📄 http:^^ai.eecs.umich.edu^people^rounds^mol.html
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Date: Tue, 14 Jan 1997 23:29:55 GMT
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<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 2.0//EN"><HTML><HEAD><title>Bill Rounds' Research Statement </title></HEAD><BODY><H2>Mathematics of Language </H2> This subject goes back a long way, to early logicians who (like Boole)were convinced that a calculus of reasoning was just around the corner;all that was required was to translate logical arguments in natural languageinto symbolic expressions. <P>This problem was a lot more difficult than imagined. It involved firstunderstanding how meanings were associated with utterances; and to do this,the structure of utterances had to be understood. <P>The foundations of today's mathematics of language were laid by(among others) Noam Chomsky in the late 1950's and early 1960's. People recognized then that simple syntactic systems, notably context-free grammars, could be used to specify both programming and natural language syntax. <P>Since those days, it has been discovered that the syntax of natural languageand programming languages is a bit more complicated, and people have workedon various ways to integrate syntax and semantics. The basic cognitive premise,however, is that humans do routinely use certain data structures to processlanguage, and that (quite possibly) humans are genetically predisposed tobe able to use these data structures for both language processing and learning.<P>Mathematics enters the picture when one wants to study the structural properties ofsuch postulated data structures, and algorithms which use them. For example,context-free grammars make heavy use of tree data structures.<P>Most recently, I have been involved with a new class of data structurescalled <I> feature structures</I> or attribute-value structures. Theseentities occur ubiquitously in computer science (a.k.a. records), andthey have a lot of interesting properties, like tree structures do.<P>One such property is that feature structures may represent <I>incomplete</I>information about a sentence. This leads to a natural ordering ofthese structures according to how much information they contain. I amnow looking at ways to "fill up" feature structures; and a very interestingapproach is to fill them up with <I> default </I> information, which mayhave to be retracted. This leads to using methods from artificialintelligence (non-monotonic logic and belief revision) together withthe mathematics of partial orders. This latter theoryhas been well-developed for programming languages, where it is called <!WA0><A HREF="ftp://theory.doc.ic.ac.uk/papers/Jung/handbook.ps.gz">domain theory</A>.More on feature systems and defaults can be found in the specific project descriptions<UL><LI><!WA1><A HREF="http://ai.eecs.umich.edu/people/rounds/feature.html">Feature Logic</A><LI><!WA2><A HREF="http://ai.eecs.umich.edu/people/rounds/nonmon.html">Default Domain Theory</A></UL></BODY></HTML>⌨️ 快捷键说明
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