2016/02/04 by Jules Hedges, Mehrnoosh Sadrzadeh, Hedges, Jules +1
Computer Science · #Artificial Intelligence (cs.AI) #Category Theory (math.CT) #Computation and Language (cs.CL) #Constraint Satisfaction and Optimization #FOS: Computer and information sciences #FOS: Mathematics #I.2.7 #Natural Language Processing Techniques #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.1602.01635
openalex publication_date 2016/02/04 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
Categorical compositional distributional semantics is a model of natural\nlanguage; it combines the statistical vector space models of words with the\ncompositional models of grammar. We formalise in this model the generalised\nquantifier theory of natural language, due to Barwise and Cooper. The\nunderlying setting is a compact closed category with bialgebras. We start from\na generative grammar formalisation and develop an abstract categorical\ncompositional semantics for it, then instantiate the abstract setting to sets\nand relations and to finite dimensional vector spaces and linear maps. We prove\nthe equivalence of the relational instantiation to the truth theoretic\nsemantics of generalised quantifiers. The vector space instantiation formalises\nthe statistical usages of words and enables us to, for the first time, reason\nabout quantified phrases and sentences compositionally in distributional\nsemantics.\n