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<?xml version="1.0" standalone="yes"?> <Paper uid="P90-1008"> <Title>A Compositional Semantics for Focusing Subjuncts</Title> <Section position="2" start_page="0" end_page="58" type="intro"> <SectionTitle> 1 Introduction </SectionTitle> <Paragraph position="0"> Focusing subjuncts such as only, even, and also are a subclass of the sentence-element class of adverbials (Quirk et al., 1985). They draw attention to a part of a sentence the focus of the focusing subjunct--which often represents 'new' information.</Paragraph> <Paragraph position="1"> Focusing subjuncts are usually realized by adverbs, but occasionally by prepositional phrases. Focusing subjuncts emphasize, approximate, or restrict their foci. They modify the force or truth value of a sentence, especially with respect to its applicability to the focused item (Quirk et al., 1985, SS8.116).</Paragraph> <Paragraph position="2"> 1.1 The problem with focusing subjuncts There are several reasons why developing any semantics for focusing subjuncts is a difficult task.</Paragraph> <Paragraph position="3"> First, focusing subjuncts are 'syntactically promiscuous'. They can adjoin to any maximal projection. They can occur at almost any position in a sentence.</Paragraph> <Paragraph position="4"> Second, focusing subjuncts are also 'semantically promiscuous'. They may focus (draw attention to) almost any constituent. They can precede or follow the item that they focus, and need not be adjacent to this item. The focus need only be contained somewhere within the syntactic sister of the focusing subjunct. Because of this behavior, it is difficult to determine the intended syntactic argument (adjunct) and focus of a focusing subjunct. Sentences *The work described in this paper was done at the University of Toronto.</Paragraph> <Paragraph position="5"> such as those in (1) can be ambiguous, even when uttered aloud with intonational effects. 1 (1) 1. John could also (SEE) his wife from the doorway (as well as being able to talk to her).</Paragraph> <Paragraph position="6"> 2. John could also see (his WIFE) from the doorway (as well as her brother).</Paragraph> <Paragraph position="7"> 3. John could also see his wife (from the DOORway) (as well as from further inside the room).</Paragraph> <Paragraph position="8"> 4. John could also (see his wife from the DOORway) (as well as being able to do other things).</Paragraph> <Paragraph position="9"> Third, the location of intonational stress has an important effect on the meaning of a sentence containing a focusing subjunct. Sentences may be partly disambiguated by intonational stress: interpretations in which stress falls outside the intended focus of the focusing subjunct are impossible. For example, the sentence (2) *John could also see (his wife) from the DOORway.</Paragraph> <Paragraph position="10"> is impossible on the indicated reading, since stress on door cannot confer focus on his wife. On the other hand, stress does not help to disambiguate between readings such as (1.3) and (1.4).</Paragraph> <Paragraph position="11"> Fourth, focusing subjuncts don't fit into the slot-filler semantics that seem adequate for handling many other sentence elements (see Section 1.3)~ At best, their semantic effect is to transform the semantic representation of the constituent they modify in some predictable compositional way (Hirst, 1987, p. 72).</Paragraph> <Paragraph position="12"> Finally, focusing subjuncts carry pragmatic &quot;baggage&quot;. The meaning of a focusing subjunct includes distinct asserted and non-asserted parts (Horn, 1969), (Karttunen and Peters, 1979). For example, 1 In the example sentences in this paper, small capitals denote intonational stress. Angle brackets 0 enclose the focus of a focusing subjunct and square brackets \[ \] set off the constituent to which the focusing subjunct adjoins. Unacceptable sentences are preceded by an asterisk.</Paragraph> <Paragraph position="13"> (3) asserts (4.1) but only presupposes (4.2) (Horn, 1969): (3) Only Muriel voted for Hubert.</Paragraph> <Paragraph position="14"> (4) 1. No one other than Muriel voted for Hubert. null 2. Muriel voted for Hubert.</Paragraph> <Paragraph position="15"> Analogously, (5) asserts (6.1) and presupposes (6.2) (Karttunen and Peters, 1979): (5) Even Bill likes Mary.</Paragraph> <Paragraph position="16"> (6) 1. Bill likes Mary.</Paragraph> <Paragraph position="17"> 2. Other people besides Bill like Mary; and of the people under consideration, Bill is the least likely to like Mary.</Paragraph> <Paragraph position="18"> The precise status of such pragmatic inferences is controversial. We take no stand here on this issue, or on the definition of &quot;presupposition&quot;. We will simply say that, for example, (4.1) is due to the asserted meaning of only, and that (4.2) is produced by the non-asserted meaning of only.</Paragraph> <Section position="1" start_page="54" end_page="54" type="sub_section"> <SectionTitle> 1.2 Requirements of a semantics for focusing subjuncts </SectionTitle> <Paragraph position="0"> We desire a semantics for focusing subjuncts that is compositional (see Section 1.3), computationally practical, and amenable to a conventional, structured, near-first-order knowledge representation such as frames. It must cope with the semantic and syntactic problems of focusing subjuncts by being cross-categorial, being sensitive to intonation, and by distinguishing asserted and non-asserted meaning. By cross-categorial semantics we mean one that can cope with syntactic variability in the arguments of focusing subjuncts.</Paragraph> <Paragraph position="1"> We will demonstrate the following: * Intonation has an effect on meaning. A focus feature is useful to mediate between intonational information and meaning.</Paragraph> <Paragraph position="2"> * It is desirable to capture meaning in a multipart semantic representation.</Paragraph> <Paragraph position="3"> * An extended frame-based semantic representation can be used in place of higher-order logics to capture the meaning of focusing subjuncts.</Paragraph> </Section> <Section position="2" start_page="54" end_page="55" type="sub_section"> <SectionTitle> 1.3 Syntactic and semantic frameworks </SectionTitle> <Paragraph position="0"> In this paper, we will use a compositionM, frame-based approach to semantics. Focusing subjuncts have been thought difficult to fit into a compositional semantics because they change the meaning of their matrix sentences in ways that are not straightforward. null A compositional semantics is characterized by the following properties: * Each word and well-formed syntactic phrase is represented by a distinct semantic object.</Paragraph> <Paragraph position="1"> * The semantic representation of a syntactic phrase is a systematic function of the representation of its constituent words and/or phrases. In a compositional semantics, the syntax drives the semantics. To each syntactic phrase construction rule there corresponds a semantic rule that specities how the semantic objects of the constituents are (systematically) combined or composed to obtain a semantic object for the phrase. Proponents of compositionM semantics argue that natural language itself is for the most part compositional. In addition, using a composition semantics in semantic interpretation has numerous computational advantages.</Paragraph> <Paragraph position="2"> The particular incarnation of a compositional semantics that serves as the semantic framework for this work is the frame-based semantic representation of Hirst's Absity system (Hirst, 1987, 1988). Absity's underlying representation of the world is a knowledge base consisting of frames. A frame is a collection of stereotypical knowledge about some topic or concept (Hirst, 1987, p. 12). A frame is usuMly stored as a named structure having associated with it a set of slots or roles that may be assigned values or fillers. Absity's semantic objects belong to the types in a frame representation language called Frail (Charniak, 1981). Absity uses the following types of semantic object: frame determiner with frame description) A frame determiner is a function that retrieves frames or adds them to the knowledge base. A frame description describes a frame in the knowledge base.</Paragraph> <Paragraph position="3"> The filler of a slot is either an atom, or it is an instance, specified by a frame statement, of a frame in the knowledge base. In order to capture the meaning of sentences containing focusing subjuncts, we will augment Absity's frame-representation language with two new semantic objects, to be described in Section 3.3.</Paragraph> <Paragraph position="4"> The notation Hirst uses for frames is illustrated in Figure 1, which is a frame statement translation of the sentence (7) Ross washed the dog with a new shampoo.</Paragraph> <Paragraph position="5"> The semantics we will outline does not depend on any particular syntactic framework or theory. However, we choose to use Generalized Phrase Structure Grammar (GPSG) (Gazdar et al., 1985), because this formalism uses a compositional semantics that</Paragraph> <Paragraph position="7"> resembles Montague grammar (Montague, 1973). A central notion of GPSG that we will make use of is that of the features of a syntactic phrase. A feature is a piece of linguistic information, such as tense, number, and bar level; it may be atom-valued or categoryvalued. null</Paragraph> </Section> <Section position="3" start_page="55" end_page="56" type="sub_section"> <SectionTitle> 1.4 Previous research </SectionTitle> <Paragraph position="0"> The groundwork for the analysis of focusing subjuncts was laid by Horn (1969). ttom describes only (when modifying an NP) as a predicate taking two arguments, &quot;the term ix\] within its scope&quot; and &quot;some proposition \[Pz\] containing that term&quot; (Horn, 1969, p. 99). The meaning of the predicate is then to presuppose that the proposition P is true of z, and to assert that x is the unique term of which P is true: -,(~y)(y # z & Py). Even takes the same arguments. It is said to presuppose (qy)(y # x & Py) and to assert Px. Horn requires a different formulation of the meaning of only when it modifies a VP.</Paragraph> <Paragraph position="1"> Since his formulation is flawed, we do not show it here.</Paragraph> <Paragraph position="2"> Jackendoff's (1972, p. 242) analysis of even and only employs a semantic marker F that is assumed to be present in surface structure and associated with a node containing stress. He calls the semantic material associated with constituents marked by F the focus of a sentence. Fie proposes a rule that states that even and &quot;related words&quot; are associated with focus by having the focus in their range. Differences between the ranges of various focusing adverbs account for their different distributions (Jackendoff, 1972, pp. 249-250). For example: Range of even: If even is directly dominated by a node X, then X and all nodes dominated by X are in its range.</Paragraph> <Paragraph position="3"> Range of only: If only is directly dominated by a node X, then X and all nodes that are both dominated by X and to the right of only are in its range.</Paragraph> <Paragraph position="4"> That is, only cannot precede its focus (nor can just, which has the same range), but even can: (8) 1. *(JOHN) only gave Mary a birthday present (no one else did).</Paragraph> <Paragraph position="5"> 2. (JOHN) even gave Mary a birthday present (and so did everyone else, but John was the person least expected to).</Paragraph> <Paragraph position="6"> We will employ several aspects of Rooth's (1985) domain selection theory. A key feature of the theory is that only takes the VP adjacent to it in S-structure as its argument (an extension of the theory allows only to take arguments other than VPs). Rooth describes technical reasons for this arrangement (1985, p. 45). Among these is the fact that focusing subjuncts can draw attention to two (or more) items that, syntactically, do not together constitute a well-formed phrase: (9) John only introduced (BILL) to (SUE).</Paragraph> <Paragraph position="7"> The prevailing linguistic theories allow a node (such as a focusing subjunct) only one argument in the syntactic or logical (function-argument) structures of a sentence.</Paragraph> <Paragraph position="8"> According to Rooth, the asserted meaning of (10) John only \[vP introduced BILL to Sue\].</Paragraph> <Paragraph position="9"> is &quot;if John has a property of the form 'introduce y to Sue' then it is the property 'introduce Bill to Sue'&quot; (Rooth, 1985, p. 44, p. 59). Rooth's theory would produce the same translation, shown in (11.2), for both sentence (10) and sentence (11.1).</Paragraph> <Paragraph position="10"> (11) 1. John only introduced Bill to SUE.</Paragraph> <Paragraph position="11"> 2. VP\[\[P(john) & P 6 C\] --* P = ^introduee'(bill, sue)\] P ranges over propositions, so (11.2) is a quantification over propositions. C is bound 2 to the p-set of the VP of whichever sentence's meaning (11.2) is intended to capture. This p-set is &quot;a set of properties, which we think of as the set of relevant properties&quot; (Rooth, 1985, p. 43).</Paragraph> <Paragraph position="12"> Different truth conditions for the two sentences (10) and (11.1) obtain because their VPs have different p-sets: the computation of p-sets is sensitive to intonational stress (actually to focus, which is signalled by stress; see below). The desired value for C in the translation of (10) is the set of propositions of the form &quot;introduce y to Sue&quot;, namely propositions satisfying (12.1). For the translation of (11.1), C is the set of propositions of the form &quot;introduce Bill to y&quot;, that is, those satisfying (12.2).</Paragraph> <Paragraph position="13"> (12) 1. AP3y\[P = ^introdued(y, sue)\] 2. AP3y\[P = ^introduee'(bill, y)\] These result in the final translations (13.1) and (13.2) respectively for sentences (10) and (11.1): (13) 1. Vy\[introducd(john, y, sue) --+ y=bilO 2. Vy\[introduce' (john, bill, y) --+ y=sue\] 2 The mechanism of this binding relies on the translation being a formula of which (11.2) is a reasonable simplification; see (Rooth, 1985, p. 59).</Paragraph> <Paragraph position="14"> The formula (13.1) corresponds to the gloss of the meaning of (10) given above. (13.2) is to be interpreted as meaning: &quot;if John has a property of the form 'introduce Bill to y' then it is the property 'introduce Bill to Sue'&quot;.</Paragraph> <Paragraph position="15"> The p-set of a complete sentence is a set of &quot;relevant propositions&quot;. Rooth defines it recursively, from the p-sets of its constituents (Rooth, 1985, p. 14) (the &quot;model&quot; is a Montague-style formal model): (14) Let a be a constituent with translation a ~. The p-set of a is: 1. if a bears the focus feature, the set of objects in the model matching a ~ in type; 2. if a is a non-focused non-complex phrase, the unit set {a'}; 3. if a is a non-focused complex phrase, the set of objects that can be obtained by picking one element from each of the p-sets corresponding to the component phrases of a, and applying the semantic rule for a to this sequence of elements.</Paragraph> <Paragraph position="16"> In other words, the p-set of a sentence consists essentially of all propositions that are &quot;like&quot; the proposition that it asserts, except that the focused constituent in the proposition is replaced by a variable. 3 We will adopt Rooth's definition of the meaning of only: A sentence containing only that (without only) has logical form a: (15) 1. asserts that any &quot;contextually relevant&quot; proposition P whose extension is true is the proposition a; 2. has a as part of its non.asserted meaning.</Paragraph> <Paragraph position="17"> (Rooth, 1985, p. 120).</Paragraph> <Paragraph position="18"> Our analogous definition of even is this: A sentence containing even that (without even) has logical form a: (16) 1. asserts a; 2. conveys the non-asserted inference that there are other &quot;contextually relevant&quot; propositions, besides a, that are true.</Paragraph> <Paragraph position="19"> 2 Devices used to solve the problems Our semantics (which is described in more detail by Lyons (1989)) employs devices described in the following sections.</Paragraph> </Section> <Section position="4" start_page="56" end_page="56" type="sub_section"> <SectionTitle> 2.1 The focus feature </SectionTitle> <Paragraph position="0"> Following Jackendoff, we propose that focus is a binary feature, similar to (say) gender and number, aThe notion that the meaning of only and even can be defined in terms of a base form (such as &quot;John introduced y to Sue&quot;) was also noted by Kaxttunen and Peters (1979) and McCord (1982).</Paragraph> <Paragraph position="1"> that is either present or absent on every constituent at surface structure. 4 Focus is initially instantiated onto the leaves of the tree that represent intonationally stressed words. The only realization of the focus feature that we accommodate is intonational accent; however, our theory can easily be extended to allow for other overt realizations of focus, including other intonational effects (e.g. (Hirschberg and Pierrehumbert, 1986)). Focus is optionally and non-deterministically percolated up the syntax tree, to any node from its rightmost daughter (rightmost because stress manifests itself only at the end of the focused constituent (Anderson, 1972)). The non-determinism of the percolation of focus is responsible for ambiguity in the interpretation of sentences with focusing subjuncts. How far the focus feature percolates up determines how wide a focus is attributed to the focusing subjunct: (17) 1. John also read the book (from the LIBRARY) (as well as the one from the store).</Paragraph> <Paragraph position="2"> signment).</Paragraph> <Paragraph position="3"> The ambiguous interpretations of a sentence with a focusing subjunct belong to an ordered set in which each reading has a wider focus for the focusing subjunct than the previous one.</Paragraph> </Section> <Section position="5" start_page="56" end_page="56" type="sub_section"> <SectionTitle> 2.2 Relevant propositions </SectionTitle> <Paragraph position="0"> Our semantics employs a computational analogue of Rooth's p-sets for a frame representation. Our p-set for a constituent is computed compositionally, along with the semantic representation, in tandem with the application of the syntactic rule used to build the constituent. The p-set turns out to be an object in the frame representation that is like the semantic assertion derived for the constituent, but lacking restrictive information associated with any focused components.</Paragraph> </Section> <Section position="6" start_page="56" end_page="57" type="sub_section"> <SectionTitle> 2.3 Two-part semantics </SectionTitle> <Paragraph position="0"> In addition to p-sets, two semantic expressions are computed for each constituent during the interpretation of a sentence. One expression represents asserted meaning, and the other, non-asserted meaning. null 4 This feature is what Jackendoffcalls the F marker, but is different from what he calls &quot;focus&quot;. Note that we use the term focus of a focusing subjunct to stand for a distinct concept: the item to which a focusing subjunct draws attention to, or focuses. This is the semantic material that corresponds to a stressed word or to a constituent containing one.</Paragraph> </Section> <Section position="7" start_page="57" end_page="57" type="sub_section"> <SectionTitle> 2.4 Linguistic features </SectionTitle> <Paragraph position="0"> Focus is marked as a binary feature on all syntactic constituents. The semantic rules use this information when constructing semantic expressions for constituents. Because the focus feature need not percolate all the way up to the level of the constituent that is adjacent to the focusing subjunct in the syntax tree, we have found it useful to employ a second feature, focus.in, that indicates whether or not any sub-phrase is focused. The restriction that a focusing subjunct adjoins only to a phrase containing focus is implemented by requiring the adjunct phrase to be (focus-in +).</Paragraph> <Paragraph position="1"> Range (see Section 1.4) is implemented as two binary features, range-right and range-left, that indicate whether or not a given focusing subjunct can adjoin to phrases to its right and left, respectively.</Paragraph> <Paragraph position="2"> (Some words, like even, have both features.)</Paragraph> </Section> <Section position="8" start_page="57" end_page="57" type="sub_section"> <SectionTitle> 2.5 Sentential operators </SectionTitle> <Paragraph position="0"> Rooth applies his even and only operators to the logical form of the constituent that is the syntactic sister of the focusing subjunct. So, for example, in the VP (18.1), only transforms the expression wash'(dog), which is the translation of the VP argument of only, into the A-expression (18.2).</Paragraph> <Paragraph position="1"> (18) 1. only \[vp washed the (DOG)\] 2. AxVP\[\[VP & P e C'\]</Paragraph> <Paragraph position="3"> For each focusing subjunct, Rooth must define a separate transformation for each different semantic type of phrase that it may take as an argument. He defines a basic sentential operator for each focusing subjunct, and then derives the other operators from these (Rooth, 1985, pp. 120-121).</Paragraph> <Paragraph position="4"> Our approach is to instead define a single operator for each focusing subjunct, essentially Rooth's basic sentential operator. This operator takes the semantic representation of a sentence as an argument and produces another semantic representation of sentential type. When sentential objects are not available, as in the interpretation of \[vp only VP\], we delay the application of the operator until such a point as fully developed propositions, the semantic objects of sentenees, are available. To do this, the grammar rules &quot;percolate&quot; focusing subjunct operators up the syntax tree to the S node. Our grammar employs the feature fs to carry this latent operator. When the interpretation of a sentence is otherwise completed, a final step is to apply any latent operators, producing expressions for the sentence's asserted and non-asserted meanings from expressions for its assertion and its p-set.</Paragraph> <Paragraph position="5"> Several pieces of evidence motivate this approach: * As Rooth observed, in order to define a family of cross-categorial operators for (say) only, a basic operator must be defined that operates on an expression of sentential type. The semantics of focusing subjuncts actually seems to take place at the sentence level.</Paragraph> <Paragraph position="6"> Focusing subjuncts normally occur at most once per sentence. Even granting the acceptability of sentences containing several focusing subjuncts, such sentences are clearly semantically complicated. null The principal advantage of our approach is that it constructs essentially the same final translation of a sentence as Rooth's, but avoids using the A-operator during the derivation of a semantic representation that does not itself contain a A-operator. This is desirable, as A-expressions would make the frame representation language less tractable.</Paragraph> </Section> <Section position="9" start_page="57" end_page="58" type="sub_section"> <SectionTitle> 3 Details of the semantics 3.1 Semantic features </SectionTitle> <Paragraph position="0"> Three semantic objects are computed for and attached to each syntactic constituent, in parallel with the syntactic processing. The objects are of the types defined in an Absity-like frame representation.</Paragraph> <Paragraph position="1"> They are attached to a node as values of the following features (an approach motivated by Shieber (1986)): Assert: The asserted meaning of the constituent, its contribution to the sentence's asserted meaning. The value is computed the same way that a Montague-style grammar would construct a constituent's logical form from those of its daughters. Figure 2 shows examples of the rules to compute this value.</Paragraph> <Paragraph position="2"> Presupp: The constituent's contribution to the sentence's non-asserted meaning. For all rules but sentence rules, the presupp feature on the parent node is undefined. In order not to commit ourselves to the status of the non-asserted meanings of focusing subjuncts, we reserve this feature for the non-asserted meanings introduced by focusing subjunct operators (see below).</Paragraph> <Paragraph position="3"> P-set: A prototype of the semantic objects in the node's p-set. All objects that match this object are in the node's p-set. The algorithm for computing p-sets distinguishes between two cases: Case 1: If the parent node X (being constructed) is (focus +), its p-set is a variable of the same type as the assert object.</Paragraph> <Paragraph position="4"> Case 2: Otherwise, the p-set of X is constructed from the p-set values of the constituent phrases in a manner exactly paralleling the construction of the assert feature.</Paragraph> </Section> <Section position="10" start_page="58" end_page="58" type="sub_section"> <SectionTitle> 3.2 Application of the focusing subjunct operators </SectionTitle> <Paragraph position="0"> There is a syntactic rule whose sole purpose is to support of the application of a sentential operator: 09) s H\[(fs 4)1 S\[fs 4\] is specified as a non-initial category in the grammar, if a C/ &quot;-&quot;. Therefore, the rule (19) must apply in the derivation of any well-formed sentence containing a focusing subjunct. The corresponding semantic rule (20) applies a focusing subjunct operator to the semantic representation of the sentence. (20) 1. Input: S\[(assert a), (p-set ~/), (fs 7)\] 2. Output: where oplv and op2v are the sentential operators for the focusing subjunct 7 (see below).</Paragraph> </Section> <Section position="11" start_page="58" end_page="58" type="sub_section"> <SectionTitle> 3.3 The sentential operators </SectionTitle> <Paragraph position="0"> The sentential operators for only and even are given below. (The one for too is the same as that for even, and those for the other focusing subjuncts are similar.) null (21) 1. oplontu(A, P) = if P then A 2. op2only (A, P) = A 3. opl~,e,(A, P) = A 4. op2~ven( (the ?x frame-descrA),</Paragraph> <Paragraph position="2"> The form if P then A is a directive to the underlying knowledge base to insert the rule that any frame matching P is just the frame A, that is, A is the unique frame matching P. This directive is a frame implication. It is similar in character to a frame determiner (Hirst, 1987), in that it is a function that manipulates the underlying knowledge base.</Paragraph> <Paragraph position="3"> The form (anew ?y ~?X frame-descrP) is also a new type of entity in the semantics. We treat it as a frame determiner. It is a directive to the knowledge base to retrieve or create a frame instance, ?y, that matches frame-descrP but is not the frame instance identified by the variable ?x. As with the frame determiner (the ?x), such a frame instance ?y should be inserted if not already present in the knowledge base.</Paragraph> <Paragraph position="4"> For example, the sentence (22.1) yields the expression (22.2) as its assertion and (22.3) as its non-asserted meaning (other readings are possible as well).</Paragraph> <Paragraph position="5"> (22) 1. Ross only washed the DOG.</Paragraph> <Paragraph position="6"> 2. if (wash ?x (agent=Ross)) then (wash ?x (agent=Ross) (patient=dog))) 3. (the ?x (wash ?x (agent=Ross) (patient=dog))) The frame instance (22.3) captures the semantic content of the sentence &quot;Ross washed the dog&quot;. The frame implication (22.3) is to be interpreted as the rule that any wash frame in the knowledge base having Ross as its agent must in addition have dog as its patient.</Paragraph> <Paragraph position="7"> A second example: sentence (23.1) yields assertion (23.2) and non-asserted meaning (23.3).</Paragraph> <Paragraph position="8"> (23) 1. Ross washed even the DOG.</Paragraph> <Paragraph position="9"> 2. (the ?x (wash ?x (agent=Ross) (patient=dog))) 3. (anew ?y ~?x (wash ?y (agent=Ross))) The expression (23.3) affirms the existence of a wash instance ?y having agent Ross but that is a distinct washing from ?z in (23.2), which has dog as its patient. null</Paragraph> </Section> </Section> class="xml-element"></Paper>