Let us first introduce certain basic assumptions concerning the theoretical status of semantic features. It seems to me most natural to consider semantic features essentially as predicate constants in the sense of the predicate calculus as developed in modern logic. This assumption has been stipulated by other authors as well. (See e.g. McCawley, 1968.) It can be motivated by several considerations. I will briefly discuss two of them here.

Firstly it turned out, as already mentioned, that mere concatenation of features as introduced in Katz and Fodor (1963) is not sufficient to account for the semantic interpretation of words and sentences. Thus additional machinery for the combination of semantic features became necessary. One of the means that has been used in this connection, e.g. in Katz (1966, 1967) and Bierwisch (1967), was that of grouping features by simple brackets. Such grouping was meant to express that certain features of a reading are more closely connected than others. It does not specify, however, how differences in grouping are to be interpreted conceptually. In fact, rather different conceptual relations between semantic features have been expressed by identical means in the references quoted.¹ This means that the burden of interpreting the formal relations between semantic elements remains with the conceptual content of particular features. The same formal relation between certain features in a given reading would be interpreted differently depending on the features involved. This is of course quite unsatisfactory. On the one hand, the formal means of semantic representations become rather empty. On the other hand, the problem is postponed, but not solved: the intrinsic interpretation of semantic features would have to provide the formal means giving substance to the empty grouping relations. This in turn would conflict with the assumption that the semantic features are linguistically primitive terms. Katz has tried to avoid difficulties of this type by using certain informal means such as of, at, etc. in combinations such as ((Condition (Possession of Y) of X at t_i) where X and Y are slots to be filled in by feature complexes and it is a variable over a time interval. These and similar means, introduced only casually, have no clear theoretical status, however. The most natural way to remedy shortcomings of this kind seems to be to construe semantic features as predicates and to reconstruct the more complicated connections among them by using the formal means of the fully fledged predicate calculus, admitting of course adaptations and controlled modifications if necessary. This appears to be at least a promising program. Some steps in this direction have been made in Bierwisch (1969).

The second point to be noted here concerns the fact that semantic features, if taken as predicates, must be assigned to suitable arguments and that, therefore, these arguments must be part of the semantic representations. They are considered most naturally as variables which are substituted by representations of the referents which are talked about by means of particular occurrences of the expressions to whose readings the variables belong. From this it follows that dictionary entries also must contain appropriate variables which are to be substituted by more specific variables if they occur in particular sentences. In this vein, Weinreich (1962) has pointed out that lexical entries even for single words should have the form of propositional functions, i.e. of (complex) predicates with unbound variables as arguments. The projection rules of Katz and Fodor’s theory, which combine the readings of composite constituents according to the relevant syntactic relations, reduce them essentially to the substitution of suitable arguments for the variables occurring in the dictionary entries. This in turn requires that these variables be indexed with respect to the syntactic relations in question. Thus for example transitive verbs such as ‘ love ’, ‘ meet ’, ‘ hit ’, etc. must contain variables indexed for the relations ‘Subject of’ and ‘Object of’, for which the pertinent variables occurring in the readings of the Subject-NP and the Object-NP respectively are substituted.² Notice that all variables appearing in the reading of a given sentence (more precisely of a sentence type) indicate identity or distinctness of reference. They do not represent particular objects referred to. Otherwise a sentence such as ‘ I saw a car ’ would have indefinitely many readings, differing only in the respective arguments.

It is important that essentially the same indication of identical or distinct reference is required for purely syntactic reasons. The relevant phenomena are primarily pronominalization, reflexivization, deletion of identical NP. Using subscripts to represent identical or distinct reference, we have examples of the following type:

I cannot comment on the details of these phenomena.³ For the aims of the present paper it is sufficient to realize that certain aspects of reference are crucial for any attempt to account for the facts displayed by (i)-(4). Chomsky (1965, p. 145) first proposed in this connection to mark certain lexical items as ‘referential’ and to assign to them integers representing identical or different reference. (For a fairly elaborate application of this idea see Isenberg (1968).) But since reference is actually not a property of lexical categories, it seems more appropriate to assign reference indexes to NPs. Though even that is an oversimplification which ignores certain complications in the analysis of NPs, it will do for the present purpose.

We may assume now that for every NP_i there is a variable X_i functioning as an argument in the semantic representation of the expression of which the NP_i is a part. This argument does not only occur in the reading of the NP_i in question, but is also substituted, by the procedure mentioned above, for variables in the readings of other constituents to which the NP_i bears the relevant syntactic relations.

This provisional sketch of the status of semantic features immediately leads to a first aspect of classification. Semantic features fall into different classes according to the number of arguments required. They may be one-place predicates representing properties, two-place predicates representing two-place relations, etc. We will see that they must be classified not only with respect to the number, but also with respect to different types of arguments.

¹ Thus in Bierwisch (1967) I used groupings such as (Physical Object (3 Space (Vertical) (Maximal) (Secondary))) to indicate that a given reading refers to a three-dimensional physical object with a vertical, a maximal, and a secondary extension. Obviously, the connection between the element ‘Physical Object’ and the rest of the configuration represents a conceptual relation completely different from that expressed by the connection between ‘ 3 Space ’ and ‘Vertical’, ‘ Maximal’, and ‘ Secondary’ respectively. We will return to the problem of a more adequate solution below. Similar problems with respect to several examples given in Katz (1967) are discussed in Bierwisch (1969).

² This process is sketched in somewhat more detail in Bierwisch (1969, section 3). - Note incidentally that the slot variables X, Y, etc. which Katz has introduced, as mentioned above, in his recent writings serve a rather similar purpose. In fact, the revised projection rules based on these variables amount roughly to a substitution of argument expressions, if the semantic markers are reformulated as (complex) predicates.

³ They are in fact rather complicated and involve several transformational processes and principles governing them. A careful investigation of some of them will be found in Postal (1968).