Presupposing the general framework of transformational generative grammar, we have discussed some formal aspects of semantic representations. These are considered as complex structures that are built up from basic primitive terms and assigned to syntactic surface representations by the syntactic rules of the grammar of a given language. We assumed that an uninterpreted grouping of the basic semantic elements, proposed previously e.g. in Katz (1966, 1967), or Bierwisch (1967), is not sufficient. We claimed that an adaptation of certain means developed in modern logic might be at least a promising program. Pursuing this proposal along certain fairly different lines, we arrived at the following provisional conclusions:

Semantic representations presuppose at least the following basic requirements (or their equivalents in certain other notation):

(1) A set of variables representing sets of objects to which linguistic expressions can refer. Variables occurring in readings of sentences are indexed with respect to sameness or difference of reference.

(2) A set of semantic features which are classified according to several aspects into at least the following subsets:

Predicative features representing properties and relations ascribed to the elements of the sets represented by the variables in (1). Predicative features are further subclassified according to the number of their arguments into one-place predicates, two-place predicates, etc. The possibility was suggested that the number of arguments might be restricted to two. Another subclassification of predicative features might be induced by the type of arguments they take: those representing true objects, facts, propositions, parasitic objects or parameters of objects.¹ Predicates may also take predicates as arguments, thus leading to higher level predication. This possibility obviously bears on the classification of semantic features. It has not been dealt with in the present paper. For some discussion see Bierwisch (1969).

Delimiting features characterizing the sets of objects referred to with respect to quantity and to the operations that constitute these sets. Delimiting features fall into two classes: features specifying reference instances and features indicating absolute and relative quantity.

The predicative semantic features correspond to predicate constants, the delimiting features to quantifiers and certain other operators of modern logic. Whereas the variables in (1) have no substantial content and serve only the purpose of representing identical and different reference, the semantic features in (2) must have a constant interpretation in terms of cognitive and perceptual conditions inherent in human organisms and governing their interaction with the physical and social environment.

(3) The elements listed under (1) and (2) are combined according to a set of rules or conventions to form semantic representations. These rules are clearly connected to the different classes of semantic features discussed above. We have touched on them only marginally in the present paper.

The requirements (1), (2), and (3) specify an infinite set of semantic representations, where the rules postulated in (3) may be considered as the syntax of such representations. These requirements then indicate, at least partially, what semantic representations look like. They are, of course, by no means a full semantic theory of natural languages. An empirically motivated formal classification of the basic elements of a semantic theory is, however, a necessary part of such a theory.

The formal classification of semantic features discussed here is not the only type of structure organizing the set of primitive semantic terms. A fairly complex system of mutual inclusion, exclusion, hierarchical subordination, etc. must be assumed to govern this basic inventory. The nature of this structure, which reflects the substantive content of semantic features, is as yet poorly understood. Some of its aspects may be expressed by redundancy rules, which are similar in certain respects to the meaning postulates of modern logic.

According to our basic assumption, semantic representations must be connected to syntactic surface representations. Let us assume that for this purpose it is sufficient to specify the connection between syntactic deep structures and semantic representations, the former being mapped by transformational rules on the appropriate surface structures. The connection between syntactic deep structures, which specify a set of basic syntactic relations, and semantic representations is provided by the lexicon, which associates semantic representations with basic syntactic formatives, and general conventions specifying the semantic effect of the basic syntactic relations.

Semantic representations of lexical entries are of the same character as those of syntactically complex expressions, with one exception: lexical entries do not contain referentially indexed variables, since lexical entries do not refer to particular sets of individuals.² Instead they contain variables that are categorized with respect to the syntactic relations defined by the syntactic deep structure. The general conventions specifying the semantic effect of syntactic relations are based on precisely these categorized variables. We have touched upon two alternative principles according to which these conventions might operate.

I have ignored throughout this paper the fact that lexical readings are generally subdivided into two parts: the proper semantic content and the selection restriction - or more generally: the presuppositions for its appropriate use. This topic involves a number of different problems. It has no bearing, however, on the classification of features. Every semantic primitive that can be part of the proper conceptual content of a lexical reading can also be part of a selection restriction, and vice versa.³

I have made only very vague claims about the precise content of the syntactic deep structure and the relations defined by it. A more precise formulation of the classification of semantic features than that given here must obviously be related to certain specific assumptions with respect to the syntactic representations. This concerns e.g. the syntactic status of quantifiers, determiners, negation, and even of noun phrases. Thus the specification of the form of semantic representations depends to a fairly large extent on the presupposed syntactic analysis. But it is equally obvious, on the other hand, that the syntactic behavior of particular lexical entries can be predicted to a large extent on the basis of its semantic structure, if this is made explicit in an appropriate way.

¹ To what extent the classification according to types of arguments is a purely formal aspect of semantic features is a dubious question, since it presupposes a subclassification of arguments. But whether e.g. primary arguments and parasitic arguments can be distinguished on purely formal grounds, i.e. without dragging ontological questions into the semantic theory, is not at all obvious. Since I know, for the time being, of no empirical consequences, the question will be left open here. Notice, however, that one has to be careful to avoid arbitrary subdivisions of the argument variables. Assume, for example, we were to introduce a set of primary variables and a set of variables ranging only over parasitic objects, i.e. properties or parameters. We might then subdivide the former into those ranging over abstract entities and those ranging over concrete, physical objects, the latter being subdivided in variables over animate and un-animate objects, etc. This would either duplicate the information expressed by the semantic features or even transfer it from the semantic features to the argument variables. But it is the set of semantic features that should formally reconstruct the substantive content of meaning.

² They do not even refer to the whole class of individuals specified by the concept in question. A word like ‘ father ’ can be used in generic sentences to refer to the class of all fathers, but it does not refer to it as a dictionary entry. The fact that unique terms like ‘the sun’, ‘New York’, etc. always refer to a particular object, is in this respect a fact of encyclopedic knowledge, not of the lexicon of a given language.

³ Katz (1967) has made a different claim, viz. that only semantic markers can appear in selectional restrictions, whereas distinguishes cannot. I have argued in Bierwisch (1967) that this claim, together with the whole notion of distinguisher, should be given up.