2022/10/14 by Aldo Figallo-Orellano, Figallo-Orellano, Aldo, Juan Sebastián Slagter +1
Computer Science · #Advanced Algebra and Logic #Bayesian Modeling and Causal Inference #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge
paper · pdf · doi:10.48550/arxiv.2210.08070
openalex publication_date 2022/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we build Fidel-structures valued models following the methodology developed for Heyting-valued models; recall that Fidel structures are not algebras in the universal algebra sense. Taking models that verify Leibniz law, we are able to prove that all set-theoretic axioms of ZF are valid over these models. The proof is strongly based on the existence of paraconsistent models of Leibniz law. In this setting, the difficulty of having algebraic paraconsistent models of law for formulas with negation using the standard interpretation map is discussed, showing that the existence of models of Leibniz law is essential to getting models for ZF.