2024/04/26 by Fredrik Engström, Engström, Fredrik
Computer Science · #FOS: Mathematics #Logic (math.LO) #Semantic Web and Ontologies
paper · pdf · doi:10.48550/arxiv.2404.17295
openalex publication_date 2024/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Dependence logic provides an elegant approach for introducing dependencies between variables into the object language of first-order logic. In [1] generalized quantifiers were introduced in this context. However, a satisfactory account was only achieved for monotone increasing generalized quantifiers. In this paper, we modify the fundamental semantical guideline of dependence logic to create a framework that adequately handles both monotone and non-monotone generalized quantifiers. We demonstrate that this new logic can interpret dependence logic and possesses the same expressive power as existential second-order logic (ESO) on the level of formulas. Additionally, we establish truth conditions for generalized quantifiers and prove that the extended logic remains conservative over first-order logic with generalized quantifiers and is able to express the branching of continuous generalized quantifiers.