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Some formal properties of stratified feature grammars

Some formal properties of stratified feature grammars In this paper, we investigate the formal expressive properties of Stratified Feature Grammar (SFG), a new logic-based linguistic framework motivated by relational grammar and metagraph grammar, as well as by Kasper-Rounds logic. The driving force behind SFG is the generalization of the conceptfeature from an unanalyzable atomic one to a sequence of so-called R-signs. The linguistic interpretation of thesestratified features is that each R-sign in such a sequence denotes a primitive grammatical relation such as subject or direct object in different syntactic “strata”. This generalization permits the specification of a rigorous feature-structure-based formalism for natural-language grammars based on the view that syntax is “multistratal” and “relational”. The introduction of stratified features leads to several other innovations, two of which might have utility in other frameworks. One is the idea of imposing a partial order on features. The other is the concept of(data) justification: essentially, this is a stipulation that for an S-graph to be well-formed with respect to some grammarG it must, in addition to satisfying the rules ofG, have each of its “core” data (each feature occurrence, each node-label occurrence and each instance of so-called structure-sharing) justified in a formally precise manner by some rule of Justification ensures that. Justification ensures that satisfying S-graphs do not have more structure than absolutely necessary and so makes it appealing to a notion of “minimal model” otiose. Justification plays a key role in a number of our proofs. The formal results presented here include the following. First, it is proved that in the unrestricted SFG framework, every type 0 (r.e.) language is generated by some SFG. Then, we restrict the framework to so-calledbounded SFG with two linguistically motivated principles: Lexical Anchoring and Boundedness. Anchoring requires, in essence, that each core datum of an S-graph be justified by aword in its yield. Boundedness insures that S-graph features are short. Although these restrictions together put the class of bounded SFG languages well within the class of recursive languages, we go on to demonstrate that the recognition problem for bounded SFG is NP-hard. Further, we establish that a bounded SFG language need not be semi-linear. On the matter of upper bounds, we show that every bounded SFL can be recognized by a nondeterministic Turing machine inn logn space and polynomial time and that the recognition problem for bounded SFL's is NP-complete. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Mathematics and Artificial Intelligence Springer Journals

Some formal properties of stratified feature grammars

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Publisher
Springer Journals
Copyright
Copyright
Subject
Computer Science; Artificial Intelligence; Mathematics, general; Computer Science, general; Complex Systems
ISSN
1012-2443
eISSN
1573-7470
DOI
10.1007/BF02451552
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Abstract

In this paper, we investigate the formal expressive properties of Stratified Feature Grammar (SFG), a new logic-based linguistic framework motivated by relational grammar and metagraph grammar, as well as by Kasper-Rounds logic. The driving force behind SFG is the generalization of the conceptfeature from an unanalyzable atomic one to a sequence of so-called R-signs. The linguistic interpretation of thesestratified features is that each R-sign in such a sequence denotes a primitive grammatical relation such as subject or direct object in different syntactic “strata”. This generalization permits the specification of a rigorous feature-structure-based formalism for natural-language grammars based on the view that syntax is “multistratal” and “relational”. The introduction of stratified features leads to several other innovations, two of which might have utility in other frameworks. One is the idea of imposing a partial order on features. The other is the concept of(data) justification: essentially, this is a stipulation that for an S-graph to be well-formed with respect to some grammarG it must, in addition to satisfying the rules ofG, have each of its “core” data (each feature occurrence, each node-label occurrence and each instance of so-called structure-sharing) justified in a formally precise manner by some rule of Justification ensures that. Justification ensures that satisfying S-graphs do not have more structure than absolutely necessary and so makes it appealing to a notion of “minimal model” otiose. Justification plays a key role in a number of our proofs. The formal results presented here include the following. First, it is proved that in the unrestricted SFG framework, every type 0 (r.e.) language is generated by some SFG. Then, we restrict the framework to so-calledbounded SFG with two linguistically motivated principles: Lexical Anchoring and Boundedness. Anchoring requires, in essence, that each core datum of an S-graph be justified by aword in its yield. Boundedness insures that S-graph features are short. Although these restrictions together put the class of bounded SFG languages well within the class of recursive languages, we go on to demonstrate that the recognition problem for bounded SFG is NP-hard. Further, we establish that a bounded SFG language need not be semi-linear. On the matter of upper bounds, we show that every bounded SFL can be recognized by a nondeterministic Turing machine inn logn space and polynomial time and that the recognition problem for bounded SFL's is NP-complete.

Journal

Annals of Mathematics and Artificial Intelligence – Springer Journals

Published: Jun 23, 2006

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