Team LeD

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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 required 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 exist do not directly offer the kind 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 exist and their performance is currently inadequate.

These problems are not insurmountable, and LED 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 automated tools for hybrid logics (which can be thought of as more expressive versions of description logics) used and developed by LED make heavy use of optimisation techniques from first-order theorem proving.

Moreover — and from a logical perspective, this is the most interesting point — the interaction between natural language and computational logic is not a one way street. The problems that arise in natural language may well be significant for developments in computational logic. As an example of this, early versions of the CURT software (an educational system for computational semantics developed by Patrick Blackburn and Johan Bos) made use of a standard first-order model builder called MACE. The inference problems that the system generated were then used as tests when the PARADOX model builder was developed, leading to considerable performance improvements. Similarly, natural language applications have also inspired significant performance enhancements to the RACER description logic prover. Feedback from natural language to logic is likely to be an important theme in future developments.


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