If Socrates is running slowly, he must be running. Likewise, if he’s not running, he must not be running slowly. Haze (2024) proposes an extension of first-order logic inspired by this characteristic inferential behaviour of words like ‘slowly’: FOL-SA (first-order logic with scoped adverbs). Haze presents the logic model-theoretically using a hierarchy of models, where the level of a model corresponds to the number of nestings of adverb formulas within adverb formulas, and leaves open the inves…
Read moreIf Socrates is running slowly, he must be running. Likewise, if he’s not running, he must not be running slowly. Haze (2024) proposes an extension of first-order logic inspired by this characteristic inferential behaviour of words like ‘slowly’: FOL-SA (first-order logic with scoped adverbs). Haze presents the logic model-theoretically using a hierarchy of models, where the level of a model corresponds to the number of nestings of adverb formulas within adverb formulas, and leaves open the investigation of its proof theory. In this paper we develop a semantic tableaux proof system for FOL-SA, prove its soundness and completeness, and outline some directions for further research.
