Lambda Dependency-Based Compositional Semantics

TL;DR

The paper introduces lambda dependency-based compositional semantics (lambda DCS), a compact, set-based formal language for semantic parsing tailored to graph-structured knowledge bases like Freebase. It achieves compactness by eliminating explicit variables and using implicit existential quantification, implemented through operators such as join, intersection, union, negation, and higher-order functions, plus mu and lambda abstractions to handle bound anaphora and compositional binary forms. The authors provide a formal definition, a translation to lambda calculus, and discuss the relationship to DCS, description logic, and SPARQL, arguing that lambda DCS aligns well with natural-language compositional structure and practical graph querying. While lambda DCS is not as expressive as full lambda calculus, it offers practical syntactic sugar and a natural representation for database-oriented semantic forms, with potential for future extensions in construction mechanisms and higher-order capabilities.

Abstract

This short note presents a new formal language, lambda dependency-based compositional semantics (lambda DCS) for representing logical forms in semantic parsing. By eliminating variables and making existential quantification implicit, lambda DCS logical forms are generally more compact than those in lambda calculus.