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Extra info for A Mathematical Formalism for Linguistic Theories with an Application in Head-Driven Phrase Structure Grammar

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2: An example of an 87 signature S = {top, car , vw , bmw , person, man, woman}, =           top, top , car , car , vw , vw , bmw , bmw person, person ,    man, man , woman, woman , car , top , vw , top , bmw , top ,  , person, top , man, top , woman, top , vw , car , bmw , car ,     man, person , woman, person A = {driver, owner, likes-best}, and         F =         car , owner , person , car , driver , person ,      vw , owner , person , vw , driver , person ,  bmw , owner , person , bmw , driver , person ,   person, likes-best , top , man, likes-best , top ,      woman, likes-best , top possible attribute values are at entities of a certain type.

Three attributes exist for specifying properties of entities: driver, owner, and likes-best. 1. 2: An example of an 87 signature S = {top, car , vw , bmw , person, man, woman}, =           top, top , car , car , vw , vw , bmw , bmw person, person ,    man, man , woman, woman , car , top , vw , top , bmw , top ,  , person, top , man, top , woman, top , vw , car , bmw , car ,     man, person , woman, person A = {driver, owner, likes-best}, and         F =         car , owner , person , car , driver , person ,      vw , owner , person , vw , driver , person ,  bmw , owner , person , bmw , driver , person ,   person, likes-best , top , man, likes-best , top ,      woman, likes-best , top possible attribute values are at entities of a certain type.

Yet, abstract feature structures do not have all of the properties that HPSG 87 requires of its feature structures. In particular, they cannot express disjunctive information, and they do not constitute a Heyting algebra under the subsumption relation. Therefore, we will proceed from abstract feature structures to disjunctive feature structures. Disjunctive feature structures are sets of abstract feature structures with certain conditions imposed on the members of the set. They are the only type of feature structure discussed here that does not have a counterpart in HPSG 94.

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