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arXiv · 2409.06966

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

Patrik Adrián·György Vaszil
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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.

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Patrik Adrián, György Vaszil. 2024-09-11. A GLR-like Parsing Algorithm for Three-Valued Interpretations of Boolean Grammars with Strong Negation. https://doi.org/10.4204/eptcs.407.3

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