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<?xml version="1.0" standalone="yes"?> <Paper uid="J81-3001"> <Title>Roles, Co-Descriptors, and the Formal Representation of Quantified English Expressions</Title> <Section position="5" start_page="0" end_page="0" type="metho"> <SectionTitle> 3. Reference and Definite Descriptions </SectionTitle> <Paragraph position="0"> Russell's \[22\] analysis of a singular definite description required the existence of a unique object satisfying the description in order for the expression to denote anything, and hence it fails to account for the successful reference of a noun phrase like &quot;the clock&quot; in (5) Did you wind the clock? Strawson \[25\] views these definite descriptions in relativistic terms: even when the referent cannot be determined in an absolute sense, as a particular clock for example, the description still has some meaning relative to whatever the context turns out to be.</Paragraph> <Paragraph position="1"> (6) When shall we say that a hearer knows what particular is being referred to by a speaker? Consider first the following case. A speaker tells a story which he claims to be factual. It begins, &quot;A man and a boy were standing by a fountain,&quot; and it continues: &quot;The man had a drink&quot;. Shall we say that the hearer knows 5 1 choose to avoid the question of formal adequacy because almost all systems, intensional as well as extensional, are formally adequate in the sense that they are capable of representing all (effective) functions. A much more interesting question is whether they are capable of representing all functions in a natural way. which or what particular is being referred to by the subject expression in the second sentence? We might say so. For, of a certain _ range of two particulars the words &quot;the man&quot; serve to distinguish the one being referred to, by means of a description which applies only to him. But though this is, in a weak sense, a case of identification, I shall call it only a story-relative or, for short, a relative identification. For it is identification only relative to a range of particulars (a range of two members) which is itself identified only as the range of particulars being talked about by the speaker. That is to say, the hearer, hearing the second sentence, knows which particular creature is being referred to of the two particular creatures being talked about by the speaker; but he does not, without this qualification, know what particular creature is being referred to. The identification is within a certain story told by a certain speaker. It is identification within his story but not identification within history.</Paragraph> <Paragraph position="2"> Following this line of thought, sentence (5) might be represented as follows, where clock-1 describes a particular clock and the-clock-1 describes the clock relative to the discourse.</Paragraph> <Paragraph position="4"> both describe the same individual. (The term co-description is chosen over co-reference or codenotation to avoid implications of intensionality and existence.) Co-description is appropriate in (7), but surely not every occurrence of the-clock will refer to clock-1. For example, Webber \[28\] points out that in (8a) Wendy bought a yellow T-shirt that Bruce had liked.</Paragraph> <Paragraph position="5"> (8b) It cost twenty dollars.</Paragraph> <Paragraph position="6"> an appropriate description of the entity referred to by &quot;it&quot; is not &quot;the yellow T-shirt that Bruce had liked,&quot; since (8a) is true even if Bruce had liked several Tshirts (and both the speaker and the listener were aware of the fact). Nor is it &quot;the yellow T-shirt that Bruce had liked and Wendy bought,&quot; since (8b) can be true even if Wendy had bought several such Tshirts. An appropriate description is something like</Paragraph> <Paragraph position="8"> 140 American Journal of Computational Linguistics, Volume 7, Number 3, July-September 1981 William A. Martin Roles, Co-Descriptors, and the Formal Representation of Quantified English Expressions Wendy bought and that was mentioned in (8b)&quot;. Accordingly, (7) needs to be amended so that the-clock-1 is relative to the sentence &quot;did you wind the clock&quot;.</Paragraph> <Paragraph position="9"> (9) r- .............. > ............... j clock-1 room-1 house.1 = ~1 discourse. 1 real-world</Paragraph> <Section position="1" start_page="0" end_page="0" type="sub_section"> <SectionTitle> 3.1 Referential and Attributive Use of Definite Descriptions </SectionTitle> <Paragraph position="0"> Donnellan \[3\] has suggested that definite descriptions like &quot;the clock&quot; have two uses: referential and attributive. Attributive use asserts something about &quot;whoever or whatever is the so-and-so&quot;; referential use is intended to allow the hearer to identify at once, in his own terms, who or what is being talked about.</Paragraph> <Paragraph position="1"> (10) I will call the two uses of definite descriptions I have in mind the attributive use and the referential use. A speaker who uses a definite description attributively in an assertion states something about whoever or whatever is the so-and-so. A speaker who uses a definite description referentially in an assertion, on the other hand, uses the description to enable his audience to pick out whom or what he is talking about and states something about that person or thing. In the first case the definite description might be said to occur essentially, for the speaker wishes to assert something about whatever or whoever fits that description; but in the referential use the definite description is merely one tool for doing a certain job-- calling attention to a person or thing-- and in general any other device for doing the same job, another description or a name, would do as well. In the attributive use, the attribute of being the so-and-so is all important, while it is not in the referential use.</Paragraph> <Paragraph position="2"> To illustrate this distinction, in the case of a single sentence, consider the sentence, &quot;Smith's murderer is insane&quot;. Suppose first that we come upon poor Smith foully murdered. From the brutal manner of the killing and the fact that Smith was the most lovable person in the world, we might exclaim, &quot;Smith's murderer is insane&quot;. I will assume, to make it a simpler case, that in a quite ordinary sense we do not know who murdered Smith (though this is not in the end essential to the case). This I shall say, is an attributive use of the definite description.</Paragraph> <Paragraph position="3"> The contrast with such a use of the sentence is one of those situations in which we expect and intend our audience to realize whom we have in mind when we speak of Smith's murderer and, most importantly, to know that it is this person about whom we are going to say something.</Paragraph> <Paragraph position="4"> For example, suppose that Jones has been charged with Smith's murder and has been placed on trial. Imagine that there is a discussion of Jones's odd behavior at his trial.</Paragraph> <Paragraph position="5"> We might sum up our impression of his behavior by saying, &quot;Smith's murderer is insane&quot;. If someone asks to whom we are referring, by using this description, the answer here is &quot;Jones&quot;. This, I shall say, is a referential use of the definite description.</Paragraph> <Paragraph position="6"> The distinction is brought out nicely by the following pair of sentences from Moore \[17\] and their corresponding semantic net representations (Figures 4 and 5).</Paragraph> <Paragraph position="7"> (1 la) The President has been married since 1945. referential (llb) The President has lived in the White House since 1800. attributive Sentence (lla) refers to the person who is currently President, while sentence (1 lb) refers to whoever was president at each point in time since 1800. The truth of (llb) is not dependent on who is filling the role of President. In fact, we can go even farther. In the past the President has been killed and it has taken a while to swear in the new President. During this time there is no President, yet (llb) is still true. In (lla), by contrast, the referent of &quot;the President&quot;, president1, is not a role in &quot;the President is married&quot;, as shown in Figure 4. Therefore, we are not at liberty to have the referent change with time.6 The referential/attributive distinction might have been ascribed to differences of scope in quantified expressions.</Paragraph> <Paragraph position="8"> (12a) (the p : president) (Y= t since 1945) p has been married at time t. referential (12b) (V t after 1800) (the p : president) p has lived in the white house at time t. attributive</Paragraph> <Paragraph position="10"/> </Section> </Section> <Section position="6" start_page="0" end_page="0" type="metho"> <SectionTitle> 6 A method for the sequential binding of quantified variables </SectionTitle> <Paragraph position="0"> in determining the truth of an expression was introduced by Hintikka \[11\]. Although he was working with predicate calculus, he obviously had in mind the same general strategy proposed here.</Paragraph> <Paragraph position="1"> My representation, in contrast, makes it easy for the interpreter to delay the decision because it minimizes the difference between the two cases. It is also possible for the interpreter never to decide which reading is intended. For example, in a sentence such as, &quot;The president has owned a terrier since February,&quot; the listener will not be able to distinguish between the two readings. If a later sentence requires the listener to make a distinction, only a minimal alteration to the representation is required. Partee \[19\] makes an argument that further supports this approach.</Paragraph> <Paragraph position="2"> (14) ... having a particular individual in mind (the &quot;referential&quot; case) and knowing nothing about an individual other than some descriptive phrase (the &quot;attributive&quot; case) may be just two extremes on a continuum of &quot;vividness&quot;. One may consider, for instance, the case of a detective tracking down a criminal and obtaining more and more clues, including fingerprints, voice recordings, photographs of varying clarity, etc. It is not at all clear at what point the detective, who may be described as &quot;looking for the man who did so-and-so&quot; stops looking for &quot;whoever it is that did so-and-so&quot; and starts looking for a particular individual.</Paragraph> <Section position="1" start_page="0" end_page="0" type="sub_section"> <SectionTitle> 3.2 Subject Co-Descriptors (Verb Phrase Deletion) </SectionTitle> <Paragraph position="0"> Both Figures 4 and 5 employ co-description between the-President and subject-of-x, where x is the sentential predicate. Sentences (15a) and (15b) from Sag \[23\] offer further support for this convention.</Paragraph> <Paragraph position="1"> (15a) The chickens are ready to eat, and the children are too.</Paragraph> <Paragraph position="2"> (15b) John likes flying planes, and Bill does too. In these examples, the subject plays the same role in both conjuncts. That is, if the chickens are ready to be eaten, then the children are also ready to be eaten, and if the chickens are ready to do the eating, then the children are ready to do the eating. However, (15a) cannot mean that the chickens are ready to be eaten and the children are ready to do the eating. Sentence (15b) illustrates the same point. It is ambiguous whether John likes to fly planes himself or whether he would prefer someone else do the flying, but whichever way he likes the flying done, Bill will want it done the same way.</Paragraph> <Paragraph position="3"> The following sentence from Partee \[20\] has the same sort of ambiguity as (15a) and (15b) above; I will use it to illustrate how such ambiguities are dealt with in my scheme of representation.</Paragraph> <Paragraph position="4"> (16) The prosecutor believed that he would win the case, and so did the defense attorney.</Paragraph> <Paragraph position="5"> The missing verb phrase can be understood in two ways, either that the defense attorney would win or that the prosecutor would win. This can be explained in terms of my representation, as shown in (17a) and (17b) below. Note that he-1 is co-descriptive with the subject role in (17a) and with the-prosecutor-1 in (17b). Thus (17a) represents the sloppy attributive interpretation where he-1 refers to whatever the sub-ject happens to be, whereas (17b) represents the nonsloppy referential interpretation where he~l refers to the-prosecutor-1 in both conjuncts.</Paragraph> <Paragraph position="6"> 142 American Journal of Computational Linguistics, Volume 7, Number 3, July-September 1981 William A. Martin Roles, Co-Descriptors, and the Formal Representation of Quantified English Expressions</Paragraph> <Paragraph position="8"/> </Section> <Section position="2" start_page="0" end_page="0" type="sub_section"> <SectionTitle> 3.3 Restrictive and Non-Restrictive Modifiers </SectionTitle> <Paragraph position="0"> Another opposition which can be captured with the attributive/referential distinction is that between re- null strictive and non-restrictive modifiers.</Paragraph> <Paragraph position="1"> (18a) My uncle, who is 70, is bald. non-restrictive (18b) My uncle who,is 70 is bald. restrictive Sentence (18a) has a non-restrictive relative clause, &quot;who is 70&quot;, modifying, &quot;my uncle&quot;. That is, &quot;who is 70&quot; is not used to pick out the uncle who is bald, but just to give extra information about him. This sentence is equivalent to the conjunction, &quot;My uncle is bald & my uncle is 70.&quot; By contrast, in the restrictive reading (18b), &quot;who is 70&quot; picks out a particular uncle. The distinction between (18a) and (18b) can be captured as follows.</Paragraph> <Paragraph position="3"> Note that the head of the relative clause must be either attributive or referential for both main and relative clauses. It is not possible to have (20), for example. This argues that the relative pronoun &quot;who&quot; should be treated as a co-descriptor of a sentence role of the main clause, not a discourse role.</Paragraph> <Paragraph position="4"> (20) *The President, who has been married since 1945, has lived in the White House since 1800.</Paragraph> <Paragraph position="5"> 4. Discourse Iteration We have seen that explicit nesting of structural descriptions can explain the referential/attributive distinction, sloppy binding, and restrictive/descriptive relative clauses. This section will show that quantifier interpretation can also be explained in a similar manner. Consider sentence (21), which is three ways ambiguous, as shown in (22a)-(22c).</Paragraph> <Paragraph position="7"> The three readings (22a)-(22c) can be interpreted as follows. In each case, want-a-lion must be true for each boy. In (22a), a-lion-1 is attributive: it can be picked as needed for each wanting. In (22b), a-lion-1 is referential, but it refers to a role in an iteration of wanting at the discourse level. (Not surprisingly, given my account, this is a difficult reading for people to construct.) Finally, (22c) gives the by-now-familiar referential case where every boy is constrained to wanting the same lion. 7 Let us now turn to a discussion of the discourse iteration construct used in (22b). The single X in CLASS that satisfies P also satisfies Q.</Paragraph> <Paragraph position="8"> The FOR statement applies the filter P(x) in turn to each element in the CLASS, and then applies Q(x) to those elements that pass the filter. The key words EVERY, SOME, GEN, THE, and so on, specify a particular enumeration function.</Paragraph> <Paragraph position="9"> I prefer to represent quantified phrases in terms of role-in links (interpretable as Skolem dependencies) rather than iteration procedures, and to use predicates on intensions and sets in addition to predicates on individuals. By converting Woods' FOR construct to my notation, the difference between the two referential readings of &quot;every boy wants a lion&quot; can be spelled out in more detail as shown in (24a) and (24b) below. (Note that (24a) is a slight elaboration of (22b), and that (24b) is identical to (22c)). (24a) captures both the EVERY and GENeric options. In both cases, lions are individuated by the boys who want them. The individuating is represented by the role-in link (Skolem modification) from lion-1 to want-boy-lion- 1.</Paragraph> <Paragraph position="10"> (24a) Every boy wants his own lion.</Paragraph> </Section> <Section position="3" start_page="0" end_page="0" type="sub_section"> <SectionTitle> 4.1 Procedural Representation of Knowledge </SectionTitle> <Paragraph position="0"> By procedural representation of knowledge, I mean knowledge in the form of procedures. For example, the knowledge that every boy wants a lion could be cast in the form &quot;if one were to check every boy in question and count those who want lions, then the count of those who want lions would be equal to the count of the boys checked&quot;. Woods \[30\] introduced a FOR iteration construct for representing knowledge of quantified propositions procedurally. 8 Examples of the use of this construct are: 7 Partee \[19\] points out that this type of sentence and those of the previous section pose a problem for the analysis of the indefinite article in terms of the features +specific \[7\]. Something more is needed to produce all the readings. Features can be used as follows: if a hearer has decided a node is definitely attributive it can be marked +attributive, if it is referential the co-descriptor is shown. Otherwise, it is unmarked and has no co-descriptor.</Paragraph> <Paragraph position="1"> languages will see that Woods' FOR is quite limited, e.g. iteration is limited to a single variable. I use it here because it is simple, is well explained by Woods, and will facilitate comparison of my suggestions with Woods' earlier work.</Paragraph> <Paragraph position="3"> In contrast to (24a), (24b) contains no iteration at all.</Paragraph> <Paragraph position="4"> In this case, all the boys want the same lion. Since lions are not individuated with respect to boys, there is no motivation to introduce an iteration (or Skolem dePendency). On this reading, &quot;every boy wants a lion&quot; can be conceptualized just like &quot;a boy wants a lion&quot;.</Paragraph> </Section> <Section position="4" start_page="0" end_page="0" type="sub_section"> <SectionTitle> 4.2 Collectives, Distributives, and Pluralities </SectionTitle> <Paragraph position="0"> In applying predicates to pluralities, we must be careful not to confuse a predicate on a plurality with a predicate on a collective. If a process, like wanting, is done by a plurality, then a plurality of wantings occurs. This contrasts with a collective, which acts as a single unit. Fauconnier \[5\] demonstrates this distinction with (25).</Paragraph> <Paragraph position="1"> As a further example, observe that in (26) Everybody gave $1000 to many of the men.</Paragraph> <Paragraph position="2"> we must decide whether the men receiving money receive $1000 apiece or just participate in a group receiving $1000. We must also decide whether &quot;everybody&quot; acted individually or collectively. Note that one cannot personally receive $1000 if $1000 is given to a group he is in, but one can be personally told the news if the news is told to a group he is in. From this we see that the distributive reading may or may not require a separate instance of some state or process for each individual.</Paragraph> <Paragraph position="3"> A plural noun group may be understood in any of the three ways. Vendler \[27\] gives examples intended to show that the choice between &quot;each&quot; and &quot;every&quot; influences our preferences.</Paragraph> <Paragraph position="4"> (27) Suppose I show you a basket of apples and I tell you, &quot;Take all of them&quot;. If you started to pick them one by one I should be surprised. My offer was sweeping: you should take the apples, if possible, &quot;en bloc&quot;. Had I said, &quot;Take every one of them,&quot; I should not care how you took them, provided you do not leave any behind. If I say, &quot;Take each of them,&quot; one feels that the sentence is unfinished. Something like, &quot;Take each of them and examine them in turn,&quot; is expected.</Paragraph> <Paragraph position="5"> Thus I expect you to take them one after the other not missing any.</Paragraph> <Paragraph position="6"> &quot;All&quot; favors collective interpretation, but permits distributive interpretation. &quot;Every&quot; favors distributive interpretation. &quot;Each&quot; strongly favors distributive interpretation and favors distinct actions for each individual. null</Paragraph> </Section> <Section position="5" start_page="0" end_page="0" type="sub_section"> <SectionTitle> 4.3 Multiple Iterations </SectionTitle> <Paragraph position="0"> The previous sections suggested that an iteration need be constrUcted only when two descriptions in the sentence are related in a special way, e.g., where one is individuated by the other. Otherwise, predicates on collectives or pluralities provide an adequate description. In this way, I avoid iteration, which &quot;is relatively expensive from a computational perspective. There are other ways to eliminate iterations. For example, the apparent double iteration in sentence (28a) can be reduced to a single iteration. Formula (28b) represents the natural reading where each cork is associated with one bottle. It might appear that it requires two nested FOR loops as in (28c), but in fact, it can be implemented with a single loop (28d).</Paragraph> <Paragraph position="1"> (28a) Each cork is fastened to each bottle by a small wire basket.</Paragraph> <Paragraph position="2"> (28b) (Y=x) (Vy) if x is a cork & y is a bottle & x is the cork in bottle y then x is fastened to y by a small wire basket.</Paragraph> <Paragraph position="3"> (28c) Forall x in corks do two nested loops Forall y in bottles if x is the cork in bottle y then x is fastened to y by a small wire basket.</Paragraph> <Paragraph position="4"> (28d) Forall y in bottles do single loop let x = the cork in bottle y x is fastened to y by a small wire basket.</Paragraph> <Paragraph position="5"> Most people understand this sentence by iterating over bottles and individuating the corks by the bottles. The single loop implementation can be derived straightforwardly from my representation. In some other representation, it may require a very clever compiler optimization, such as &quot;loop jamming&quot;.</Paragraph> <Paragraph position="6"> Sentences (29a) and (29b) are similar to (28a) in this respect.</Paragraph> <Paragraph position="7"> (29a) All the boys kissed all the girls.</Paragraph> <Paragraph position="8"> (29b) Each man and each woman will be joined in marriage here tonight.</Paragraph> <Paragraph position="9"> These sentences provide evidence that a quantifier like &quot;each&quot; doesn't necessarily set up an iteration. It usually does, and therefore these sentences are a bit odd. But these sentences are understood when each distributed quantified expression has a discourse co-American Journal of Computational Linguistics, Volume 7, Number 3, July-September 1981 145 William A. Martin Roles, Co-Descriptors, and the Formal Representation of Quantified English Expressions description which participates in an iteration. Setting up an iteration in (29a) and (29b) expresses the specific dependence of boys on girls, and of each man and woman on each other.</Paragraph> <Paragraph position="10"> (34) sail-boat motor-boat</Paragraph> </Section> <Section position="6" start_page="0" end_page="0" type="sub_section"> <SectionTitle> 4.4 Human Processing of Quantified Expressions </SectionTitle> <Paragraph position="0"> In the previous example we could have had each man married to each woman! Indeed, it is not always obvious how an iteration should be constructed.</Paragraph> <Paragraph position="1"> When someone hears the statement (30) A requirement for the course is the carving of a block of wood into each of the 12 designs.</Paragraph> <Paragraph position="2"> his reasoning might be as follows: &quot;Well, let's see. We take the wood and carve the first design. (He pursues the distributive referential reading with one block.) Oh! Oh! Now how do we carve a second design, the block is used up. Well, maybe we could fit the twelve designs on one block, or we could cut the block into twelve pieces. Or maybe I should abandon the referential reading and use twelve blocks.&quot; There can be no doubt that world knowledge (pragmatics) is required to choose between such readings. Consider now the following pair of sentences.</Paragraph> <Paragraph position="3"> (31a) Everybody at MIT knows a dialect of LISP.</Paragraph> <Paragraph position="4"> (31b) Everybody at IJCAI knows a dialect of LISP.</Paragraph> <Paragraph position="5"> Everyone at a university might conceivably know the same specific dialect, while everyone at an international conference might not.</Paragraph> <Paragraph position="6"> Van Lehn \[26\] reports that when people are given a sentence like (32) A quick test confirmed that every drug was psychoactive.</Paragraph> <Paragraph position="7"> they claim they understand it, but are then unable to state whether there was one test per drug or only one test for all. This ambiguity can be expressed in predicate calculus using quantifiers.</Paragraph> <Paragraph position="9"> But in my representation, the ambiguity is represented by the presence or absence of a role-in link, which makes it easy to delay disambiguation. There is no shuffling of quantifiers to shift between the two interpretations; instead, disambiguation is achieved by simply inserting a role-in link, when and if appropriate.</Paragraph> </Section> <Section position="7" start_page="0" end_page="0" type="sub_section"> <SectionTitle> 4.5 Ambiguity and Generality </SectionTitle> <Paragraph position="0"> The problem with (32) arises in part because of the difficulty of distinguishing between a general expression and an ambiguous one. For example, illustrates that both a sail boat and a motor boat can be described by the general expression boat. This contrasts with (35) = = pronoun-mine mineral-mine where there is no generalization of the pronoun-mine and mineral-mine senses of &quot;mine&quot;. Finally, (36) A quick test confirmed ? th~t every drug /////%',,,,,,~,~ p sy c h o act i ve forall drugs forsome test forsome test forall drugs points out that it is uncertain whether &quot;a quick test confirmed that every drug was psychoactive&quot; has a general sense. The general sense of &quot;boat&quot; is resolved semantically -- by choosing between more specific concepts such as &quot;sailboat&quot; or &quot;motorboat&quot;. If (35) does have a general sense it might be resolved semantically, but it might also be resolved pragmatically -by binding the concept into the discourse structure in different ways. Philosophers have largely ignored this issue since they have been interested in formal languages whose terms are logically unambiguous. Van Lehn's results would tend to indicate that people do have a general sense of this expression.</Paragraph> <Paragraph position="1"> The advantage of the representational scheme proposed here is that it allows the resolution of ambiguity by incrementally adding to what is already present. We have discussed many reasons why scoping decisions should be delayed, ranging from computational efficiency to Van Lehn's empirical observations.</Paragraph> <Paragraph position="2"> Role-in links provide a simple way to accomplish this.</Paragraph> </Section> </Section> class="xml-element"></Paper>