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features - Feature Structures Information can be encoded in...

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Sheet1 Page 1 Feature Structures ------- ---------- Information can be encoded in `feature structures', which are rooted labeled graphs. To explain, a feature structure is a set of graph nodes (points), a set of directed edges between pairs of nodes (arrows), and an assignment of labels (symbols of some kind) to SOME of the nodes and ALL of the arrows. No node may be the source of two arrows with the same label. One of the nodes is distinguished as the root node, and all of the nodes are reachable from the root by following the directed edges (going only in the direction of the arrows). An example feature structure is CATEGORY HEAD * -----------> cat ------> noun ------> nominative \ \ \ \ SUBCAT \ +------> empty-list \ \ CONTENT INDEX PERSON +-------> ppro -----> ref ------> 3rd |\ | \ NUMBER | +------> singular | | GENDER +---------> feminine This is part of the dictionary entry for the word `she' for a typical computer English parser. Feature struct- ures seem to be the most natural way to describe lin- guistic information and grammar rules, and because of this, it is conceivable that the human mind uses some analog of feature structures to parse sentences. a From now on we will use single upper case characters as arrow labels, and single decimal digits as node labels. Unlabeled nodes will be represented by `#', and the root node will be marked by `*'. With this in mind, consider the feature structure A B E #* ---------> # ------>9 -----+ \ ^ | \ C D | | +--------> 4 -------+ |
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Sheet1 Page 2 ^ | | | +---------------+ A path from the root to a node N in feature structure is a list of edges starting at the root and going to N, where the target of one edge is the source of the next edge. A path can be named by giving the edge labels in sequence, which we do separated by dots, with an initial dot added to make it easy to distinguish the empty path that names the root. A path is said to name the target of its last edge. Thus in the above example, `.' names the root node, `.A' names the other unlabeled node, and `.A.B' and `.C.D' name the node with value `9'. Actual- ly this node has an infinite number of names, including `.A.B.E.D' and `.C.D.E.D.E.D'. ` A feature structure can be described by a set of equa- tions. Let P, P1, P2 be a path names, and V be a node value.
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