2004/08/15 by Jørgen Villadsen, Villadsen, Jørgen
Computer Science · #Advanced Algebra and Logic #Artificial Intelligence (cs.AI) #Computation and Language (cs.CL) #FOS: Computer and information sciences #I.2.7 #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #cs.AI #cs.CL #cs.LO
paper · pdf · doi:10.48550/arxiv.cs/0408037
20 pages
arxiv created 2004/08/15 · openalex publication_date 2004/08/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the possibility of modelling the syntax and semantics of natural language by constraints, or rules, imposed by the multi-dimensional type theory Nabla. The only multiplicity we explicitly consider is two, namely one dimension for the syntax and one dimension for the semantics, but the general perspective is important. For example, issues of pragmatics could be handled as additional dimensions. One of the main problems addressed is the rather complicated repertoire of operations that exists besides the notion of categories in traditional Montague grammar. For the syntax we use a categorial grammar along the lines of Lambek. For the semantics we use so-called lexical and logical combinators inspired by work in natural logic. Nabla provides a concise interpretation and a sequent calculus as the basis for implementations.