The application of compositional semantics involves analyzing how different syntactic structures contribute to overall sentence meaning. For instance, in the sentence "The cat chased the mouse," the meaning is composed of the individual meanings of "cat," "chase," and "mouse," along with the syntactic information that "cat" is the subject (agent) and "mouse" is the object (patient) of the action. This approach becomes particularly important when dealing with complex sentences, quantifiers, and abstract concepts. While compositional semantics provides a powerful framework for understanding meaning construction, it faces challenges in accounting for idiomatic expressions, metaphors, and context-dependent interpretations, areas where the meaning of the whole is not always a straightforward sum of its parts.