2012/07/24 by Daniele Mundici, Mundici, Daniele
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge
paper · pdf · doi:10.48550/arxiv.1207.5713
openalex publication_date 2012/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The classical condition "ϕ is a semantic consequence of Θ" in infinite-valued propositional Łukasiewicz logic Ł_∞ is refined using enriched valuations that take into account the effect on ϕ of the stability of the truth-value of all θ∈ Θ under small perturbations (or, measurement errors) of the models of Θ. The differential properties of the functions represented by ϕ and by all θ∈ Θ naturally lead to a new notion of semantic consequence \models_∂ that turns out to coincide with syntactic consequence \vdash.