Multiplicative-Additive Focusing for Parsing as Deduction

TL;DR

This paper addresses the challenge of spurious ambiguity in parsing by employing proof-theoretic focalisation to analyze multiplicative-additive structures, aiming to improve parsing efficiency and understanding.

Contribution

It introduces a novel proof-theoretic approach using focalisation to analyze multiplicative-additive spurious ambiguity in parsing.

Findings

Identifies the mathematical structure of derivations in parsing.

Applies focalisation to multiplicative-additive proof nets.

Provides insights into reducing redundancy in parse search space.

Abstract

Spurious ambiguity is the phenomenon whereby distinct derivations in grammar may assign the same structural reading, resulting in redundancy in the parse search space and inefficiency in parsing. Understanding the problem depends on identifying the essential mathematical structure of derivations. This is trivial in the case of context free grammar, where the parse structures are ordered trees; in the case of categorial grammar, the parse structures are proof nets. However, with respect to multiplicatives intrinsic proof nets have not yet been given for displacement calculus, and proof nets for additives, which have applications to polymorphism, are involved. Here we approach multiplicative-additive spurious ambiguity by means of the proof-theoretic technique of focalisation.