Metalanguage and 5. Montague got a job from HP. Metareasoning." Submitted for 6. Montague's job is at HP presentation at the AAAI National 7. HP's offer was to Capulet. Conference on Artificial Intelligence, 8. Montague had a meeting with Capulet. Carnegie-Mellon University, Pittsburgh, 9. Capulet has an offer from Xerox. Pennsylvania. 10. Capulet is competent. Gallaire, Herv$, and Jack Minker, eds. 1978. Logic and Data Bases. New York: Plenum IMPERATIVES AND QUESTIONS Press. Gallaire, Herv$, Jack Minker, and Jean Marie 11. Find the programmers in CRC Nicolas, eds. 1981. Advances in Date who attended the meeting. Base Theory. New York: Plenum Press. 12. How many applicants for the Gazdar, Gerald. 1981. "Unbounded position are there? Dependencies and Coordinate Structure." 13. Which manager interviewed Capulet? Linguistic Inquiry 12, 155-184. 14. Whose job did Capulet accept? Gazdar, Gerald. 1982. "Phrase Structure 15. Who is a department manager? Grammar." In Pauline Jacobson and 16. Is there a LISP programmer Geoffrey K. Pullum, eds. The Nature of who Xerox hired? Syntactic Representation. Dordrecht: D. 17. Whose job does Montague have? Reidel. 18. How many applicants Gazdar, Gerald, Geoffrey K. Pullum, and Ivan did Capulet interview? A. Sag. In press. "Auxiliaries and Related Phenomena." Language. RELATIVE CLAUSES Gazdar, Gerald, Geoffrey K. Pullum, Ivan A. Sag, and Thomas Wasow. 1982. 19. The professor whose student Xerox "Coordination and Transformational hired visited HP. Grammar". Linguistic Inquiry 13. 20. The manager Montague met with hired Jackendoff, Ray. 1977. ~" Syntax. Cambridge: the student who attended Berkeley. MIT Press. Kay, Martin. 1982. "When Metarules are not NOUN-NOUN COMPOUNDS Metarules." Ms. Xerox Palo Alto Research Center. 21. Some Xerox programmers visited HP. Montague, Richard. 1970. "The Proper 22. Montague interviewed a job applicant. Treatment of Quantification in English." 23. Who are the department managers? in Richmond Thomason, ed. 1974. Formal 24. How many applicants have a LISP Philosophy. New Haven: Yale University programming background? Press. Pratt, Vaughan R. 1975. "LINGOL a COORDINATION progress report." Advance Papers of the Fourth /nternational Joint Conference on 25. Who did Montague interview and visit? Artificia/ /nte//igence, Tbilisi, Georgia, 26. Which department's position did USSR, 3-8 September 1975. Cambridge, every programmer and a manager MA: Artificial Intelligence Laboratory. from Xerox apply for? 422-428. Pullum, Geoffrey K. and Gerald Gazdar. PASSIVE AND EXISTENTIAL SENTENCES 1982. Natural languages and context-free languages. Linguistics and phitos.ophy 4. 27. Egon was interviewed by Montague. Sag, Ivan A. 1982. "Coordination, Extraction, 28. There is a programmer and Generalized Phrase Structure who knows LISP in CRC. Grammar." Linguistic Inquiry 13. Weyhrauch, Richard W. 1980. "Prolegomena to INFINITIVAL COMPLEMENTS a theory of mechanized formal reasoning." Artificial Intelligence, 1, pp. 133-170. 29. Montague managed to get a job at HP. 30. HP failed to hire a programmer with Lisp programming background.