## 4 Results
### Results of the Bubble Parser  
Figure 7 shows the percentage of correct answers calculated from the number of interpretations provided by our (rule-based) bubble parser after analyzing the word classes, the type of the clauses (main- or sub-clause), and the grammar cases of the nouns grouped by the sentences. The complete results of the analyses of each sentence are presented in Appendix B. In Figure 7, a value of 100% in the y-axis represents a bi-unique determination (one interpretation remains), and a value of, for example 33.3%, indicates that three interpretations are left. A significant result is that our parser always provides the correct answer among the interpretations under all circumstances. Figure 7: Percentage of correct answers calculated from the number of interpretations proposed by the (rule-based) bubble parser for the determination of the word classes (turquoise bars), clause types (violet bars), and noun case (olive bars) grouped by sentences. The correct answer has a value of 100%, which means only one interpretation is proposed by the parser. Each interpretation corresponds to its own bubble model of the given sentence. Most of these interpretations are contradictory and are systematically eliminated during the parsing process. Figure 2 presents the bubble model for sentence 5. In fact, there are two remaining bubble models, where the cases of two nouns are switched; however, the cases of the nouns are not marked in the shown model. The underlying logic of bubble models is detailed in the work of [PERSON] et al. [13]. The parser shows perfect results for the word class determination (turquoise bars in Figure 7), except for sentence 6, where the two words \"um\" and \"vor\" have an ambiguity of two possible word classes each. These two unsolved ambiguities lead to four resulting interpretations, which represent four possible combinations (two options for two words) of these two unsolved word class ambiguities. The parser perfectly solves the recognition of clause types and numbers (violet bars). In all ten sentences, the part clauses are linked correctly and are identified unambiguously as the main- or sub-clause. Regarding the detection of the grammar cases of the nouns (olive bars), our parser provides perfect results for 6 out of 10 sentences (4, 5-10). In sentence 1, there are two nouns \"Beschluse\" and \"Positionen\", which both can be the sentence subject. Commonly, the first of the nouns occurring in a sentence acts as a subject of the sentence, but in general, the second occurring noun may also represent the sentence subject. In this case, the semantics of the sentence is decisive. Our parser, working solely on the grammatical basis, lists both possibilities in this case. In the sentence 2, the noun \"Rosen\" occurs with no further articles or adjectives. Therefore, in principle, this noun may be in one of the three grammar cases, which results in three different interpretations provided by the parser. In sentences 3 and 5, two options are provided by the parser for the subject of the relative clause. There is no strict rule implemented yet saying that a relative pronoun in a relative clause always acts as the subject. The results presented in Figure 7 show that although many interpretations are created during the parsing process, many of them are rejected by contradiction tests, and only a few interpretations remain after applying all parsing steps. Figure 8 shows the number of rejected interpretations for every example sentence. The number of rejected interpretations does not correlate with the length of the sentence or its structural complexity. Rather, it depends on the word class ambiguities of the used words and their ambiguous arrangement in a sentence. For example, sentence 5 contains two nested relative clauses and has a medium length of 24 words (including punctuation), but the parser rejects only 18 interpretations during the sentence recognition.