By Frank Richter
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Additional info for A Mathematical Formalism for Linguistic Theories with an Application in Head-Driven Phrase Structure Grammar
LANGUAGE AS PARTIAL INFORMATION 33 however, HPSG 87 does not directly focus on the entities in the domain. Instead, it is mainly interested in information and in the structuring of information about the empirical domain; and pieces of information are expressed as feature structures. As a consequence, HPSG 87 turns to the definition of the representations of linguistic information first. 3, where I will say more about the relationship between HPSG 87 grammars and the empirical domain of natural languages.
Since the sorts that stand lower in the sort hierarchy are labels for more specific information, I will call all sort symbols that are properly subsumed by some sort σ more specific than σ. A collection of feature structures is a collection of feature structures relative to a signature, where a signature comprises a sort hierarchy and a set of attributes. That means that the feature structures may only employ sorts and attributes from the signature. However, our signatures will contain more than just a sort hierarchy and a set of attributes.
LANGUAGE AS PARTIAL INFORMATION 27 We have already noted that the feature structures stand in a subsumption hierarchy. A second subsumption hierarchy of the sort labels of feature structures, as well as conditions on the appropriateness of attributes to certain sorts increase the capability of the formalism to capture the structure of a complex empirical domain. One of the main concerns of HPSG 87 that results naturally from this architecture is the question of how information is distributed or packaged together in feature structures.
A Mathematical Formalism for Linguistic Theories with an Application in Head-Driven Phrase Structure Grammar by Frank Richter