A Mathematical Formalism for Linguistic Theories with an by Frank Richter

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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

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The approximation in a Heyting algebra is the join of the pseudocomplement of x, and y, which is the relative pseudocomplement of x and y. The representation of 20 A lower semilattice is a partial order in which each pair of elements has a greatest lower bound. Therefore, each Heyting algebra is is a lower semilattice. 1.

FORMAL FOUNDATIONS I appropriate, I will refer to the literature that clarified issues that were still unclear in Pollard and Sag 1987, and the reader interested in formal issues of HPSG 87 is invited to follow the references. In summation, I will not present an information-based formalism for HPSG that takes advantage of the readily available insights into possible generalizations of the formalism that is sketched in Pollard and Sag 1987. My presentation of HPSG 87 is motivated by the need to provide a simple but mathematically precise reconstruction of the predecessor of HPSG 94 that illuminates the internal structure and development of HPSG 94.

The largely aesthetical reason for that is that partial orders of a set-sized collection of feature structures are mathematically more familiar and tractable. 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.

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