By Frank Richter
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Additional resources for A Mathematical Formalism for Linguistic Theories with an Application in Head-Driven Phrase Structure Grammar
5) a. Let n2 = owner likes-best . . likes-best n ∈ IN 2∗n times n is an odd ∪ driver likes-best . . likes-best natural number n times and n3 = driver likes-best . . likes-best n ∈ IN 2∗n times n is an odd ∪ owner likes-best . . likes-best . natural number n times With the sets n2 and n3 , I define 16 1 as follows: It might be interesting to notice that the feature tree structures of Smolka and Treinen 1994, p. 234, are weaker than abstract feature structures, since they lack a re-entrancy relation.
The technical step from the preorders of concrete feature structures to partial orders of feature structures can also be motivated informally with intuitions about which properties of pieces of partial information are really important to us. Given what we want to do with them, making a distinction between two concrete feature structures that are identical up to their nodes is superfluous. It is not necessary to distinguish between the two 87 concrete feature structures of (4) as information-bearing entities.
That means that if a node is labeled by sort σ then it may only have attributes that are appropriate to σ. Pollard and Sag are not as clear about whether they want to enforce the appropriateness of attribute values in feature structures. On the one hand, they say that “[i]t should also be clear that for different attributes, different types of values are appropriate” (ibid, p. 39). On the other hand, in a comment to an AVM depiction of a feature structure,11 they say that “[b]y virtue of not being mentioned, the phonology attribute is implicitly specified as ” (ibid, p.
A Mathematical Formalism for Linguistic Theories with an Application in Head-Driven Phrase Structure Grammar by Frank Richter