Complexity of Scrambling - Semantic Scholar
Complexity of Scrambling: A New Twist to the Competence|Performance Distinction Aravind K. Joshi Department of Computer and Information Science University of Pennsylvania and Institute for Research in Cognitive Science Philadelphia, PA 19104 [email protected] Tilman Becker DFKI GmbH Saarbrucken, D-66123 Germany [email protected] Owen Rambow CoGenTex Inc. Ithaca, NY 14850 [email protected] Abstract
In this paper we discuss the following issue: How do we decide whether a certain property of language is a competence property or a performance property? Our claim is that the answer to this question is not given apriori. The answer depends on the formal devices (formal grammars and machines) available to us for describing language. We discuss this issue in the context of the complexity of processing of center embedding (of relative clauses in English) and scrambling (in German, for example) from arbitrary depths of embedding.
1 Introduction
How do we decide whether a certain property of language is a competence property or a performance property? This is an old question. In this pa The authors want to thank two referees of this paper for the very valuable comments, which helped to improve both the content and presentation of this paper. This work was partially supported by NSF Grant SBR8920230 and ARO Grant DAAH0404-94GE-0426.
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per, we will investigate this question in the context of the complexity of processing of scrambling (in German, for example) from arbitrary depths of embedding. We carry out this investigation using the framework of lexicalized tree-adjoining grammars (LTAG). We show that in the case of scrambling we are able to nd a class of LTAG which have the property that as a class they are adequate (i.e., for providing appropriate structural descriptions) to describe scrambling from up to two levels of embedding, and beyond two levels they fail. This gives us the choice of either regarding the diculty of interpreting sentences with scrambling from depth greater than two as a competence property (i.e., a property of the class of grammars), or adopting the traditional view of characterizing this diculty as a processing issue (i.e., a performance issue). We will point out that in the case of center embedding of relative clauses in English we are not provided with such a choice. Hence, we are led to the traditional wisdom of describing the diculties of interpretation as a performance property. Thus our main point in this paper is that the answer to the question posed in the beginning of this section is not given a-priori. Rather, the answer depends on the formal devices available to us for describing the phenomenon. The lack of such a choice for the case of center embedding of relative clauses in English has led to the traditional assumption that the kinds of properties discussed in this paper are to be automatically treated as performance properties. We show in this paper that this assumption is quite unjusti ed. The paper is organized as follows. In Section 2, we will discuss the case of center embedding of relative clauses in English and show why we are not o ered the choice mentioned above. In Section 3, we formulate our question in the context of scrambling. We then give some examples to motivate the discussion and then present an analysis of scrambling in the framework of LTAGs. Our goal is not to present a detailed linguistic analysis. We will only consider the formal issues that are relevant to the development of our argument. Finally, we conclude the discussion by restating the new twist to the competence-performance distinction that we have introduced in this paper.
2 Center Embedding of Relative Clauses in English
What properties of language are considered as belonging to `competence' and what properties to `performance' is not something given a-priori. Let us assume a property P which says that center embedding of relative clauses in English (as in the rat the cat chased ate the cheese ) beyond two levels of embedding is very dicult to process for humans, i.e., it is not just that the performance degrades beyond two levels of embedding but rather that somehow whatever the processing device is, it simply fails beyond two levels of embedding.1 1
We could assume that the processing device fails after level 1 or a level higher than
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Should this property be part of competence in the sense that P is a property of the grammar which characterizes competence? If P can be shown to follow from the formal characterization of the grammar (or the associated formal device or automaton) then we may as well say that the grammar itself has the property P in the sense that the grammar assigns linguistically adequate structural descriptions to all sentences up to two levels of embedding and beyond two levels of embedding the grammar just fails to do so. The accepted wisdom is that we should not require P to follow from the properties of the grammar, i.e., P is a property of performance. How do we arrive at this conclusion? The argument goes somewhat as follows.2 1. If the grammar is a nite state grammar (FSG) which allows for exactly two levels of embedding then trivially P is a property of the grammar. However there are two problems here. a. A FSG does not give us linguistically meaningful structural descriptions. The rules of a FSG are of the form A ! bC , where A and C are nonterminals and b is a terminal symbol. Thus for the sentence The dog likes bananas we will have a structural description of the form shown in Figure 1 using the following rules: S ! theXP XP ! dog Y P Y P ! likes ZP ZP ! bananas XP is not well motivated linguistically. Hence, FSGs are descriptively inadequate. b. Even if one accepts FSGs as linguistically adequate, there is still a problem. The requirement that a FSG should allow only two levels of embedding is quite arbitrary. Clearly, we can construct a FSG that will accommodate center embedding up to some speci ed level, say m. That is, as a class of grammars, FSGs accommodate center embedding up to any xed but arbitrary level. Thus the class of FSGs as a class does not have the property P , i.e., there are some (i.e., nontrivially in nitely many) FSGs for which P does not hold. ; ****So far, there is no succinct characterization of the ; subset 2 as long as it is a xed number. What is important for our discussion here is that the device fails beyond this level. What we are disallowing is a continuous degradation of performance for arbitrary levels of embedding. We chose level 2 as it corresponds very nearly to the data reported in the literature. 2 Miller and Chomsky (Miller and Chomsky 1963) were the rst to discuss the relationship between formal grammars (and associated machines) and center embedding constructions. Since then there have been a large number of publications on this issue.
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for which P holds. Tilman and I propose not to ; include this sentence.*** S
the
XP
dog
YP
likes ZP
bananas FIGURE
1 FSG Structural description
2. Since FSGs are inadequate from the point of view of providing linguistically appropriate structural descriptions, we must consider at least context-free grammars (CFG). Then for the previous example (Figure 1), we can easily obtain the structural description shown in Figure 2 with the following CFG: S ! NP V P NP ! DET N V P ! V NP DET ! the N ! dog NP ! bananas. 3. Once we leave FSGs and choose CFGs then, as we know, allowing for one level of center embedding automatically allows arbitrary levels of center embedding. Putting a constraint on the level of center embedding in a CFG is quite unnatural in the sense that this constraint on the class of CFGs cannot be stated in the framework of CFGs themselves. Thus, as a class, CFGs do not have the property P , i.e., there are some (i.e., nontrivially in nitely many) CFGs for which P does not hold. ; ****So far, there is no succinct characterization of the subset ; for which P holds. Tilman and I propose not to include ; this sentence.*** 4. Thus, we have reached the conclusion that it is better not to insist
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S NP
VP
DET
N
the
dog
FIGURE
V
NP
likes bananas
2 CFG Structural description
that P is a property of the class of grammars. It is better to treat P as a performance property. Now consider an alternate scenario. Suppose there is a class of grammars, G which has the following features: (a) the grammars provide linguistically adequate structural descriptions, and (b) the class has the property P , i.e., each grammar in this class has the property P . Of course, to the best of our knowledge, such a class of grammars does not exist. But suppose G did exist. Then it seems quite reasonable that we would adopt G as it will be linguistically adequate and coincidentally capture the property P . So, why not accept G and take credit for the fact that the property P follows from the formal properties of G, i.e., P can be viewed as a competence property. To summarize, given a property P whether or not P is a performance property or a competence property depends on the formal character of the grammars available to us. If we can nd a class of grammars G, which is both linguistically adequate and also captures the property P , then we adopt G and P becomes a competence property. On the other hand, if we cannot nd such a class of grammars then we try to look for another class of grammars, say, G0 which is linguistically adequate but which does not have the property P . If we nd such a class of grammars then we adopt G0 . In this case P becomes a performance property. For the case of center embedding in English, as we have already shown, this latter situation prevails. That is, we have no choice but to choose G0 and treat P as a performance property. These considerations, although not expressed in this way before, as far as we know, have led to the accepted wisdom that the fact that arbitrary number of center embeddings do not really occur is to be treated as a performance property.
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3 Scrambling
We will now describe a new situation that is similar on the surface to the case of center embedding of relative clauses in English. However, in this new situation we are o ered a choice that is not available in the case of center embedding of relative clauses in English. As far as we know, this is the rst known situation where such a choice is available. Thus this situation provides a sharp example for our claim that whether a property is a performance property or a competence property really depends on the formal characterization of the class of grammars that we have at our disposal for describing the linguistic facts. The situation we have in mind is scrambling, both local and long-distance, which has recently attracted considerable attention among linguists and computational linguists. We will investigate this situation in the context of LTAGs. In deciding whether scrambling as a linguistic phenomenon can be adequately described by an LTAG formalism, it is crucial to decide whether or not sentences corresponding to the strings with two or more levels of embedding are indeed grammatical. Sentences involving scrambling from more than two levels of embedding are indeed dicult to interpret and native speakers show reluctance in accepting these sentences. Now there are two directions we can follow. 1. The reluctance that some native speakers show for accepting the more complex sentences (i.e., with scrambling from more than two levels of embedding) is due mainly to processing diculties, rather than to the ungrammaticality of the sentences. This position is analogous to the accepted wisdom for the complexity of center embedded relative clauses in English. If we accept this position then we should proceed as follows. Since it is known that LTAGs are inadequate to describe (i.e., assign appropriate structural descriptions to) all sentences with scrambling from depths beyond 2 (Becker, Rambow and Niv 1992), we should look for further extensions of TAGs that will allow scrambling from any arbitrary level of embedding. Indeed such classes of grammars have been investigated by the authors elsewhere (Becker, Joshi and Rambow 1991), but especially, in a very extensive manner, by Rambow (Rambow 1994). 2. To follow the other direction (and the one we want to pursue in this paper), let us de ne a property Q such that a class of grammars, G has the property Q if G not only produces the scrambled strings for scrambling up to two levels of embedding but also assigns appropriate structural descriptions (appropriate in a sense made precise in Section 4 and further that beyond two levels of embedding G fails, i.e., even though it can produce the scrambled strings it fails to assign the correct structural descriptions. Suppose we can nd a class of grammars, say, G, such that every grammar in this class has the
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property Q, then we can adopt G and claim that the property Q is a competence property because it is a property that follows from the formal nature of the grammar itself. Now it can be shown that the class of tree-local multi-component LTAG (tree-local MC-LTAG)3 (de ned in Section 4) has the property Q, i.e., there are grammars in this class that can handle scrambling from up to two levels of embedding but all grammars in this class will fail to derive all scrambled sequences beyond two levels of embedding. So if we adopt tree-local MC-LTAG then Q is a competence property and not a performance property. Note that in the case of center embedding of relative clauses in English we do not have this kind of choice. However, in the case of scrambling we have the choice. Thus the phenomenon of scrambling in the context of tree-local MC-LTAG provides a unique situation allowing us to make the competence-performance distinction in a novel way. In the rest of the paper we will give an informal discussion of the various points made above.
3.1 Scrambling|Some Linguistic Data
In German (and in many other SOV languages, such as Korean, Hindi, and Japanese), a constituent of an embedded clause may be moved from that clause into the matrix clause. Now consider the following sentences. In sentences (1) the object of the embedded clause can be moved to any position in the matrix clause, as in sentences (1b) and (1c). How much freedom is there for scrambling? There appear to be no systematic syntactic restrictions on the number of verbal arguments that undergo \movement," nor on the distances over which they may move. Thus, any ordering of the arguments from all clauses is possible. To illustrate this freedom we will present two additional examples in which scrambling of a more complex nature occurs. 1. More than one constituent may undergo movement into higher clauses. The scrambled constituents need not retain their original relative order to each other after scrambling. In sentence (2b), two NPs are scrambled out of the embedded clause into the top-level clause. 2. Constituents may be moved over an unbounded number of clauses. In sentence (3b), NP die Witwen has been moved into its immediately dominating clause, while NP der Opfer has been moved from the most deeply embedded clause into the top-level clause, beyond the intermediate clause. 3 Tree-local MC-LTAGs are weakly equivalent to LTAGs (i.e., both generate the same sets of strings and derived trees), but the tree-local MC-LTAGs are more expressive with respect to the derivations they allow.
8/ (1a) . . . da keiner dem Kunden [den Kuhlschrank zu reparieren] . . . that no-one the clientDAT the refrigeratorACC to repair versprochen hat promised has . . . that no-one has promised the client to repair the refrigerator (1b) . . . da keiner den Kuhlschrankj dem Kunden [ tj zu reparieren] . . . that no-one the refrigeratorACC the clientDAT to repair versprochen hat promised has (1c) . . . da den Kuhlschrankj keiner dem Kunden [ tj zu reparieren] . . . that the refrigeratorACC no-one the clientDAT to repair versprochen hat promised has dem Klienten [den Verdachtigen (2a) . . . da der Detektiv . . . that the detectiveNOM the clientDAT the suspectACC des Verbrechens zu uberfuhren] versprochen hat promised has the crimeGEN to indict . . . that the detective has promised the client to indict the suspect of the crime den Verdachtigeni (2b) . . . da des Verbrechensj der Detektiv . . . that the crimeGEN the detectiveNOM the suspectACC dem Klienten [tj tk zu uberfuhren] versprochen hat promised has the clientDAT to indict dem Pfarrer [die Witwen (3a) . . . da der Rat . . . that the councilNOM the priestDAT the widowsACC gedenken] zu lassen] versprochen hat [ der Opfer promised has the victimsGEN commemorate to let . . . that the council has promised the priest to let the widows commemorate the victims dem Pfarrerk der Opferj (3b) . . . da die Witweni . . . that the widowsACC the victimsGEN the priestDAT [ti [ gedenken] tj zu lassen] versprochen hat der Rat tk commemorate to let promised has the councilNOM FIGURE 3 Example sentences
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In deciding whether scrambling as a linguistic phenomenon can adequately be described by an LTAG or an extension of LTAG, it is crucial to decide whether or not sentences corresponding to the strings given above are indeed grammatical. In the case of the embedded two-argument clauses, examples are readily available, as in sentences (2a) and (2b). In the case of the embedded one-argument sentences, it is more dicult (but not impossible) to construct an adequate example because of the great depth of embedding. Sentences (3a) and (3b) show scrambled NPs can move over two clauses. Sentences involving scrambling from more than two levels of embedding are indeed dicult to interpret and native speakers show reluctance in accepting these sentences.
4 An LTAG Analysis for Scrambling
The LTAG formalism provides a larger domain of locality than a CFG or other augmented CFG-based formalisms such as HPSG or LFG and it allows factoring of recursion from the domain of dependencies. LTAGs are known to handle both crossed and nested dependencies. The question now is whether LTAGs can handle scrambling. By this we mean, of course, can LTAGs not only generate the scrambled strings but also assign the correct structural descriptions. We will describe quite informally a series of results that relate to this question and then return to the question raised at the end of Section 1. The string language of scrambled sentences is context-free. We can represent the set of strings corresponding to the set of scrambled sentences as the set (1) (NP 1 NP 2 : : : NP n )V n V n?1 : : : V 1 where is some permutation of the NP 's and V 1 is the nite verb. We are assuming here that all verbs except V n subcategorize for one overt NP , an empty subject (PRO) and an S . Clearly this string language is context-free as it is of the form fan bn jn 1g, ignoring the case markings on the NP 's. From a linguistic perspective, the existence of some grammar that generates the string language of German scrambling is not in itself of much interest. For example, if we de ne an LTAG that generates the strings of scrambled sentences but has some elementary trees which encapsulate a verb with the arguments of some other verb, then we have not described the linguistic structure appropriately. We are really only interested in linguistically appropriate grammars, namely those that exploit the extended domain of locality and whose trees obey the constraint that each elementary tree encapsulates the lexical anchor and positions4 for all of its arguments and no other arguments. We can require that all substitution nodes be 4 In LTAG, an argument position is either a substitution node or a footnode (in predicative auxiliary trees).
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lled with the appropriate trees | i.e., the trees of those lexical items which are the arguments of the lexical anchor. (During an LTAG derivation, typically the NP arguments are substituted, while the matrix clause adjoins into its S argument.) We will refer to such a constraint as a (weak) co-occurrence constraint (WCC). (In WCC, we make no assumptions about which tree a predicative auxiliary tree adjoins into.) It can be shown that no LTAG satisfying WCC can generate the sentences of German scrambling if scrambling from arbitrary levels of embedding is allowed. We will argue this point by considering two cases { clauses with two overt nominal arguments and clauses with one overt nominal argument. In the rst case, the verb of the embedded clause subcategorizes for three NP s, one of which is an empty subject (PRO), and the matrix verb subcategorizes for two NP s and an S . (There is no verb in German that subcategorizes for three NP s and an S , so in this case a recursively embedded structure is impossible, and we can have at most one level of embedding.) We show that the language (2) f(NP 1 1 ; NP 1 2 ; NP 2 1 ; NP 2 2 )V 2 V 1 j a permutationg cannot be generated by an LTAG that contains only elementary trees obeying WCC. A linguistically plausible set of two such trees is shown in Figure 4. Now consider the string (3) NP 22 NP 1 1 NP 2 1 NP 1 2 V 2 V 1 which corresponds to the ordering in sentence (2b) in Figure 3. (The subscripts denote which clause the NP or V comes from, while the superscript is used to distinguish the two NP s in each clause.) It can be easily seen that this string cannot be generated by an LTAG of the speci ed sort: after an adjunction the yield of the adjoined tree is segmented into at most two sections, while the yield of both trees and would need to be segmented into three sections in order to be composed into the desired string. FIGURE
4 An initial tree with two verbal arguments and an auxiliary tree
In the second case, the verbs of the embedded clauses subcategorize for two NP s, one of which is again an empty subject (PRO), and an S (for example, see (1a), (1b) and (1c) in Figure 3). We will show that the language (4) f(NP 1 ; : : : ; NP k )V k : : : V 1 j k 2 N and a permutationg cannot be generated by an LTAG which obeys WCC. The idea in selecting this language is as follows: we keep the verbs at the end in the inverted order required by embedding, and then consider all possible permutations of the NP s. For k 4 it is possible to construct LTAGs obeying WCC that generate the possible permutations. For k = 1; 2; and 3 the construction is
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fairly easy. For k = 4 the construction is not obvious but we will not give the details here. However, for k = 5 it is impossible to construct an LTAG satisfying WCC. Consider the string (5) w = NP 3NP 1 NP 5 NP 2 NP 4 V 5 V 4 V 3 V 2 V 1 For this string, it can be shown that it is impossible to construct an LTAG which satis es WCC. The proof consists of an exhaustive case analysis and we will not present the details in this paper. The weak co-occurrence constraint (WCC) we have considered so far only requires that positions for the arguments for a lexical anchor appear in the same elementary tree which is anchored on this lexical item, and that the appropriate NP arguments are substituted by the appropriate NP during the derivation. But what about the S arguments? If a verb V i subcategorizes for an S then we must make sure that, when during a derivation the elementary tree anchored on V i is adjoined to an S node in a tree anchored by a verb V j , then V j is an argument of V i , i.e., the V i tree cannot be adjoined to any arbitrary S node. It can only be adjoined to an S node that belongs to the V j tree. This derivational constraint together with WCC will be called the strong co-occurrence constraint (SCC). SCC assures that each elementary tree is semantically coherent and all trees are combined in a semantically coherent manner. We say that an LTAG assigns correct structural description to a string when the derivation of the string obeys SCC. It is easily shown that under SCC, LTAGs can handle scrambling from up to one level of embedding only. Thus, for example, for the string (6) below corresponding to a sentence with scrambling from depth two, there is no LTAG obeying SCC that can derive it. (6) NP 2NP 3 NP 1 V 3 V 2 V 1 We will now consider an extension of LTAG called tree-local multicomponent LTAG (Tree-local MC-LTAG). In an MC-LTAG an auxiliary tree can be a set of trees, say, 1 and 2 , with at least one of the trees anchored on a lexical item. The derivation proceeds in the same manner as in an LTAG; however the tree local requirement speci es that if a multi-component auxiliary tree set is used in a derivation then all components of the auxiliary tree set must be adjoined or substituted at distinct nodes of the same elementary tree5 . It can be shown that treelocal MC-LTAGs are weakly equivalent to LTAGs, i.e., they both generate exactly the same set of strings. However, tree-local MC-TAGs can produce structural descriptions not obtainable by LTAGs (for some early work on MC-TAGs see (Joshi 1987, Weir 1988)). Tree-local MC-LTAGs are a very well motivated extension of LTAGs. 5 In the actual linguistic applications the two distinct nodes are such that one of them dominates the other
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In an LTAG when an auxiliary tree is adjoined to a tree at a node p in we can view the situation as follows. Split the tree at p into the supertree of (denoted by n p, i.e., the tree above above p) and the subtree of (denoted by =p, i.e., the tree below p). Now adjoining to at p can be seen as \wrapping" n p and =p around . This wrapping can be expressed by a combination of substitution and adjunction of the two components of into the tree . Thus the standard adjunction in LTAG can be viewed as a special case of the tree-local MC-LTAG derivation. This is the main idea behind the de nition of tree-local MC-LTAG.6 An immediate consequence of adopting tree-local MC-LTAG is that the previously considered string (3), now represented here as the string (7) below (7) NP 22 NP 1 1 NP 1 2 NP 2 1 V 2 V 1 which was not derivable by any LTAG can be now obviously derived in a tree-local MC-LTAG. The tree in Figure 4 can be thought of in terms of two components, 11 and 12 by splitting at the S node below the root node (see Figure 5). Now the string (7) can be derived by adjoining 11 at the S node immediately below the root node and 12 at the other interior node S . This derivation is shown in Figure 6.
β: 1
{β :
β12:
S
11
1 NP1
S
S
e FIGURE
}
1 NP1
VP 2
NP1
S
V1
5 Splitting an elementary tree into two parts
Now, surprisingly, it turns out that tree-local MC-LTAGs under SCC can handle all sentences with scrambling from up to two levels of embedding and beyond two levels they fail to do so, in the sense that beyond two levels they fail to assign correct structural descriptions (i.e., obeying SCC) to all sentences. Thus, for example, for the string (8) below corresponding to scrambling from three levels of embedding (8) NP 2 NP 4 NP 3NP 1 V 4 V 3 V 2 V 1 6 The component trees of the elementary tree set in a tree-local MC-TAG are not arbitrary trees. They can be thought of as coming from either splitting an elementary tree of an LTAG at a given node, as described above, or by splitting an elementary tree at a non-branching edge (not described in this paper, for further information see Joshi and Vijay-Shanker (1999)).
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S NP22
S 1
NP1
β1
S 1
NP2
S 1
NP1 e
β2
VP 2
NP1
S
V
NP PRO
FIGURE
1
VP 1
2
NP2
NP2
e
e
V2
6 Tree-local adjunction of an MC-LTAG tree set
it can be shown that there is no tree-local MC-LTAG that can derive it while obeying SCC. Thus tree-local MC-LTAG is a class of grammars which satis es the property Q (see section 3, item 2), i.e., all7 grammars in this class assign correct structural descriptions to all sentences with scrambling from depths up to two and beyond two they fail8. So now we are presented with a choice (unlike the case of center embedding of relative clauses in English). We can either opt for the traditional way, i.e., continue to regard the diculty of scrambling from depths greater than two as due to processing diculties, i.e., go along with the accepted wisdom derived from the complexity of the center embedding of relative clauses in English. Then we would continue to look for extensions of LTAGs that will permit scrambling from arbitrary depths of embedding and relegate the reluctance of native speakers to accept such sentences to performance factors. Alternatively, we can adopt tree local MC-LTAGs as adequate for describing scrambling. Then since tree-local MC-LTAGs as a Strictly speaking, almost all, i.e., all except for a nite set of grammars. For further work on derivations in tree-local MC-LTAG and their use in describing clitic movement, see (Joshi and Kulick 1998, Kulick 1998). Kulick (Kulick 1998) has also investigated all other scrambling patterns (i.e., all patterns other than those indicated in (1) in Section 4) in German for depths up to two and shown the adequacy of tree-local MC-LTAG 7 8
14 / Bibliography
class have the property Q, we conclude that Q is a competence property and not a performance property!
5 Conclusion
We have discussed the following issue: How do we decide whether a certain property of language is a competence property or a performance property? We stated the claim that the answer to this question is not given a-priori. It depends on the formal devices (formal grammars and machines) available to us for describing language. We showed that in the case of center embedding of relative clauses in English, we were forced to conclude that the property that sentences with more than two levels of embedding are dicult to interpret is a performance property and not a competence property. In contrast, for the case of scrambling (in German) with respect to a corresponding property we can indeed exhibit a class of grammars such that for all grammars in this class the corresponding property holds. Thus we are given the possibility of claiming this property to be a competence property rather than a performance property. To the best of our knowledge, this is the rst such case where a choice of this kind presented. The lack of such a choice before this case was discovered has led to the traditional assumption that all properties similar to the properties considered in this paper should be treated as performance properties. Our main conclusion is that this assumption is not justi ed at all.
Bibliography
Tilman Becker, Aravind K. Joshi and Owen Rambow. 1991. Long-distance scrambling and tree-adjoining grammars. In Proceedings of the European Association of Computational Linguistics (EACL) Meeting, Berlin, April 1991. Tilman Becker, Owen Rambow and Michael Niv. 1992. The Derivational Generative Power, or, Scrambling is Beyond LCFRS. Technical Report IRCS-92-38, Institute for Research in Cognitive Science, University of Pennsylvania. A version of this paper was presented at MOL3, Austin, Texas, November 1992. Aravind K. Joshi and K. Vijay-Shanker Compositional semantics with lexicalized tree-adjoining grammar (LTAG): How much underspeci caion is necessary? Proceedings of the Third International Workshop on Computational Semantics,Tilburg, The Netherlands, January 1999. Seth Kulick 1998. Non-local dependencies and multicomponent lexicalized tree-adjoining grammars. Ph. D. Dissertation proposal, University of Pennsylvania. Aravind K. Joshi and Seth Kulick 1998. Derivations in MC-LTAG. Work in progress.
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Aravind K. Joshi. 1987. An Introduction to Tree Adjoining Grammars. In A. Manaster-Ramer, editor, Mathematics of Language. John Benjamins, Amsterdam. George A. Miller and Noam Chomsky. 1963. Finitary models of language users. In R.D. Luce. R. Bush and E. Galanter (Eds.), Handbook of Mathematical Psychology, Volume II, Wiley, New York. Owen Rambow. 1994. Formal and Computational Aspects of Natural Language Syntax. Ph.D. thesis, Department of Computer and Information Science, University of Pennsylvania. David J. Weir. 1988. Characterizing Mildly Context-Sensitive Grammar Formalisms. Ph.D. thesis, Department of Computer and Information Science, University of Pennsylvania.
In this paper we discuss the following issue: How do we decide whether a certain property of language is a competence property or a performance property? Our claim is that the answer to this question is not given apriori. The answer depends on the formal devices (formal grammars and machines) available to us for describing language. We discuss this issue in the context of the complexity of processing of center embedding (of relative clauses in English) and scrambling (in German, for example) from arbitrary depths of embedding.
1 Introduction
How do we decide whether a certain property of language is a competence property or a performance property? This is an old question. In this pa The authors want to thank two referees of this paper for the very valuable comments, which helped to improve both the content and presentation of this paper. This work was partially supported by NSF Grant SBR8920230 and ARO Grant DAAH0404-94GE-0426.
1
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per, we will investigate this question in the context of the complexity of processing of scrambling (in German, for example) from arbitrary depths of embedding. We carry out this investigation using the framework of lexicalized tree-adjoining grammars (LTAG). We show that in the case of scrambling we are able to nd a class of LTAG which have the property that as a class they are adequate (i.e., for providing appropriate structural descriptions) to describe scrambling from up to two levels of embedding, and beyond two levels they fail. This gives us the choice of either regarding the diculty of interpreting sentences with scrambling from depth greater than two as a competence property (i.e., a property of the class of grammars), or adopting the traditional view of characterizing this diculty as a processing issue (i.e., a performance issue). We will point out that in the case of center embedding of relative clauses in English we are not provided with such a choice. Hence, we are led to the traditional wisdom of describing the diculties of interpretation as a performance property. Thus our main point in this paper is that the answer to the question posed in the beginning of this section is not given a-priori. Rather, the answer depends on the formal devices available to us for describing the phenomenon. The lack of such a choice for the case of center embedding of relative clauses in English has led to the traditional assumption that the kinds of properties discussed in this paper are to be automatically treated as performance properties. We show in this paper that this assumption is quite unjusti ed. The paper is organized as follows. In Section 2, we will discuss the case of center embedding of relative clauses in English and show why we are not o ered the choice mentioned above. In Section 3, we formulate our question in the context of scrambling. We then give some examples to motivate the discussion and then present an analysis of scrambling in the framework of LTAGs. Our goal is not to present a detailed linguistic analysis. We will only consider the formal issues that are relevant to the development of our argument. Finally, we conclude the discussion by restating the new twist to the competence-performance distinction that we have introduced in this paper.
2 Center Embedding of Relative Clauses in English
What properties of language are considered as belonging to `competence' and what properties to `performance' is not something given a-priori. Let us assume a property P which says that center embedding of relative clauses in English (as in the rat the cat chased ate the cheese ) beyond two levels of embedding is very dicult to process for humans, i.e., it is not just that the performance degrades beyond two levels of embedding but rather that somehow whatever the processing device is, it simply fails beyond two levels of embedding.1 1
We could assume that the processing device fails after level 1 or a level higher than
/
3
Should this property be part of competence in the sense that P is a property of the grammar which characterizes competence? If P can be shown to follow from the formal characterization of the grammar (or the associated formal device or automaton) then we may as well say that the grammar itself has the property P in the sense that the grammar assigns linguistically adequate structural descriptions to all sentences up to two levels of embedding and beyond two levels of embedding the grammar just fails to do so. The accepted wisdom is that we should not require P to follow from the properties of the grammar, i.e., P is a property of performance. How do we arrive at this conclusion? The argument goes somewhat as follows.2 1. If the grammar is a nite state grammar (FSG) which allows for exactly two levels of embedding then trivially P is a property of the grammar. However there are two problems here. a. A FSG does not give us linguistically meaningful structural descriptions. The rules of a FSG are of the form A ! bC , where A and C are nonterminals and b is a terminal symbol. Thus for the sentence The dog likes bananas we will have a structural description of the form shown in Figure 1 using the following rules: S ! theXP XP ! dog Y P Y P ! likes ZP ZP ! bananas XP is not well motivated linguistically. Hence, FSGs are descriptively inadequate. b. Even if one accepts FSGs as linguistically adequate, there is still a problem. The requirement that a FSG should allow only two levels of embedding is quite arbitrary. Clearly, we can construct a FSG that will accommodate center embedding up to some speci ed level, say m. That is, as a class of grammars, FSGs accommodate center embedding up to any xed but arbitrary level. Thus the class of FSGs as a class does not have the property P , i.e., there are some (i.e., nontrivially in nitely many) FSGs for which P does not hold. ; ****So far, there is no succinct characterization of the ; subset 2 as long as it is a xed number. What is important for our discussion here is that the device fails beyond this level. What we are disallowing is a continuous degradation of performance for arbitrary levels of embedding. We chose level 2 as it corresponds very nearly to the data reported in the literature. 2 Miller and Chomsky (Miller and Chomsky 1963) were the rst to discuss the relationship between formal grammars (and associated machines) and center embedding constructions. Since then there have been a large number of publications on this issue.
4/
for which P holds. Tilman and I propose not to ; include this sentence.*** S
the
XP
dog
YP
likes ZP
bananas FIGURE
1 FSG Structural description
2. Since FSGs are inadequate from the point of view of providing linguistically appropriate structural descriptions, we must consider at least context-free grammars (CFG). Then for the previous example (Figure 1), we can easily obtain the structural description shown in Figure 2 with the following CFG: S ! NP V P NP ! DET N V P ! V NP DET ! the N ! dog NP ! bananas. 3. Once we leave FSGs and choose CFGs then, as we know, allowing for one level of center embedding automatically allows arbitrary levels of center embedding. Putting a constraint on the level of center embedding in a CFG is quite unnatural in the sense that this constraint on the class of CFGs cannot be stated in the framework of CFGs themselves. Thus, as a class, CFGs do not have the property P , i.e., there are some (i.e., nontrivially in nitely many) CFGs for which P does not hold. ; ****So far, there is no succinct characterization of the subset ; for which P holds. Tilman and I propose not to include ; this sentence.*** 4. Thus, we have reached the conclusion that it is better not to insist
/
5
S NP
VP
DET
N
the
dog
FIGURE
V
NP
likes bananas
2 CFG Structural description
that P is a property of the class of grammars. It is better to treat P as a performance property. Now consider an alternate scenario. Suppose there is a class of grammars, G which has the following features: (a) the grammars provide linguistically adequate structural descriptions, and (b) the class has the property P , i.e., each grammar in this class has the property P . Of course, to the best of our knowledge, such a class of grammars does not exist. But suppose G did exist. Then it seems quite reasonable that we would adopt G as it will be linguistically adequate and coincidentally capture the property P . So, why not accept G and take credit for the fact that the property P follows from the formal properties of G, i.e., P can be viewed as a competence property. To summarize, given a property P whether or not P is a performance property or a competence property depends on the formal character of the grammars available to us. If we can nd a class of grammars G, which is both linguistically adequate and also captures the property P , then we adopt G and P becomes a competence property. On the other hand, if we cannot nd such a class of grammars then we try to look for another class of grammars, say, G0 which is linguistically adequate but which does not have the property P . If we nd such a class of grammars then we adopt G0 . In this case P becomes a performance property. For the case of center embedding in English, as we have already shown, this latter situation prevails. That is, we have no choice but to choose G0 and treat P as a performance property. These considerations, although not expressed in this way before, as far as we know, have led to the accepted wisdom that the fact that arbitrary number of center embeddings do not really occur is to be treated as a performance property.
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3 Scrambling
We will now describe a new situation that is similar on the surface to the case of center embedding of relative clauses in English. However, in this new situation we are o ered a choice that is not available in the case of center embedding of relative clauses in English. As far as we know, this is the rst known situation where such a choice is available. Thus this situation provides a sharp example for our claim that whether a property is a performance property or a competence property really depends on the formal characterization of the class of grammars that we have at our disposal for describing the linguistic facts. The situation we have in mind is scrambling, both local and long-distance, which has recently attracted considerable attention among linguists and computational linguists. We will investigate this situation in the context of LTAGs. In deciding whether scrambling as a linguistic phenomenon can be adequately described by an LTAG formalism, it is crucial to decide whether or not sentences corresponding to the strings with two or more levels of embedding are indeed grammatical. Sentences involving scrambling from more than two levels of embedding are indeed dicult to interpret and native speakers show reluctance in accepting these sentences. Now there are two directions we can follow. 1. The reluctance that some native speakers show for accepting the more complex sentences (i.e., with scrambling from more than two levels of embedding) is due mainly to processing diculties, rather than to the ungrammaticality of the sentences. This position is analogous to the accepted wisdom for the complexity of center embedded relative clauses in English. If we accept this position then we should proceed as follows. Since it is known that LTAGs are inadequate to describe (i.e., assign appropriate structural descriptions to) all sentences with scrambling from depths beyond 2 (Becker, Rambow and Niv 1992), we should look for further extensions of TAGs that will allow scrambling from any arbitrary level of embedding. Indeed such classes of grammars have been investigated by the authors elsewhere (Becker, Joshi and Rambow 1991), but especially, in a very extensive manner, by Rambow (Rambow 1994). 2. To follow the other direction (and the one we want to pursue in this paper), let us de ne a property Q such that a class of grammars, G has the property Q if G not only produces the scrambled strings for scrambling up to two levels of embedding but also assigns appropriate structural descriptions (appropriate in a sense made precise in Section 4 and further that beyond two levels of embedding G fails, i.e., even though it can produce the scrambled strings it fails to assign the correct structural descriptions. Suppose we can nd a class of grammars, say, G, such that every grammar in this class has the
/
7
property Q, then we can adopt G and claim that the property Q is a competence property because it is a property that follows from the formal nature of the grammar itself. Now it can be shown that the class of tree-local multi-component LTAG (tree-local MC-LTAG)3 (de ned in Section 4) has the property Q, i.e., there are grammars in this class that can handle scrambling from up to two levels of embedding but all grammars in this class will fail to derive all scrambled sequences beyond two levels of embedding. So if we adopt tree-local MC-LTAG then Q is a competence property and not a performance property. Note that in the case of center embedding of relative clauses in English we do not have this kind of choice. However, in the case of scrambling we have the choice. Thus the phenomenon of scrambling in the context of tree-local MC-LTAG provides a unique situation allowing us to make the competence-performance distinction in a novel way. In the rest of the paper we will give an informal discussion of the various points made above.
3.1 Scrambling|Some Linguistic Data
In German (and in many other SOV languages, such as Korean, Hindi, and Japanese), a constituent of an embedded clause may be moved from that clause into the matrix clause. Now consider the following sentences. In sentences (1) the object of the embedded clause can be moved to any position in the matrix clause, as in sentences (1b) and (1c). How much freedom is there for scrambling? There appear to be no systematic syntactic restrictions on the number of verbal arguments that undergo \movement," nor on the distances over which they may move. Thus, any ordering of the arguments from all clauses is possible. To illustrate this freedom we will present two additional examples in which scrambling of a more complex nature occurs. 1. More than one constituent may undergo movement into higher clauses. The scrambled constituents need not retain their original relative order to each other after scrambling. In sentence (2b), two NPs are scrambled out of the embedded clause into the top-level clause. 2. Constituents may be moved over an unbounded number of clauses. In sentence (3b), NP die Witwen has been moved into its immediately dominating clause, while NP der Opfer has been moved from the most deeply embedded clause into the top-level clause, beyond the intermediate clause. 3 Tree-local MC-LTAGs are weakly equivalent to LTAGs (i.e., both generate the same sets of strings and derived trees), but the tree-local MC-LTAGs are more expressive with respect to the derivations they allow.
8/ (1a) . . . da keiner dem Kunden [den Kuhlschrank zu reparieren] . . . that no-one the clientDAT the refrigeratorACC to repair versprochen hat promised has . . . that no-one has promised the client to repair the refrigerator (1b) . . . da keiner den Kuhlschrankj dem Kunden [ tj zu reparieren] . . . that no-one the refrigeratorACC the clientDAT to repair versprochen hat promised has (1c) . . . da den Kuhlschrankj keiner dem Kunden [ tj zu reparieren] . . . that the refrigeratorACC no-one the clientDAT to repair versprochen hat promised has dem Klienten [den Verdachtigen (2a) . . . da der Detektiv . . . that the detectiveNOM the clientDAT the suspectACC des Verbrechens zu uberfuhren] versprochen hat promised has the crimeGEN to indict . . . that the detective has promised the client to indict the suspect of the crime den Verdachtigeni (2b) . . . da des Verbrechensj der Detektiv . . . that the crimeGEN the detectiveNOM the suspectACC dem Klienten [tj tk zu uberfuhren] versprochen hat promised has the clientDAT to indict dem Pfarrer [die Witwen (3a) . . . da der Rat . . . that the councilNOM the priestDAT the widowsACC gedenken] zu lassen] versprochen hat [ der Opfer promised has the victimsGEN commemorate to let . . . that the council has promised the priest to let the widows commemorate the victims dem Pfarrerk der Opferj (3b) . . . da die Witweni . . . that the widowsACC the victimsGEN the priestDAT [ti [ gedenken] tj zu lassen] versprochen hat der Rat tk commemorate to let promised has the councilNOM FIGURE 3 Example sentences
/
9
In deciding whether scrambling as a linguistic phenomenon can adequately be described by an LTAG or an extension of LTAG, it is crucial to decide whether or not sentences corresponding to the strings given above are indeed grammatical. In the case of the embedded two-argument clauses, examples are readily available, as in sentences (2a) and (2b). In the case of the embedded one-argument sentences, it is more dicult (but not impossible) to construct an adequate example because of the great depth of embedding. Sentences (3a) and (3b) show scrambled NPs can move over two clauses. Sentences involving scrambling from more than two levels of embedding are indeed dicult to interpret and native speakers show reluctance in accepting these sentences.
4 An LTAG Analysis for Scrambling
The LTAG formalism provides a larger domain of locality than a CFG or other augmented CFG-based formalisms such as HPSG or LFG and it allows factoring of recursion from the domain of dependencies. LTAGs are known to handle both crossed and nested dependencies. The question now is whether LTAGs can handle scrambling. By this we mean, of course, can LTAGs not only generate the scrambled strings but also assign the correct structural descriptions. We will describe quite informally a series of results that relate to this question and then return to the question raised at the end of Section 1. The string language of scrambled sentences is context-free. We can represent the set of strings corresponding to the set of scrambled sentences as the set (1) (NP 1 NP 2 : : : NP n )V n V n?1 : : : V 1 where is some permutation of the NP 's and V 1 is the nite verb. We are assuming here that all verbs except V n subcategorize for one overt NP , an empty subject (PRO) and an S . Clearly this string language is context-free as it is of the form fan bn jn 1g, ignoring the case markings on the NP 's. From a linguistic perspective, the existence of some grammar that generates the string language of German scrambling is not in itself of much interest. For example, if we de ne an LTAG that generates the strings of scrambled sentences but has some elementary trees which encapsulate a verb with the arguments of some other verb, then we have not described the linguistic structure appropriately. We are really only interested in linguistically appropriate grammars, namely those that exploit the extended domain of locality and whose trees obey the constraint that each elementary tree encapsulates the lexical anchor and positions4 for all of its arguments and no other arguments. We can require that all substitution nodes be 4 In LTAG, an argument position is either a substitution node or a footnode (in predicative auxiliary trees).
10 /
lled with the appropriate trees | i.e., the trees of those lexical items which are the arguments of the lexical anchor. (During an LTAG derivation, typically the NP arguments are substituted, while the matrix clause adjoins into its S argument.) We will refer to such a constraint as a (weak) co-occurrence constraint (WCC). (In WCC, we make no assumptions about which tree a predicative auxiliary tree adjoins into.) It can be shown that no LTAG satisfying WCC can generate the sentences of German scrambling if scrambling from arbitrary levels of embedding is allowed. We will argue this point by considering two cases { clauses with two overt nominal arguments and clauses with one overt nominal argument. In the rst case, the verb of the embedded clause subcategorizes for three NP s, one of which is an empty subject (PRO), and the matrix verb subcategorizes for two NP s and an S . (There is no verb in German that subcategorizes for three NP s and an S , so in this case a recursively embedded structure is impossible, and we can have at most one level of embedding.) We show that the language (2) f(NP 1 1 ; NP 1 2 ; NP 2 1 ; NP 2 2 )V 2 V 1 j a permutationg cannot be generated by an LTAG that contains only elementary trees obeying WCC. A linguistically plausible set of two such trees is shown in Figure 4. Now consider the string (3) NP 22 NP 1 1 NP 2 1 NP 1 2 V 2 V 1 which corresponds to the ordering in sentence (2b) in Figure 3. (The subscripts denote which clause the NP or V comes from, while the superscript is used to distinguish the two NP s in each clause.) It can be easily seen that this string cannot be generated by an LTAG of the speci ed sort: after an adjunction the yield of the adjoined tree is segmented into at most two sections, while the yield of both trees and would need to be segmented into three sections in order to be composed into the desired string. FIGURE
4 An initial tree with two verbal arguments and an auxiliary tree
In the second case, the verbs of the embedded clauses subcategorize for two NP s, one of which is again an empty subject (PRO), and an S (for example, see (1a), (1b) and (1c) in Figure 3). We will show that the language (4) f(NP 1 ; : : : ; NP k )V k : : : V 1 j k 2 N and a permutationg cannot be generated by an LTAG which obeys WCC. The idea in selecting this language is as follows: we keep the verbs at the end in the inverted order required by embedding, and then consider all possible permutations of the NP s. For k 4 it is possible to construct LTAGs obeying WCC that generate the possible permutations. For k = 1; 2; and 3 the construction is
/
11
fairly easy. For k = 4 the construction is not obvious but we will not give the details here. However, for k = 5 it is impossible to construct an LTAG satisfying WCC. Consider the string (5) w = NP 3NP 1 NP 5 NP 2 NP 4 V 5 V 4 V 3 V 2 V 1 For this string, it can be shown that it is impossible to construct an LTAG which satis es WCC. The proof consists of an exhaustive case analysis and we will not present the details in this paper. The weak co-occurrence constraint (WCC) we have considered so far only requires that positions for the arguments for a lexical anchor appear in the same elementary tree which is anchored on this lexical item, and that the appropriate NP arguments are substituted by the appropriate NP during the derivation. But what about the S arguments? If a verb V i subcategorizes for an S then we must make sure that, when during a derivation the elementary tree anchored on V i is adjoined to an S node in a tree anchored by a verb V j , then V j is an argument of V i , i.e., the V i tree cannot be adjoined to any arbitrary S node. It can only be adjoined to an S node that belongs to the V j tree. This derivational constraint together with WCC will be called the strong co-occurrence constraint (SCC). SCC assures that each elementary tree is semantically coherent and all trees are combined in a semantically coherent manner. We say that an LTAG assigns correct structural description to a string when the derivation of the string obeys SCC. It is easily shown that under SCC, LTAGs can handle scrambling from up to one level of embedding only. Thus, for example, for the string (6) below corresponding to a sentence with scrambling from depth two, there is no LTAG obeying SCC that can derive it. (6) NP 2NP 3 NP 1 V 3 V 2 V 1 We will now consider an extension of LTAG called tree-local multicomponent LTAG (Tree-local MC-LTAG). In an MC-LTAG an auxiliary tree can be a set of trees, say, 1 and 2 , with at least one of the trees anchored on a lexical item. The derivation proceeds in the same manner as in an LTAG; however the tree local requirement speci es that if a multi-component auxiliary tree set is used in a derivation then all components of the auxiliary tree set must be adjoined or substituted at distinct nodes of the same elementary tree5 . It can be shown that treelocal MC-LTAGs are weakly equivalent to LTAGs, i.e., they both generate exactly the same set of strings. However, tree-local MC-TAGs can produce structural descriptions not obtainable by LTAGs (for some early work on MC-TAGs see (Joshi 1987, Weir 1988)). Tree-local MC-LTAGs are a very well motivated extension of LTAGs. 5 In the actual linguistic applications the two distinct nodes are such that one of them dominates the other
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In an LTAG when an auxiliary tree is adjoined to a tree at a node p in we can view the situation as follows. Split the tree at p into the supertree of (denoted by n p, i.e., the tree above above p) and the subtree of (denoted by =p, i.e., the tree below p). Now adjoining to at p can be seen as \wrapping" n p and =p around . This wrapping can be expressed by a combination of substitution and adjunction of the two components of into the tree . Thus the standard adjunction in LTAG can be viewed as a special case of the tree-local MC-LTAG derivation. This is the main idea behind the de nition of tree-local MC-LTAG.6 An immediate consequence of adopting tree-local MC-LTAG is that the previously considered string (3), now represented here as the string (7) below (7) NP 22 NP 1 1 NP 1 2 NP 2 1 V 2 V 1 which was not derivable by any LTAG can be now obviously derived in a tree-local MC-LTAG. The tree in Figure 4 can be thought of in terms of two components, 11 and 12 by splitting at the S node below the root node (see Figure 5). Now the string (7) can be derived by adjoining 11 at the S node immediately below the root node and 12 at the other interior node S . This derivation is shown in Figure 6.
β: 1
{β :
β12:
S
11
1 NP1
S
S
e FIGURE
}
1 NP1
VP 2
NP1
S
V1
5 Splitting an elementary tree into two parts
Now, surprisingly, it turns out that tree-local MC-LTAGs under SCC can handle all sentences with scrambling from up to two levels of embedding and beyond two levels they fail to do so, in the sense that beyond two levels they fail to assign correct structural descriptions (i.e., obeying SCC) to all sentences. Thus, for example, for the string (8) below corresponding to scrambling from three levels of embedding (8) NP 2 NP 4 NP 3NP 1 V 4 V 3 V 2 V 1 6 The component trees of the elementary tree set in a tree-local MC-TAG are not arbitrary trees. They can be thought of as coming from either splitting an elementary tree of an LTAG at a given node, as described above, or by splitting an elementary tree at a non-branching edge (not described in this paper, for further information see Joshi and Vijay-Shanker (1999)).
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13
S NP22
S 1
NP1
β1
S 1
NP2
S 1
NP1 e
β2
VP 2
NP1
S
V
NP PRO
FIGURE
1
VP 1
2
NP2
NP2
e
e
V2
6 Tree-local adjunction of an MC-LTAG tree set
it can be shown that there is no tree-local MC-LTAG that can derive it while obeying SCC. Thus tree-local MC-LTAG is a class of grammars which satis es the property Q (see section 3, item 2), i.e., all7 grammars in this class assign correct structural descriptions to all sentences with scrambling from depths up to two and beyond two they fail8. So now we are presented with a choice (unlike the case of center embedding of relative clauses in English). We can either opt for the traditional way, i.e., continue to regard the diculty of scrambling from depths greater than two as due to processing diculties, i.e., go along with the accepted wisdom derived from the complexity of the center embedding of relative clauses in English. Then we would continue to look for extensions of LTAGs that will permit scrambling from arbitrary depths of embedding and relegate the reluctance of native speakers to accept such sentences to performance factors. Alternatively, we can adopt tree local MC-LTAGs as adequate for describing scrambling. Then since tree-local MC-LTAGs as a Strictly speaking, almost all, i.e., all except for a nite set of grammars. For further work on derivations in tree-local MC-LTAG and their use in describing clitic movement, see (Joshi and Kulick 1998, Kulick 1998). Kulick (Kulick 1998) has also investigated all other scrambling patterns (i.e., all patterns other than those indicated in (1) in Section 4) in German for depths up to two and shown the adequacy of tree-local MC-LTAG 7 8
14 / Bibliography
class have the property Q, we conclude that Q is a competence property and not a performance property!
5 Conclusion
We have discussed the following issue: How do we decide whether a certain property of language is a competence property or a performance property? We stated the claim that the answer to this question is not given a-priori. It depends on the formal devices (formal grammars and machines) available to us for describing language. We showed that in the case of center embedding of relative clauses in English, we were forced to conclude that the property that sentences with more than two levels of embedding are dicult to interpret is a performance property and not a competence property. In contrast, for the case of scrambling (in German) with respect to a corresponding property we can indeed exhibit a class of grammars such that for all grammars in this class the corresponding property holds. Thus we are given the possibility of claiming this property to be a competence property rather than a performance property. To the best of our knowledge, this is the rst such case where a choice of this kind presented. The lack of such a choice before this case was discovered has led to the traditional assumption that all properties similar to the properties considered in this paper should be treated as performance properties. Our main conclusion is that this assumption is not justi ed at all.
Bibliography
Tilman Becker, Aravind K. Joshi and Owen Rambow. 1991. Long-distance scrambling and tree-adjoining grammars. In Proceedings of the European Association of Computational Linguistics (EACL) Meeting, Berlin, April 1991. Tilman Becker, Owen Rambow and Michael Niv. 1992. The Derivational Generative Power, or, Scrambling is Beyond LCFRS. Technical Report IRCS-92-38, Institute for Research in Cognitive Science, University of Pennsylvania. A version of this paper was presented at MOL3, Austin, Texas, November 1992. Aravind K. Joshi and K. Vijay-Shanker Compositional semantics with lexicalized tree-adjoining grammar (LTAG): How much underspeci caion is necessary? Proceedings of the Third International Workshop on Computational Semantics,Tilburg, The Netherlands, January 1999. Seth Kulick 1998. Non-local dependencies and multicomponent lexicalized tree-adjoining grammars. Ph. D. Dissertation proposal, University of Pennsylvania. Aravind K. Joshi and Seth Kulick 1998. Derivations in MC-LTAG. Work in progress.
Bibliography /
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Aravind K. Joshi. 1987. An Introduction to Tree Adjoining Grammars. In A. Manaster-Ramer, editor, Mathematics of Language. John Benjamins, Amsterdam. George A. Miller and Noam Chomsky. 1963. Finitary models of language users. In R.D. Luce. R. Bush and E. Galanter (Eds.), Handbook of Mathematical Psychology, Volume II, Wiley, New York. Owen Rambow. 1994. Formal and Computational Aspects of Natural Language Syntax. Ph.D. thesis, Department of Computer and Information Science, University of Pennsylvania. David J. Weir. 1988. Characterizing Mildly Context-Sensitive Grammar Formalisms. Ph.D. thesis, Department of Computer and Information Science, University of Pennsylvania.
