A semantic ``Trampe'' for HPSG: Easy ways from bottom to top and back in Trondheim

Frank Richter and Manfred Sailer

Invited talk given at HPSG 01 in Trondheim, Norway, on August 3rd, 2001.


HPSG offers linguists a choice between a fairly wide range of semantic representation languages. Some of these representation languages endorse ideas of underspecified semantic systems and are usually influenced by computational considerations, while others are inspired by fully specified systems.
In this talk we want to clarify some important theoretical issues pertaining to the architecture and potential range of semantic systems in HPSG. For our investigation, we start with an easily accessible, type-theoretical language, Ty2, which is similar to Richard Montague's Intensional Logic. We use techniques offered by the HPSG formalism outlined in Pollard & Sag 94 in order to build different combinatorial semantic systems for that language in HPSG grammars and to explore various ways of underspecification. The techniques that we apply will allow us to distinguish at least four possible semantic systems available in HPSG: systems with a truly underspecified denotation, systems that use an indirect representation, systems with discontinuous representations, and systems that only employ classical, ``fully specified'' representations with a traditional combinatorial system such as lambda abstraction and functional application. With respect to this small taxonomy of semantic systems, we can classify the current semantic representation languages of the HPSG literature.
Having characterized a range of interesting options that are technically available, we then turn to questions of the empirical adequacy of the resulting alternative architectures of grammar. Drawing on well-known empirical phenomena in various languages, we will show that different semantic systems force the linguist to express certain empirical generalizations in different modules of the grammar. Depending on the module in which the generalizations are expressed, different natural classes of data are predicted. To the extent to which these predictions can be tested, the choice between the semantic systems becomes accessible to empirical tests. Besides arguments of computational feasibility and largely aesthetical differences in elegance, we thus obtain an additional dimension for choosing a suitable semantic system for HPSG grammars of natural languages.
There is one more important issue concerning semantic systems that we will pay attention to throughout the talk. HPSGians adopt two kinds of underlying mathematical foundations. While some follow the non-unification, constraint-based framework introduced by Pollard & Sag 94, others adhere to the unification-based formalism of Pollard & Sag 87. Concrete formalisms that currently represent these two directions are RSRL for Pollard & Sag 94 and the unification formalism underlying the LKB system for Pollard & Sag 87, which is inspired by the unification formalism developed and implemented by Carpenter and Penn. When we formalize the four types of semantic systems distinguished above, we do so in RSRL. We will thus have to keep an eye on where particular properties of the RSRL formalism that have no direct counterpart in a unification-based formalism might come into play at each step and tie the choice of the semantic framework to a particular formalism for HPSG. Moreover, the different ontological status of the structures in the denotation of a grammar and the different function of the mathematically corresponding structures in an information-based approach leads to plausible alternatives for the interpretation of the structures that are used as semantic representations.

Then handout of the talk is available in two formats:

Frank Richter