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<Paper uid="E93-1005">
  <Title>Decidability and Undecidability in stand-alone Feature Logics</Title>
  <Section position="6" start_page="33" end_page="35" type="concl">
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5 Discussion
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    <Paragraph position="0"> The results of this investigation are easy to summarise: the ability to express both re-entrancy and  generalisations about feature structures lead to algorithmically unsolvable satisfiability problems even if most Boolean expressivity is dropped. What are the implications of these results? Stand-alone feature formalisms offer (elegant) expressive power in a way that is compatible with the lexically driven nature of much current linguistic theorising. One of their disadvantages (at least in their current incarnations) is that they tend to hide computationally useful information. For example, as \[Johnson 1992\] points out, it is difficult even to formulate such demands as offiine parsability for existing stand-alone formalisms; the configurational information required is difficult to isolate. The problem is that stand-alone formalisms tend to be too homogeneous. It is certainly elegant to treat information concerning complex categories and configurational information simply as 'features'; but unless this is done sensitively it runs the risk of 'reducing' a computationally easy problem to an uncomputable one.</Paragraph>
    <Paragraph position="1"> Now, much current work on feature logic can be seen as attempts to overcome the computational bluntness of stand-alone formalisms by making visible computationally useful structure. For example, recent work on typed feature structures (see \[Carpenter 1992\]) explicitly introduces the type inheritance structure into the semantics; whereas in \[Blackburn et al. 1993\] composite entities consisting of trees fibered across feature structures are constrained using two distinct 'layers' of modal language. What is common to both these examples is the recognition that linguistic theories typically have subtle internal architectures. Only when feature logics become far more sensitive to the fine grain of linguistic architectures will it become realistic to hope for general decidability results.</Paragraph>
    <Paragraph position="2"> Acknowledgements We would like to thank the anonymous referees for their comments on the abstract. Patrick Blackburn would like to acknowledge the financial support of the Netherlands Organization for the Advancement of Research (project NF 102/62-356 'Structural and Semantic Parallels in Natural Languages and Programming Languages').</Paragraph>
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