By Frank Richter

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

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Definition 5 For each 87 signature Σ = S, , A, F , for each ✁ ✄✂ Σ ✁ ✄✂ Σ ˆ1 , ∆1 , Λ1 ∈ ˆ2 , ∆2 , Λ2 ∈ 1 = Q1 , q 2 = Q2 , q 87 , for each 87 , µ is a morphism from 1 to 2 under Σ iff µ is a total function from Q1 to Q2 , µ(ˆ q1 ) = qˆ2 , for each q ∈ Q1 , for each α ∈ A, if ∆1 q, α is defined, then ∆2 µ(q), α is defined and ∆2 µ(q), α = µ(∆1 q, α ), and for each q ∈ Q1 , Λ2 (µ(q)) Λ1 (q). The existence of a morphism from 1 to 2 means that 1 is in some sense embedded in 2 , or 2 is an extension of 1 .

1 illustrates the basic idea of feature structures. The root node of the informal example is labeled category, and it has two attributes, subcat and head, with values of sort list and verb, respectively. 1: Illustration of the idea of feature structures category • 333 33 subcat 33head 33 3% Õ • verb list • 333 33 aux inv 33vform 33 3%  Õ boolean • • • vform plus The recursive embedding of attribute bearing values makes feature structures a flexible tool as arbitrarily complex information-bearing entities.

If a top element exists, feature structures of sort ‘ ’ carry the least information. They are information about all objects in the domain. A feature structure labeled by the bottom element—if it exists—indicates inconsistent information. 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.

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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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