2013/01/22 by Michele Abrusci, Abrusci, Michele, Christian Retoré +1
Computer Science · Mathematics · #Advanced Algebra and Logic #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #cs.LO #math.LO
paper · pdf · doi:10.48550/arxiv.1301.5304
arxiv created 2013/01/22 · openalex publication_date 2013/01/22 · arxiv updated 2013/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper surveys the common approach to quantification and generalised quantification in formal linguistics and philosophy of language. We point out how this general setting departs from empirical linguistic data, and give some hints for a different view based on proof theory, which on many aspects gets closer to the language itself. We stress the importance of Hilbert's oper- ator epsilon and tau for, respectively, existential and universal quantifications. Indeed, these operators help a lot to construct semantic representation close to natural language, in particular with quantified noun phrases as individual terms. We also define guidelines for the design of the proof rules corresponding to generalised quantifiers.