A Unified Account of Semantic Ambiguity Quantifier Using First- and Second-Order Logic (Aybak - Language and Literature)
Synopsis
Quantifier scope ambiguity constitutes one of the central challenges in formal semantics because a single syntactic structure may correspond to multiple logically distinct interpretations. While first-order predicate logic has traditionally served as the principal framework for representing quantificational relations, certain complex scope interactions reveal limitations in purely first-order approaches. This chapter proposes a unified logical account of quantifier scope that integrates first-order and second-order predicate logic within a single representational framework. The study examines a range of naturally occurring English sentences exhibiting quantifier interaction, nested quantification, and multiple scope readings. Formal representations are developed for each interpretation and compared with respect to expressive power and semantic transparency. The analysis demonstrates that first-order logic adequately captures many standard scope ambiguities, whereas second-order representations provide greater flexibility for modeling higher-level semantic dependencies and generalized quantificational structures. By establishing explicit correspondences between first-order and second-order analyses, the proposed framework offers a systematic method for representing alternative readings while preserving logical rigor. It contributes to ongoing discussions in formal semantics and logical linguistics by clarifying the relationship between logical expressiveness and semantic interpretation and by providing a unified account of scope ambiguity that bridges established and higher-order approaches to natural language meaning.
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