2025/01/15 by Hayato Nasu, Nasu, Hayato · 1 citation
Computer Science · #03G30 #18C50 #18D70 #18N10 #Category Theory (math.CT) #FOS: Mathematics #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2501.17869
openalex publication_date 2025/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This thesis deals with two main topics: virtual double categories as semantics environments for predicate logic, and a syntactic presentation of virtual double categories as a type theory. One significant principle of categorical logic is bringing together the semantics and the syntax of logical systems in a common categorical framework. This thesis is intended to propose a double-categorical method for categorical logic in line with this principle. On the semantic side, we investigate virtual double categories as a model of predicate logic and illustrate that this framework subsumes the existing frameworks properly. On the syntactic side, we develop a type theory called FVDblTT that is designed as an internal language for virtual double categories.