Multi-dimensional Type Theory: Rules, Categories, and Combinators for Syntax and Semantics
Jørgen Villadsen
Abstract
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.
Create a lesson
Related papers
Lumen-bench: Cross-Lingual Safety Gaps and the Say-Do Problem in Tool-Calling Large Language Models
Giovana Kerche Bonás, Thiago Laitz, Thales Sales Almeida et al.
RegExtract: A Benchmark for PFAS Regulatory Information Extraction with LLMs
Defne Circi, Krystelle Lionti, Sarathkrishna Swaminathan et al.
Have You Been Convinced? A Neuro-symbolic Argumentation Reasoning Approach to Detecting Persuasiveness in ChangeMyView Discussions
Siddharth Bhargava, Sara Tonelli, Patricia Martín-Rodilla
Select or Rewrite: Oracle-Guided Fine-Tuning for Generative ASR Post-Editing from N-Best Hypotheses
Shiran Liu, Gaohui Xu, Sergio Burdisso et al.
PAT: A Personality-Driven Augmentation and Transfer Learning Framework for Depression Detection on Social Media
Shengwu Zheng, Yuzhe Ding, Xiaohui Liang et al.
Toward System One Clinical Intelligence: Parameter-Efficient Fine-Tuning and Counterfactual Explainability of Decision Foundation Models
S. M. Mahbub Uddin Ahmed