TY - GEN
T1 - An algebraic approach to multiple context-free grammars
AU - Clark, Alexander
AU - Yoshinaka, Ryo
PY - 2014
Y1 - 2014
N2 - We define an algebraic structure, Paired Complete Idempotent Semirings (pcis), which are appropriate for defining a denotational semantics for multiple context-free grammars of dimension 2 (2-mcfg). We demonstrate that homomorphisms of this structure will induce well-behaved morphisms of the grammar, and generalize the syntactic concept lattice from context-free grammars to the 2-mcfg case. We show that this lattice is the unique minimal structure that will interpret the grammar faithfully and that therefore 2-mcfgs without mergeable nonterminals will have nonterminals that correspond to elements of this structure.
AB - We define an algebraic structure, Paired Complete Idempotent Semirings (pcis), which are appropriate for defining a denotational semantics for multiple context-free grammars of dimension 2 (2-mcfg). We demonstrate that homomorphisms of this structure will induce well-behaved morphisms of the grammar, and generalize the syntactic concept lattice from context-free grammars to the 2-mcfg case. We show that this lattice is the unique minimal structure that will interpret the grammar faithfully and that therefore 2-mcfgs without mergeable nonterminals will have nonterminals that correspond to elements of this structure.
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U2 - 10.1007/978-3-662-43742-1_5
DO - 10.1007/978-3-662-43742-1_5
M3 - Conference contribution
AN - SCOPUS:84903769913
SN - 9783662437414
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 57
EP - 69
BT - Logical Aspects of Computational Linguistics - 8th International Conference, LACL 2014, Proceedings
PB - Springer Verlag
ER -