LECTURETTE #12: INTRODUCTION TO THETA-THEORY Back in Lecturette #5 on DS and LF i mentioned that 'DS is a representa- tion of *thematic* relations'. REST describes nominal constituents as bearing *thematic roles* and taking part in thematic relations with each other and the verbs and other constituents licensing them. The word 'thematic' is in REST normally abbreviated by the Greek letter theta (which of course in this medium i have to spell out). So instead of speaking of 'thematic roles' or 'thematic relations' one speaks of 'theta-roles' and 'theta-relations'. When i was writing my dissertation, my advisor expressed some anxiety about the propriety of using a capital Theta in referring to 'Theta-Theory' or the 'Theta-Criterion' (which i shall discuss below). But since then i have seen the capital Theta used in print by others, so it seems to be quite legitimate nowadays. One of our participants responded to the statement quoted above from Lec- turette #5 by saying, 'This view seems exactly the same as what Fillmore argued in "Case Grammar" in the 1970's', and this is very true (except that Fillmore's views actually began appearing in print no later than 1968, with the publication of 'The Case for Case' in Bach & Harms' Uni- versals in Linguistic Theory). REST's 'theta-roles' are in general equi- valent to Fillmorean 'deep case' relations. They are formal semantic roles like Agent, Patient, Experiencer, Theme, Instrument, Path, that sort of thing. (Bear in mind, however, that these are generalized labels; a theta-role is really an idiosyncratic property of the verb, predictable from its semantics but not necessarily having much in common with any theta-role assigned by any other verb) For a detailed discussion of these doohickeys within a general REST context i refer you to Ray Jacken- doff's 1990 book (which i mentioned earlier in my posting 'Clarification on Semantic Roles') Semantic Structures (Current Studies in Linguistics #18, MIT Press); most of the details of Jackendoff's analysis are not relevant to syntactic theory per se, at least according to the assump- tions of REST as generally practiced. What's important for this discus- sion is not so much precisely what theta-role a given nominal bears as merely the fact that it bears one. Theta Theory assumes a fundamental asymmetry amongst syntactic categories (as we proceed, it shall become evident that similar asymmetries pervade the framework). In this case, the basic asymmetry relates to the cate- gorial feature +/- N or, in terms of Jackendoff's 1977 version of X-Bar Theory, +/- Object. Archetypically, nouns, being +N (Jackendoff's -Ob- ject), *bear* theta-roles; verbs and adpositions, being -N (Jackendoff's +Object) *assign* them. The fundamental axiom of Theta-Theory is the Theta-Criterion. The basic idea of the Theta-Criterion is that any given clause has a set of NPs and a set of theta-roles, and THERE MUST BE A ONE-TO-ONE CORRESPONDENCE BE- TWEEN THESE TWO SETS. Each NP must bear one and only one theta-role, and each theta-role must be borne by exactly one NP. Of course, the number of theta-roles varies from clause to clause, just as does the number of nominals; there is absolutely no notion that any given clause must manifest all possible theta-roles. Thus a verb like 'walk' has only one theta-role to assign (typically labelled 'Agent'), and the Theta-Criterion is trivially satisfied in a sentence like (1a). Similarly, the verb 'like' has two theta-roles to assign ('Experiencer' and 'Theme', perhaps), as in (1b), and 'give' has three ('Agent', 'Bene- ficiary/Recipient', and 'Theme' or 'Patient'), as in (1c). The list of theta-roles that a given verb can assign is sometimes spoken of as its 'theta-grid', a term roughly synonymous with the terms 'valency' and 'subcategorization frame' in other frameworks. A nominal bearing one of those theta-roles is then said to fill the appropriate 'slot' in the verb's theta-grid. (1) a. I walked b. I like chocolate. c. I gave Claude a pen. These are simple cases. A number of questions can easily be raised, lead- ing to refinements and improved understanding of Theta-Theory. First of all, i said that in a given clause the number of NPs and the number of theta-roles must be equal. And i said that 'walk' has only one theta-role to assign. So what about a sentence like (2), in which there are nevertheless two NPs? (2) I walked to the store. This brings up the question of *adjuncts*. The lexical head of (2) is 'walked' (although strictly speaking the head of a clause is Infl or Agr, this functional category is typically realized on the lexical verb, and that verb can informally be referred to as the 'lexical head'. However, in a sentence with a composite verb, like 'I was walking', the 'main verb' must for semantic reasons still be thought of as the 'lexical head' even though Infl/Agr is realized on the auxiliary instead.), and as it has only one theta-role to assign it can have only one *argument*, 'argu- ment' being understood here as an NP satisfying a slot in the head's the- ta-grid. Loosely defined, an adjunct is any constituent that is neither a head nor an argument of that head; semantically it can be thought of as providing unnecessary but useful, interesting, or relevant information. In (2) the phrase 'to the store' is an adjunct. It takes the form of a PP, and the head of that PP, 'to', has a theta-grid of its own, being able to assign a theta-role ('Goal' or 'Path') to its complement (unlike verbs, adpositions generally can only assign one theta-role apiece; i don't know of any exceptions). So 'store' gets a theta-role not from the verb 'walk' but from the preposition 'to'. So (2) has two NPs and two theta-roles, which last lie in the assignment of two different lexical heads. Having briefly addressed the possibility of adjunct NPs, whose theta- roles are typically assigned by adpositions (or by morphological case- markers, in those languages that have this option), i must now address the flip side of the issue. Consider (3), an alternative version of (1c). I said above that 'give' has three theta-roles to assign, and in (1c) three are three NPs to bear them. In (3) we find the same three NPs, but one of them is in a PP. Is 'Claude' then, like 'store' in (2), an argument of 'to' and assigned a theta-role thereby rather than by 'gave' as in (1c)? (3) I gave a pen to Claude. In a word, no. 'Claude' is still an argument of the verb and gets its theta-role thence. In (3) the preposition 'to' is a 'dummy' preposition inserted for reasons of Case Theory, as shall be discussed when we get to that subject. We can to some extent regard it as a syntactically minimal case-marker, like the dative case-marking that would take its place in some other language like Latin or Hungarian that has the option. (One obvious difference between the 'dummy case-markers' in English and the case morphemes in the more traditional Indo-European languages like Latin is that they are attached to whole NPs rather than to individual words. But it can be claimed that this is because Latin has a morpho- syntactic rule of case-agreement which requires all +N words dominated by an NP node to agree with that NP (and/or its head N0) in case. Hungarian has a large number of 'case-markers' that are commonly treated as suf- fixes, just like Latin case-markers, but they are affixed to whole NPs and Hungarian has no rule of case-agreement within NPs. So actually the case-markers in Hungarian closely resemble the 'dummy case-markers' in English in a lot of ways.) In comparing (1c) and (3) we see two different possibilities in English for the manifestation of three distinct theta-roles assigned by the same lexical head. What about more? It can be argued that a verb like 'sell' has four theta-roles to assign, Agent (the seller), Beneficiary/Recipient (the buyer), Theme (the thing sold), and the sale price, which might in formal terms, for lack of anything better, be called the Path. As we can see from (4), the last of these has no choice in English but to be ex- pressed superficially as a PP, though it arguably gets its theta-role from the verb. (4) a. I sold a pen to Claude for 15c. b. I sold Claude a pen for 15c. But if 'sell' has four theta-roles to assign, what about a sentence like (5), in which one of them isn't expressed? Isn't this a violation of the Theta-Criterion? (5) I sold Claude a pen. There are two approaches to this problem, both trying to salvage the spi- rit of the Theta-Criterion. One is to suggest that all the theta-roles in the verb's theta-grid are present and assigned, but one of them is assigned to a phonologically null NP (as we shall see in the discussion of Case Theory, if the NP in question has no phonological realization it doesn't need Case, and therefore doesn't need a 'dummy' preposition to case-mark it.) The other is to suggest that 'sell' may have four theta- roles to assign but doesn't insist on assigning all of them in every instance. This approach brings in the possibility of 'optional argu- ments', and can be invoked to account for the fact that some verbs are optionally transitive while others are obligatorily so; cf. (6-7). If both 'eat' and 'devour' are defined in the lexicon as transitive in the sense of having two theta-roles to assign (not necessarily the best, let alone only useful, definition of transitivity) but 'eat' is additionally defined as being allowed to *withhold* one of them, then its optional transitivity, contrasting with the obligatory transitivity of 'devour', is accounted for. I like this approach because it facilitates an under- standing of the fact that not all verbs having multiple theta-roles to assign have optional arguments. After all, if both (6a-b) have two the- ta-roles, why can't we say the same for (7a-b)? But if we can say in- stead that 'devour' is lexically obligated to assign both its theta-roles in all circumstances, the unacceptability of (7b) is accounted for. (6) a. Have you eaten anything? b. Have you eaten? (7) a. He devoured the sandwich. b. *He devoured. It should, however, be noted that among the verbs with optional arguments a generalization may be made about those arguments: I'm not absolutely sure about this, but from what i've seen it seems to be the case that (1) certain kinds of theta-roles (e.g., 'Beneficiary/Recipient' and loca- tional arguments) are more typically to be optional than others, and (2) there is a general ranking, roughly corresponding to the 'Obliqueness Hierarchy' in frameworks like HPSG, as to which arguments are optional: the most 'oblique' argument ('sell's Path, 'eat's Patient) is the most optional. This fact, if it is a fact, as well as the general feasibility of optional arguments, may be susceptible to a functional/semantic expla- nation outside the bounds of REST. Whether such an explanation could also account for the above-discussed fact that synonymous verbs may dif- fer in the optionality of their arguments is another question. One remaining problem with the Theta-Criterion i am prepared to discuss at this time, but it will have to wait till the next Lecturette, on the Projection Principle. Best, Steven --------------------- Dr. Steven Schaufele 712 West Washington Urbana, IL 61801 217-344-8240 fcosws@prairienet.org **** O syntagmata linguarum liberemini humanarum! *** *** Nihil vestris privari nisi obicibus potestis! ***