Well-founded semantics for Boolean grammars

Boolean grammars [A. Okhotin, Boolean grammars, Information and Computation 194 (1) (2004) 19–48] are a promising extension of context-free grammars that supports conjunction and negation in rule bodies. In this paper, we give a novel semantics for Boolean grammars which applies to all such grammars...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Information and computation Jg. 207; H. 9; S. 945 - 967
Hauptverfasser: Kountouriotis, Vassilis, Nomikos, Christos, Rondogiannis, Panos
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier Inc 01.09.2009
Elsevier
Schlagworte:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Computer science; control theory; systems
Exact sciences and technology
Language theory and syntactical analysis
Miscellaneous
Programming theory
Theoretical computing
Computer theory
Negation
Symbol
Normal form
Programming
Algorithm
Area
Fix point
Semantics
Grammar form
Context free grammar
Logic
Syntax
Time complexity
Fixed point
ISSN:0890-5401, 1090-2651
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:Boolean grammars [A. Okhotin, Boolean grammars, Information and Computation 194 (1) (2004) 19–48] are a promising extension of context-free grammars that supports conjunction and negation in rule bodies. In this paper, we give a novel semantics for Boolean grammars which applies to all such grammars, independently of their syntax. The key idea of our proposal comes from the area of negation in logic programming, and in particular from the so-called well-founded semantics which is widely accepted in this area to be the “correct” approach to negation. We show that for every Boolean grammar there exists a distinguished (three-valued) interpretation of the non-terminal symbols, which satisfies all the rules of the grammar and at the same time is the least fixed-point of an operator associated with the grammar. Then, we demonstrate that every Boolean grammar can be transformed into an equivalent (under the new semantics) grammar in normal form. Based on this normal form, we propose an O ( n 3 ) algorithm for parsing that applies to any such normalized Boolean grammar. In summary, the main contribution of this paper is to provide a semantics which applies to all Boolean grammars while at the same time retaining the complexity of parsing associated with this type of grammars.
ISSN:0890-5401
1090-2651
DOI:10.1016/j.ic.2009.05.002