Semantic representation

In referring to the ‘ logical well-formedness ’ of a semantic representation, I used the terms ‘ proposition ’ and ‘ predicate ’ as they are used in symbolic logic. I will in fact argue that symbolic logic, subject to certain modifications, provides an appropriate system for semantic representation within the framework of transformational grammar. I thus hold that the much-criticized title, The laws of Thought, which George Boole gave to the first work on symbolic logic, is actually much more appropriate than has generally been thought the case.

Since the representations of symbolic logic appear at first glance to be of a quite different formal nature from the labeled trees which constitute syntactic representation, one might expect that the mechanisms which link semantic representation and surface syntactic representation would divide into two separate systems, a system of ‘semantic rules’, which would operate on representations of the one kind, and a system of ‘ syntactic rules ’, which would operate on representations of the other kind, and that the two kinds of representation would meet at an intermediate ‘ level ’ corresponding to what Chomsky calls ‘ deep structure However, as pointed out by Lakoff (remarks at the Texas Conference on Language Universals, 15 April 1967), the difference in formal nature between syntactic and semantic representation is only apparent. Lakoff observes that some of the traditional categories of symbolic logic are reducible to others (e.g. quantifiers can be considered as two-place predicates, one place corresponding to a propositional function and the other to a set) and that only a small inventory of syntactic categories functions in the ‘ deeper ’ stages of the ‘derivational history’ of sentences (Lakoff 1965; Bach 1968). Many syntactic categories are ‘ derived ’ rather than basic; for example, most prepositions originate as parts of verbs, so that prior to a transformation which adjoins the ‘ prepositional ’ part of a verb to its object, a verb-plus-PrepP combination has the form verb-plus-NP. Likewise, many category differences which had figured in previous analyses have turned out to hinge merely on whether certain lexical items do or do not ‘ trigger ’ certain transformations. For example, there is no need to set up the categories PredP, Aux, and Modal, which appear in Chomsky (1965): one can treat the various auxiliary verbs as simply verbs¹ which (like the verbs seem, appear, etc.) trigger a transformation of ‘ VP-promotion’, which detaches the VP from the embedded sentence and puts it after the verb in question :²

and which have the additional peculiarity of being combined with the tense element by a fairly early transformation  and which are thus affected by all subsequent transformations that mention the ‘topmost verb’ of a clause.

Lakoff and Ross concluded (lectures at Harvard and M.I.T., Autumn 1966) that the only ‘ deep ’ syntactic categories are Sentence, Noun-Phrase, Verb-Phrase, Conjunction, Noun, and Verb, and that all other traditionally recognized categories are special cases of these categories that correspond to the ‘ triggering ’ of transformations by certain lexical items. Bach (1968) then discovered some quite convincing arguments that the Noun-Verb distinction need not be part of this inventory of categories. He argues that all nouns originate in predicate position (e.g. the anthropologist arises from a structure paraphrasable as ‘ the x such that x is an anthropologist ’) and that the difference between nouns and verbs is that nouns but not verbs trigger a transformation which replaces a relative clause by its predicate element. At the Texas Conference on Language Universals, Lakoff observed that the resulting inventory of categories (Sentence, NP, VP, Conjunction, and ‘ Contentive ’ - the term introduced by Bach for the category containing nouns, verbs, and adjectives) matches in almost one-to-one fashion the categories of symbolic logic, the only discrepancy being that the category VP has no corresponding logical category. However, Lakoff argued, there is in fact virtually no evidence for a syntactic category of VP; the various facts that have been cited as evidence for such a category actually have nothing to do with node labels but only with the surface immediate constituent structure, and (as argued in Fillmore 1966 and McCawley (forthcoming)), a surface structure having a constituent consisting of a verb and its objects arises anyway, regardless of whether there is an underlying constituent VP, just as long as tenses and auxiliary verbs are assumed to originate outside of the clauses that they appear in.³ If one accepts one of the proposals that would do away with VP as an underlying category (and thus do away with the phrase structure rule S → NP VP in favor of a rule S → V NPⁿ or something such), then not only is the correspondence between ‘deep’ syntactic categories and the categories of symbolic logic exact, but the ‘phrase structure rules ’ governing the way in which the ‘ deep ’ syntactic categories may be combined correspond exactly to ‘formation rules’ for symbolic logic, e.g. the ‘phrase structure rule’ that a Sentence consists of a ‘Contentive’ plus a sequence of Noun Phrases corresponds to the ‘ formation rule ’ that a proposition consists of an n-place predicate plus an ‘ argument ’ for each of the n places in the predicate.⁴

Since I believe that the correspondence between syntactic and logical categories is slightly different from that proposed by Lakoff (in that I believe that a slightly different kind of symbolic logic is needed for semantic representation), I will not go into the details of the correspondence which Lakoffset up. However, I observe that if such a correspondence is valid, then semantic representations can be considered to be objects of exactly the same formal nature as syntactic representations, namely trees whose non-terminal nodes are labeled by symbols interpretable as syntactic categories. One might object that the trees of syntax are different in formal nature from those which formulas of symbolic logic may be interpreted as, in that the nodes of syntactic trees have a left-to-right ordering relation, whereas it is not clear that there is any left-to-right ordering on the nodes of the trees that I am proposing as semantic representations.

Whether this objection is correct depends on whether one holds that things which mean the same must have the same semantic representation or merely that ‘ equivalence ’ of semantic representations can be defined in such a way that things which mean the same have ‘equivalent’ representations. The former position would, of course, imply that semantic representations cannot have ordered nodes, since

(12) John and Harry are similar.

(13) Harry and John are similar.

would have to have the same semantic representation, and that representation thus could not have the node corresponding to John preceding the node corresponding to Harry or vice versa. However, no evidence has as yet been adduced for accepting this position rather than the other one. Until such evidence is found, the question of the ordering of nodes gives no reason for believing semantic representations to be different in formal nature from syntactic representation. I will thus treat the elements of semantic representations as having a linear order and assume that there are rules such as

(14) p or q = q or p

which define an equivalence relation on these representations.

These considerations suggest that there is no natural breaking point between a ‘ syntactic component ’ and a ‘ semantic component ’ of a grammar such as the level of ‘deep structure’ was envisioned to be in Chomsky (1965)⁵ and imply that the burden of proof should be on those who assert that such a breaking point exists. In McCawley (1968a), I argue that setting up a level of ‘deep structure’ makes it impossible to treat as unitary processes certain phenomena which in fact are unitary processes, in particular, that the use of respective and respectively in English involves a phenomenon which can be stated as a single rule if there is no level of ‘ deep structure ’, but must be divided into special cases, some of which correspond to ‘semantic interpretation rules’ and others to ‘transformations’, if a level of ‘deep structure’ is accepted. Since the argument is rather involved, I will not reproduce it here but refer the reader to McCawley (1968a) for details; the general outline of this argument for rejecting a level of ‘ deep structure ’ is, of course, identical to that of Halle’s celebrated argument (Halle 1959) for rejecting a ‘ phonemic ’ level.

¹ This proposal was first made in Ross (1969). A slight change which I have made in Ross’s analysis forces me to use the term ‘VP-promotion’ for the analogue of the transformation which he and Lakoff call ‘it-replacement’. I argue in McCawley (1970) that English has underlying verb-initial order and that that is still the constituent order when this transformation applies. This implies that the transformation is acutally one that raises the subject and not the VP into the next higher clause; indeed, under the newer analysis there is no such constituent as VP.

² The analysis of seem, etc. as intransitive verbs with a sentence subject is due to Jespersen (1937:57); details of this analysis are given by Rosenbaum (1967: 71-9). The application of ‘VP-promotion’ to the first of the two trees causes the topmost two NP nodes and the two S nodes in the left branch to vanish by virtue of the ‘tree-pruning’ principles presented in Ross (1966).

³ Fillmore (1966) does not accept Ross’s analysis of auxiliaries as verbs but has an alternative proposal in which (as in Ross’s proposal) auxiliaries originate outside of the clause that they appear in.

⁴ The rules will, however, probably differ to the extent that in natural languages n will be required to be small, say, at most 4.

⁵ Since the publication of Chomsky (1965), Chomsky has modified his conception of the role of deep structure considerably. He no longer regards ‘deep structure’ as a ‘level’ intermediate between semantic representation and surface structure but instead holds (Chomsky 1967:407) that ‘deep structure completely determines certain highly significant aspects of semantic representation. . . [but] surface structure also contributes in a restricted but important way to semantic interpretation’.