By Frank Richter
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Extra info for A Mathematical Formalism for Linguistic Theories with an Application in Head-Driven Phrase Structure Grammar
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. In summary, an HPSG 87 grammar construes a natural language as partial information that is represented by feature structures. Every piece of partial information that is true of the language is said to model or to represent the language. Feature structures are located in a Heyting algebra according to their degree of informativeness.
1 has a finite set of nodes, and the attributes obey the appropriateness conditions of the signature. The concrete feature structure 3 of (1c) violates two conditions on 87 concrete feature structures. Firstly, its set of nodes, Q3 , is infinite, and secondly, nodes of sort top are not allowed to have the attribute likes-best because likes-best is not appropriate to top. 3 is thus not an 87 concrete feature structure. The second concrete feature structure in (1) that satisfies all conditions on 87 concrete feature structures is 2 .
44 CHAPTER 2. FORMAL FOUNDATIONS I ✂ Σ If Σ is an 87 signature, I write for the set of abstract feature structures under Σ. If = β, , λ , I call β the basis set in , the re-entrancy relation in , and λ the label function in . The basis set in is a prefix closed set of paths, the re-entrancy relation in is a right invariant equivalence relation on the basis set in , and the label function in is a total function from the basis set in to the set of sorts, S, which respects the re-entrancy relation in .