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By Frank Richter

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They are distinct 87 concrete feature structures with different nodes. That means that the subsumption relation is not antisymmetric, and ✁ ✂ Σ ✁ ✄✂ Σ is, therefore, not a partial order. 14 We must conclude that in order to obtain a Heyting algebra of feature structures under subsumption, a different kind of feature structure is needed. 13 A preorder is a set S together with a reflexive and transitive relation in S. Of course, the fact that the subsumption relation is not antisymmetric is not the only reason for why ✂✁☎✄ Σ is not the right choice.

1. LANGUAGE AS PARTIAL INFORMATION 43 them by equivalence classes of paths. Whichever representation we choose, we obtain the desired property of identity under mutual subsumption of the new, less concrete kind of feature structure, and the collection of feature structures becomes set-sized. 15 Moshier 1988 calls the new feature structures abstract feature structures. Parallel to concrete feature structures, I present a general definition first before I introduce the more restricted abstract feature structures that HPSG 87 demands.

Feature structures are located in a Heyting algebra according to their degree of informativeness. The operations of the algebra function as a recipe for constructing the total information that speakers have about their language from the set of feature structures specified by the grammar. 6 Occasionally, I adopt a reading of Pollard and Sag 1987 that is slightly closer to HPSG 94 than the more literal reading of King, and I change some minor technical details of the sketch of a formalism of Pollard and Sag where subsequent research showed that the technical choices of the authors had been erroneous or misled.

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A Mathematical Formalism for Linguistic Theories with an Application in Head-Driven Phrase Structure Grammar by Frank Richter


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