A GLR-like Parsing Algorithm for Three-Valued Interpretations of Boolean Grammars with Strong Negation

TL;DR

This paper introduces a parsing algorithm for Boolean grammars with strong negation, utilizing a three-valued logic to handle contradictions and extend the expressive power beyond traditional context-free languages.

Contribution

It presents a novel GLR-like parsing algorithm tailored for three-valued interpretations of Boolean grammars with negation, addressing contradictions in language recognition.

Findings

Algorithm effectively determines string membership in three-valued Boolean languages.

Enables handling of contradictory rules in Boolean grammars.

Extends parsing capabilities beyond classical context-free languages.

Abstract

Boolean grammars generalize context-free rewriting by extending the possibilities when dealing with different rules for the same nonterminal symbol. By allowing not only disjunction (as in the case of usual context-free grammars), but also conjunction and negation as possible connections between different rules with the same left-hand side, they are able to simplify the description of context-free languages and characterize languages that are not context-free. The use of negation, however, leads to the possibility of introducing rules that interplay in such a way which is problematic to handle in the classical, two-valued logical setting. Here we define a three valued interpretation to deal with such contradictory grammars using a method introduced originally in the context of logic programming, and present an algorithm to determine the membership status of strings with respect to the resulting three valued languages.