Abstract: I wish to consider whether different views of the organization of grammar recognize significant structural mismatches between the syntactic and semantic representations and if so, how they deal with them. I will be particularly interested in the question of principles of grammar that serve, among other things, to limit the degree to which such discrepancies are sanctioned.

I. A Rough Categorization of Grammatical Theories Based on Syntax-Semantics Mismatches

Various architectures of grammar differ with regard to whether they are philosophically at ease with the existence of significant mismatches between syntactic and semantic form. Thus Montague 1970 went on record as committed to the idea that the grammatical organization of sentences could be taken as a sufficient representation of the logic of the sentences with no modification whatsoever, though most implementations of Montague's ideas in fact contain, for convenience, rules of translation, usually accompanied with apologies. We may include in this group GPSG (Gazdar et al. 1985), early HPSG (Pollard and Sag 1994), and Categorial Grammar (for example, Dowty 1982, Steedman 1987). Similarly, some functionally oriented views, Langacker's influential Cognitive Grammar (1987a,b), for example, read as if the form of language is a pretty direct representation of its content, despite sporadic explicit assurances to the contrary. On the extreme version of this view, if such exists, we have a kind of Bauhaus grammar in which form not only follows, but actually is function.

Most conceptions of the organization of grammar, however, tolerate or even relish structural, categorial, and/or ordering discrepancies between the (or a) syntactic level of description and the (or a) conceptual level. Here we may divide the theories into two camps depending on whether or not there is a derivational relation between the formal and the meaningful levels, i.e., whether or not there is a calculation that can be done to translate one level into another. In the category of theories that derive one level of structure, say logical form, from another, say surface structure, fall the earliest to the latest versions of transformational grammar, the standard theory of Aspects, (Chomsky 1985), generative semantics as compiled in McCawley 1998, GB, (Chomsky 1981) P&P and most versions of Minimalism (see Webelhuth 1995 and the references cited there). It is, of course, always possible to cast a derivation as a complex representation consisting of a number of ordered trees (cf. the level of "transformational structure" of LSLT (Chomsky 1975) or Syntactic Structures (Chomsky 1957)) or even encode all of this information in a single static tree, but the metaphor of movement may still remain. If it doesn't, that is, if we take a tree replete with binders in their ultimate position and traces in their "original" position, then interestingly, the tree becomes a simultaneous representation of syntactic and logical relations and the theory then becomes one of the previously discussed type, in which there is no significant mismatch between two kinds of structures.

Several fairly recent theories do not start with a single, complete representation at one distinguished level, translating it step-wise into another, but rather develop two (or more) representations simultaneously. The clearest example of such a technique is to be found in LFG, where the functional structure and constituent structure are built up simultaneously from units that simultaneously fit into both kinds of system, though possibly in different ways. The lock-step construction of the formal and contentful aspects of complex signs from component signs that characterizes recent work in HPSG is also of this type. While very different from HPSG in its assumptions about the nature and identity of levels of representation, RRG also seems to operate under some version or another of the "rule-to-rule hypothesis", as Bach (1976) called it.

Finally, there are at least two views of how grammar ought to operate that radically segregate the representational levels, deriving each according to its own units and principles with complete, or near-complete disregard for what is going on in the other levels. I am thinking here of Jackendoff's recent model (Jackendoff 1997) and my own autolexical view (Sadock 1991) Such theories work by comparing full simultaneous representations and deciding whether or not they are similar enough to count as representations of a single expression in the language under description. While derivational theories operate by constraining their derivations, theories of autonomous components constrain possible associations of structures.

In what follows I wish to compare, albeit briefly, similarities and differences in the nature of the constraints on grammars of the derivational type with constraints on grammars of the simultaneous, autonomous-component type. I will take as a representative of the derivational type what might be called classical GB and will, unsurprisingly, choose my own ideas about the structure of grammars as representative of the non-derivational type. GB is quite well known, but despite my efforts and those of a few stalwarts, the autolexical model remains unfamiliar to many. Therefore, and for the sake of concreteness, let me sketch out just enough of an autolexical model to allow for the comparison to proceed.

II. Basic style of autonomous modular grammar

The grammar consists of several generative devices, each capable of characterizing an infinite number of structures and their associated terminal strings. Here I will only consider a syntactic and a semantic module and the lexicon that helps to tie them together.

Because complexity arises through the interaction of autonomous components, each of these can be kept relatively simple. It has proven adequate to assume a very straightforward, context free phrase structure syntax which, notation aside, is a proper, and very small subpart of just about every reasonably well-described syntactic theory, e.g., something containing perhaps the following rules, among others.

    (1) Syntax:

        a. S --> NP, V'

        b. V' --> V XP

        c. PP --> P NP

        d. NP --> DetP N

        e. CP --> Comp S

For the grammar of semantic representations, let us assume a system of similar type, but with different categories and related, though not identical rules, say something along the following lines.

    (2) Semantics:

        a. Prop --> Arg, Pred

        b. Prop --> Prop, Op

        c. Pred --> Arg, Rel

        d. Pred --> Prop, RelOp

        e. Arg --> QP(Prop)

Rules 2a. and 2b. state respectively that a proposition can consist of an argument and a predicate or a proposition and an operator (e.g. negation). 2c. and 2d. indicate that predicates can consist of an argument and a relation (e.g., the meaning of a transitive verb) or of a proposition and what I have called a relational operator (for example, the meaning of complement-taking verb like believe.) Rule 2e. provides the structure of argument expressions in terms of quantifiers phrases and propositions. Note that there is a strong but not exceptionless tendency for there to be a correspondence between the categories of the semantics and the categories of syntax. Clauses, for example, strongly tend to be the counterparts of propositions.

The lexicon is part of the interface system that ties the several independent components together. Lexical items typically (but not always) have a function in both the syntax and the semantics, and thus to be well formed, the semantic value of each lexical item that figures in an expression must be discharged in the semantic component and its syntactic category discharged in the syntactic component. The following is a presumably self-explanatory sample.

    (3) Lexicon:

        a. dog: syntax: N
                semantics: Pred

        b. bark: syntax: V
                semantics: Pred

        c.mother: syntax: N
                semantics: Rel

        d. love: syntax: V [/_NP/]
                semantics: Rel

        e. believe: syntax: V [/_CP/]
                semantics: RelOp

        f. belief: syntax: N
                semantics: RelOp

        g. seem: syntax: V [/_VP/]
               semantics: Op

Now one of the things we find when comparing the syntax and semantics is a fairly pervasive possibility of mismatch in terms of the categories that lexical items represent. The two major syntactic categories, N and V, crosscut the set of semantic categories Pred, Rel, Op, and RelOp. There are, however, higher-level default correspondences in category between semantics and syntax that can be stated in the interface component independently of lexical specifications. The most important of these are given in the following table:

    (4)        Syntax             Semantics

                    S                     Prop

                    NP                 Arg

                    VP                 Pred

Because of the existence of these supra-lexical correspondences, verbs like bark and nouns lime dog will ordinarily be found to have different semantic functions, even though they belong to the same semantic category. Thus we can't say *Barks dog to mean something like "Barking things are dogs" since the lexicon and syntax of English do not allow bark to head an NP that corresponds to an argument, nor do they allow dog to head a VP corresponding to a predicate. While there is nothing wrong with the meaning structure that arises from this combination of the meanings that *Barks dog, should represent, the syntax that would have to correspond to it through the correspondences expressed in (4) is ill formed.

A second type of mismatch that arises directly out of a system such as I am describing concerns the structural relations that obtain in the representations of an expression from the various modules. Consider where seem will occur given its lexical entry and the modular grammars set out above:

(5)              Syntax                       Semantics

                         S                                 Prop
                       /    \                              /        \
                   NP     VP                SEEM       Prop
                            /    \                                /      \
                          seem VP                       Arg     Pred

Note that the position of the boxed NP in the syntax and the position of the boxed Arg(ument) in semantics are necessarily different given the grammars in (1) and (2) and the lexical specifications of seem in (3g). Such a discrepancy is tantamount to the rule of NP movement (nee Raising to Subject) - but without movement or traces thereof.

III. Principles of Grammar on a Multi-Modular View

Movement rules in derivational grammars are constrained by various principles such as the cyclic principle, Case Theory, the Theta Criterion, and the ECP. But on the view of grammar I advocate there are no movement rules. How, then, does multimodular grammar keep discrepancies between autonomous representations from growing to monstrous proportions? How, if at all, do the various principles that constrain transformational grammar work out in the present system?

First of all, certain important principles simply follow from the architecture of a multimodular grammar. Consider the Theta Criterion and the Case Filter of the traditional GB literature. The Theta Criterion states that each referential NP must be assigned one and only one theta role and that each theta role that is assigned by a theta role assigner must be assigned to one and only one NP. I think it is clear that theta roles ("agent" and "patient", for example) are semantic roles. In the present framework, semantics has its own grammar in which functors and predicates automatically combine with exactly the right number of arguments and all arguments must automatically be arguments of something. This follows just from the nature of a phrase structure grammar of semantic form such as the one presented in (2) above. Nothing else needs to be said to achieve the effect of the Theta Criterion.

Similarly, the Case Filter, which requires that every pronounced NP be assigned case, is taken care of automatically through the structure of the grammar. Although this principle seems a little more abstract, its effect, I think, is basically to assure that the actual NPs that are found in the syntax of an expression have appropriate syntactic roles to play as subjects, objects, or objects of prepositions. Once again, this follows directly from the adoption of a phrase structure grammar of surface form as is assumed here. According to the rules in (1), NPs only get into syntax as subjects of S, as complements of V, or as objects of P. All grammatical occurrences of NPs are therefore "assigned Case" (and in languages with case systems, are also assigned case) without the need for any external principle such as the Case Filter, indeed without the need for an abstract notion like Case.

While the Theta Criterion and the Case Filter constrain individual levels of representation, or at least do so on the multi-modular view, other principles deal more directly with mismatches. Chief among these is surely the Projection Principle of Chomsky (Chomsky 1981), which demands that the subcategorization requirements of lexical items be satisfied at all syntactic levels including, viz., Deep Structure, Surface Structure, and Logical Form. In automodular terms, such a requirement would mean that the complements of a lexical item in syntax would always correspond to the arguments of its semantic value, and vice versa, thus effectively preventing certain sorts of mismatches between syntax and semantics from even arising. This version of the Projection Principle therefore cannot be adopted in the framework that I am considering here. While this might be taken to be a good thing in view of the fact that the Projection Principle has fallen on rather hard times lately (Chomsky 1995:187-8), investigations in the framework of autonomous modular grammar indicate that there is something quite right about such a constraint, at least as a default mechanism. Over a wide range of data it appears to be clear that categories and structural relations tend to match between any two representations, an observation that was termed the Generalized Interface Principle in Sadock and Schiller 1993. The tendency is even more thoroughgoing than the Projection Principle, since it holds not just for subcategorization, but for category, order, and constituency. The crucial difference between the Projection Principle and the Generalized Interface Principle is that the latter is violable. Mismatches are allowed, but only when they are forced by some other factor or combination of factors.

A constraint that follows as a violable corollary of the Generalized Interface Principle is Baker's Mirror Principle (Baker 1985). The Mirror Principle states that morphological derivations must directly reflect syntactic derivations (and vice versa). Take a language in which the morphology is left branching and the syntax is head last, a rather common type represented by Turkish, Japanese, and Eskimo, among others. Now consider a causative of an intransitive predicate and assume that it can be shown that the syntax is that of a two-clause sentence.

    (6)                S
                      /    \
                    /        \
               NP            VP
                                / \
                              VP \
                            /    \   \
                        VP     \    \
                        / \        \     \
                    NP   V     V    V
            Dog baby cry make can
                             V     V     V
                                \   /      /
                                 V      /
                                    \   /
                                      V

By the Generalized Interface Principle, the hierarchical relations that are found within the morphological verb should match the hierarchical relations that are found in syntax as much as possible. Since can c-commands make, and make c-commands cry in the syntax, the same c-command relations should obtain in the morphology, as they do in the diagram above.

Consider next the much more specific principle known as Burzio's generalization which, as cited by Haegeman 1994: 321 states that if a verb fails to assign Case to its complement, then it must not assign a Theta role to an external argument. On my view Case is a matter of syntax and theta roles are a matter of semantics. In multimodular terms this principle has to do with the fact that the lexical specifications of certain verbs does not allow for enough NPs in the syntactic complement of the verb to fill all the argument roles that are required by the semantic predicate that the verb expresses. Therefore, if the meaning of the verb were such as to require a referential item in the semantic subject position, then there would be too many arguments in semantic structure for the number of NPs in syntax. Therefore, for the meaning requirements of the verb to be satisfied, there must be an extra NP slot somewhere in syntax. The subject, since it is always an available syntactic position, fits this bill. Hence something like Burzio's generalization without stipulation.

The final principle I would like to mention is the principle that movement is generally upward, something that I will call the syntactic Buoyancy Principle. It follows, in a way, from the ECP and other considerations in GB and related theories. Suppose we can identify DS with semantic structure in an automodular theory and SS with syntactic structure. Then it should be possible to translate the Buoyancy Principle in non-movement terms by requiring that an element whose topological position in semantic and syntactic structure differ must be higher in the syntactic tree than the semantic tree. This can be done by defining an notion of intermodular c-command (the details of which I will not burden the reader with) and then stipulating something like the following:

    (7) Syntactic Superiority Principle (SSP)

        If A is a syntactic node and A' is its semantic correspondent, then A must
        intermodularly c-command A'.

But there is an immediate problem. If something has floated to the syntactic surface, then it must have displaced something else that will then not meet the SSP. Despite the initial plausibility of the enterprise of redefining the Buoyancy Principle in automodular terms, it turns out to be remarkably difficult to do. Thus while the subject in (nn) intermodularly c-commands the position of the corresponding argument in (nn), not that the verb seem does not intermodularly c-command the operator SEEM.

But this might not turn out to be a disaster for automodular theory given the fact that there are well-known exceptions to the syntactic buoyancy including all those examples (like quantifier lowering, adverb lowering, and so on) that in movement theories are made to conform by applying the principle to SS and LF, rather than DS and SS. Raising at LF is, in fact, lowering between semantic and syntactic structure. I therefore think it is worthwhile considering the possibility that the Buoyancy Principle is either an artifact of the derivational theory or, as Yehudah Falk suggested in a comment to this paper, a self-fulfilling prophecy of the transformational project. At the moment, this is merely a conjecture, but it is one that I intend to test in future work.

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