Language models represent and reason about scope relations in their internal representations through the hierarchical structure of their neural networks. When processing sentences with scope ambiguities, the models encode the relationships between different semantic operators, such as quantifiers and negations, in their hidden layers. These relationships are learned during the training process, where the models adjust their weights to capture the patterns and dependencies in the input data. By doing so, the models can differentiate between different scope readings and make predictions based on the most likely interpretation.
In terms of reasoning, language models use their learned representations to make inferences about the scope of different operators in a sentence. This involves analyzing the interactions between quantifiers, negations, adverbs, and other linguistic elements to determine the most probable interpretation. The models can then generate responses or predictions based on this analysis, demonstrating their ability to reason about scope relations in natural language.