In the analysis of these constructions we are guided by the way how the constructions are read. The following rules obtain:
Rule 1: The analyzed complex is divided into two parts, one expressing the number and one expressing the counted objects (i.e. the nouns with their modifications). The inner structure of the latter part is determined according to the general rules on Atr and will not be dealt with in this section. In the sequel we refer to the whole construction expressing the counted object as to the representative.
If such expressions as tisíc (thousand), milion (million), sto (hundred), stovka (a hundred), setina (a hundredth) behave as nous, they are treated as such. The following constructions are easy to analyze by general rules:
In general it may be said that the part expressing the quantity begins (if processed from the end to the left) with the first real numeral, or, as the case may be (as we will see with more complex examples in Rule 3) where there is a place for such a numeral, though the numeral itself is missing because of a specific shape of the whole number. This part, too, is later analyzed in order to get a single representative.
Even in this part there may occur a noun and an embedded segment that is analyzed as if it were another part with a numerical expression of quantity (see Rule 3).
Rule 2: We determine which part is the governor and which is the dependent; this relation is represented by suspending the representative of the second part on the representative of the first one. The counted objects have priority - if an expression of quantity agrees with the representative of the counted objects, then this representative is the governor. If the agreement is not observed, the role of the governor is taken over by the expression of quantity.
In the following examples both parts are present, both filled in by a single node, which is also their representative. In the first example, the counted object is the governor, in the second case the counted object depends on the expression for the quantity.
The governor is assigned afun according to the function of the whole complex in the sentence, the representative of the dependent is assigned afun Atr.
Rule 3: In order to determine the structure of an expression of quantity, we have first to divide the whole part into segments each of which stands for one rank; it should be noted that these ranks are not ranks in the mathematical sense. These segments contain the number of units, tens, hundreds and then thousnads, millions etc. the rank of units and tens will have a one-word expression (i.e. they will be represented by a single node), the rank of hundreds can be expressed by two words (tři sta three hundred-Plural) and higher ranks by more complex expressions (pět set padesát pět milionů is a single segment). With these more complex examples a noun occurs that expresses the rank, and their inner structure is accounted for by the same rules as the structure of the whole (the noun renders the counted object, the rest is the quantity). On a higher level we work with the head nodes of all these ranks (segments).
The most important rank is chosen, the head node of which becomes the representative of the whole part expressing the quantity, and it becomes the governor of all the remaining nodes. The governing rank is usually the lowest rank, but there are exceptions to the rule. If the part expressing the quantity is subordinated to the part of the counted objects, the lowest rank is determined as the governor. However, if the quantity is superordinated to the objects counted, the governing rank is the lowest of those that agree with the noun of the counted objects; this might be also the second rank from the left.
All dependent ranks (their governing nodes) are assigned afun Atr.
The following examples illustrate the case when two ranks are present. In the first two examples the part rendering the counted objects is superordinated and therefore the lowest rank is the highest node in that part. In examples that follow, the nodes rendering the counted objects are subordinated to those expressing the quantity.
Let us exemplify some more complex structures with higher ranks rendered by multi-word expressions. In the following example, the counted object is vrány (crows); the word dvě (two) is a proper numeral and therefore the rest of the whole construction (i.e. tři miliony čtyři sta pět tisíc třicet dvě three million four hundred (and) five thousand (and) thirty two) belongs to the quantity part. The word vrány (crows) is in the corresponding inflected form as determined by the verb viděl (he-saw) and as such will be the governor of the whole complex expression. The part expressing the quantity can be decomposed into the following rank segments: tři miliony (three million), čtyři sta pět tisíc (four hundred (and) five thousand), pět set (five hundred), třicet (thirty), dvě (two). Since in our example the quantity part depends on the part expressing the counted object, the lowest rank will be the governor. The node for dvě will be thus suspended under vrány and the representatives of other ranks will be suspended under it. The second lowest rank is that of třicet; it consists of a single node and it may depend directly on the node dvě. Other ranks include also nouns expressing the quantity (set, tisíc, miliony); these nouns acquire the function of "embedded" counted objects. Let us analyze the rank pět set (five hundred). The quantity is expressed by pět, the counted object is set; to determine the direction of dependency, we have to consider that the Genitive form set is determined ("governed") by the numeral, and as such it functions as a dependent. The node pět is thus suspended under the node dvě and the node set depends on the node pět. A similar situation obtains with the rank tři miliony (three million), only the direction of dependency will be opposite. The most difficult situation occurs with the rank of thousands: the quantity part is constituted by čtyři sta pět (four hundred (and) five), and in turn it has two ranks. The counted part tisíc (Genitive here) will depend on the quantity part, where the lowest rank will be the governor, so that the node for pět will be suspended under the node for dvě and the latter will be the governor of both tisíc and the second rank present, in which sta will be the governor with the node čtyři suspended under it.
The second example will be described only briefly. The counted object is vran (crows); since it does not have the form required by the verb, this node will depend on the representative of the quantity part. This part has two ranks: tři sta padesát čtyři milionů (three hundred fifty four million) and šest set tisíc (six hundred thousand). The lowest rank in the whole expression is the rank of thousands, and therefore it will be the governor. The representative of this rank is the node šest (six) and as such will be suspended as the highest one; the node for the counted object (vran crows) and the represenatrive of the second rank padesát (fifty) will be suspended on it. The inner structure of both ranks is clear.
Let us note one important fact: The boundary line between the quantity part and that of the counted object has been drawn after the word tisíc (thousand), which is considered here to be a noun in Genitive. This was possible because the quantity of crows is expressed by two ranks and the words tisíc and milionů are in a sense on the same level. In the following example, only one rank is present, so that the words tisíc and even set can be included into the part of counted objects; the quantity part is then consituted only by the node for šest.
However, not even the rules formulated above can cover all cases of numerical expressions. For example, the issue of decimal numbers still remains problematic.
In the following examples, morphology determines which words will act as governors: celých ('wholes'-Genitive), desetiny (tenths) or the figures 2 or 5. The afun assigned to the governor (or, as the case may be, to the coordination) follows from its syntactic position in the sentence (in our case, it is the subject). The number of units determines the representation of the whole decimal number; in our examples, this is the node for procenta (percent), which is not identical to the notion of a representative from the preceding paragraphs. This is given by the special feature of decimal expressions, namely by the two-member character of their representation.
Such numerals as více (more), méně (less), mnoho (many), málo (few), středně (medium) etc., if in Nominative or Accusative case, can act as governors for both Adv and Atr (at the same time).
The conjunction než (than) is discussed in Phrases of comparison with conjunctions jako (as), než (than), esp. in paragraph IV, Appendix 3.
With numerals such as jedna (one) through čtyři (four) the general rules stated in the coresponding sections on sentence parts obtain. The direction of dependency and agreement functions quire naturally with them.
With numerals from pět (five) on, the situation is more complicated. With Nominative (Sb) and Accusative (Obj), the counted object has the form of Genitive and the verb agrees in Number and Gender with the numeral; since this phenomenon is very problematic, we had to accept a solution that is not very clean from the linguistic point of view.
A partitive Genitive thus can be a Sb or an Obj, but if the sentence includes some quantitative expression which governs the noun in Genitive, then Sb or Obj is the governor of this expression and the noun in Genitive is its Atr.
A noun in Genitive becomes the Sb only with sentences of the type tam je lidí (there is people-Genitive = there are many people there), přibývá jich (it-grows they-Genitive = they grow in number).
The following examples illustrate an analysis of the inner structure of arithmetical expressions.