Every logic program has a natural stratification and an iterated least fixed point model
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory
Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory
Journal of Automata, Languages and Combinatorics - Special issue: selected papers of the second internaional workshop on Descriptional Complexity of Automata, Grammars and Related Structures (London, Ontario, Canada, July 27-29, 2000)
Information and Computation
Minimum model semantics for logic programs with negation-as-failure
ACM Transactions on Computational Logic (TOCL)
Locally stratified Boolean grammars
Information and Computation
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Well-Founded semantics for boolean grammars
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
Fast parsing for Boolean grammars: a generalization of Valiant's algorithm
DLT'10 Proceedings of the 14th international conference on Developments in language theory
A simple P-complete problem and its language-theoretic representations
Theoretical Computer Science
A game-theoretic characterization of Boolean grammars
Theoretical Computer Science
Language equations with complementation: Expressive power
Theoretical Computer Science
Defining contexts in context-free grammars
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
Parsing Boolean grammars over a one-letter alphabet using online convolution
Theoretical Computer Science
Parsing by matrix multiplication generalized to Boolean grammars
Theoretical Computer Science
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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.