2011/07/10 by Michele Abrusci, Abrusci, Michele, Christian Retoré +1
Computer Science · Mathematics · Psychology · #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Philosophy and Theoretical Science #math.LO
paper · pdf · doi:10.48550/arxiv.1107.1883
14TH Congress of Logic, Methodology and Philosophy of Science, Nancy : France (2011)
arxiv created 2011/07/10 · openalex publication_date 2011/07/10 · arxiv updated 2011/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We firstly show that the standard interpretation of natural quantification in mathematical logic does not provide a satisfying account of its original richness. In particular, it ignores the difference between generic and distributive readings. We claim that it is due to the use of a set theoretical framework. We therefore propose a proof theoretical treatment in terms of proofs and refutations. Thereafter we apply these ideas to quantifiers that are not first order definable like "the majority of".