An Expanded Logical Formalism for Head-driven Phrase Structure Grammar

Though Pollard and Sag 1994] assumes that an unspeciied variant of the formal logic of Carpenter 1992] will provide a formalism for HPSG, a precise formulation of the envisaged formalism is not immediately obvious, primarily because a principal tenet of Carpenter 1992], that feature structures represent partial information, seems to connict with a principal tenet of Pollard and Sag 1994], that feature structures represent abstract linguistic entities. This has caused many HPSGians to be mistakenly concerned with partial-information speciic notions, such as subsumption, that are appropriate for the Carpenter 1992] logic but inappropriate for the formalism Pollard and Sag 1994] envisages. This paper hopes to allay this concern and the confusion it engenders by substituting King 1989] for Carpenter 1992] as the basis of the envisaged formalism. It demonstrates that the formal logic of King 1989] provides a formalism for HPSG that meets all Pollard and Sag 1994] asks of the envisaged formalism. It further shows that the most credible variant of the Carpenter 1992] logic consistent with the aims of Pollard and Sag 1994] is not only incompatible with the tenet that feature structures represent partial information, but also an instance of the King 1989] logic.