Well-Founded Semantics for Boolean Grammars

Abstract. Boolean grammars [A. Okhotin, Information and Computation 194 (2004) 19-48] are a promising extension of context-free grammars that supports conjunction and negation. 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) language which is a model of the grammar and at the same time the least fixed point of an operator associated with the grammar. 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(n3 ) algorithm for parsing that applies to any such normalized boolean grammar. In summary, the ma...

• Type: Conference
• Year: 2006
• Where: DLT
• Authors: Vassilis Kountouriotis, Christos Nomikos, Panos Rondogiannis
• Keywords: Boolean Grammars, Context-free Grammars, DLT 2006, DLT 2007, So-called Well-founded Semantics