The dissertation of Andreas Stolcke is approved: University of ...

andiisI8inÖ=ÕCHAPTER 5. PROBABILISTIC ATTRIBUTE GRAMMARS 105the language. The context-free productions are augmented with attribute specifications that determine how anonterminals attributes are computed as a function other nonterminals’ attribute values and terminals. 1Many linguistic formalisms based on context-free grammars employ a related concept, typicallyknown by the name of ‘features.’ Like attributes, these are attachments to the nonterminals in the grammar,but their values and their specifications are usually more restricted, in the form of directed acyclic graphs andunification equations (Shieber 1986).The attribute grammar model used here is a much simplified variant of either of these two traditionalCFG extensions, with a probabilistic component added to yield the usual notions of sample probability,likelihood, etc. We will use the terms attribute and feature interchangeably.5.2.1 DefinitionsThe model can be characterized as follows.Definition 5.1 A probabilistic attribute grammar (PAG) is a stochastic context-free grammar with the followingadditional provisions.a) Each )nonterminal a SCFG derivation has an associated finite set a features from a setf.a function that assigns an element from the finite set of valuesh feature to theA featuregIfnonterminals it is defined on. Following the traditional precedents mentioned above, we denote the factthat featuregon nonterminal )has valueiby6Li )g£jgb) An extended context-free production specifies the feature values attached to the LHS nonterminal interms of either constant values or the features of RHS nonterminals. Thus, a production1Ö2can have feature specifications) ¸ =£££+=Õ6ÖÕandkfor H some , VH 1 Vl",the value featurekon=Õo@YÖofis.6Li )g£jgÕa@aÖ£k )g£jg"6T=If. The latter specification determines that the value of )g£jgis whateverfor somegIfIh, orc) Feature equations have associated probabilities, written)g£gK6mif01+-,Certain ordering constraints are typically imposed to guarantee that these attribute values can actually be computed effectively andefficiently.