Section: Scientific Foundations

Logic Engineering

Once again, in the ideal world, not only would computational semanticists not have to worry about the linguistic resources at their disposal, but they would not have to worry about the inference tools available either. These could be taken for granted, applied as needed, and the semanticist could concentrate on developing linguistically inspired inference architectures. But in spite of the spectacular progress made in automated theorem proving (both for very expressive logics like predicate logics, and for weak logics like description logics) over the last decade, we are not yet in the ideal world. The tools currently offered by the automated reasoning community still have a number of drawbacks when it comes to natural language applications.

For a start, most of the efforts of the first-order automated reasoning community have been devoted to theorem proving; model building, which is also a useful technology for natural language processing, is nowhere nearly as well developed, and far fewer systems are available. Secondly, the first-order reasoning community has adopted a resolutely `classical' approach to inference problems: their provers focus exclusively on the satisfiability problem. The description logic community has been much more flexible, offering architectures and optimisations which allow a greater range of problems to be handled more directly. One reason for this has been that, historically, not all description logics offered full Boolean expressivity. So there is a long tradition in description logic of treating a variety of inference problems directly, rather than via reduction to satisfiability. Thirdly, many of the logics for which optimised provers exists do not directly offer the kinds of expressivity required for natural language applications. For example, it is hard to encode temporal inference problems in implemented versions of description logics. Fourth, for very strong logics (notably higher-order logics) few implementations exists and their performance is currently inadequate.

These problems are not insurmountable, and TALARIS members are actively investigating ways of overcoming them. For a start, logics such as higher-order logic, description logic and hybrid logic are nowadays thought of as various fragments of (or theories expressed in) first-order logic. That is, first-order logic provides a unifying framework that often allows transfer of tools or testing methodologies to a wide range of logics. For example, the hybrid logics used in TALARIS (which can be thought of as more expressive versions of description logics) make heavy use of optimization techniques from first-order theorem proving.