Friendship paradox: Difference between revisions

Revision as of 05:04, 22 January 2014

Discontinuous-constituent Phrase Structure Grammar (DCPSG) (distinct from Discontinuous Phrase Structure Grammar/DPSG) is a formalism for describing discontinuous phrase structures in natural language, such as verb phrases in VSO languages. The formalism was introduced in the slightly more constrained form of Discontinuous-constituent Phrase Structure Grammar with Subscripts and Deletes (DCPSGsd) in Harman (1963).^[1] DCPSGs describe a superset of the context-free languages, by means of rewrite rules that permit a limited amount of wrapping, similar to that found in Head grammar. Template:Tocright

Description

Rewrite rules of a DCPSG are identical to those of a CFG, with the addition of a meta-symbol, denoted here as an underscore. DCPSG rules therefore have the general form $X \to α$ where $α$ is a string of terminal symbols and/or non-terminal symbols and at most one underscore.

The rewrite semantics of DCPSG are identical as those of a CFG when the rule being used does not contain an underscore: given a rule $X \to α$ , an occurrence of $X$ may be rewritten as $α$ .

For rules with an underscore, the rewrite semantics are slightly different: given a rule $X \to α_β$ , an occurrence of $X$ can be rewritten as $α$ , with $β$ being inserted immediately after the next non-terminal that is introduced at the same time. Using strict left-most productions, $β$ is simply inserted immediately after the non-terminal that follows $X$ prior to the rewrite.

Example

We can characterize the gross sentence structure of a VSO language such as Irish with the following rules (substituting English words for Irish words, and using subscripts solely for demonstration of discontinuity):

$S \to V P N P_{s u b j}$

$V P \to I T V | T V_N P_{o b j}$

$N P \to J o h n | S u s a n | . . .$

$I T V \to r a n | d a n c e d | . . .$

$T V \to s a w | m e t | . . .$

A derivation for the sentence saw John Susan, where John is the subject, and Susan is the direct object forming a VP with saw is:

$S \to V P N P_{s u b j} \to T V N P_{s u b j} N P_{o b j} \to s a w N P_{s u b j} N P_{o b j} \to s a w J o h n N P_{o b j} \to s a w J o h n M a r y$

References

↑ Harman, Gilbert H. 1963. Generative Grammars without Transformation Rules: A Defense of Phrase Structure. Language 39(4), 597-616.

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[harman1963-1] Harman, Gilbert H. 1963. Generative Grammars without Transformation Rules: A Defense of Phrase Structure. Language 39(4), 597-616.

[1]

@@ Line 1: / Line 1: @@
+{{underlinked|date=October 2012}}
+{{Orphan|date=December 2010}}
+'''Discontinuous-constituent Phrase Structure Grammar''' (DCPSG) (distinct from Discontinuous Phrase Structure Grammar/DPSG) is a formalism for describing discontinuous phrase structures in natural language, such as verb phrases in VSO languages. The formalism was introduced in the slightly more constrained form of Discontinuous-constituent Phrase Structure Grammar with Subscripts and Deletes (DCPSGsd) in Harman (1963).<ref name="harman1963">Harman, Gilbert H. 1963. Generative Grammars without Transformation Rules: A Defense of Phrase Structure. ''Language'' 39(4), 597-616.</ref> DCPSGs describe a superset of the context-free languages, by means of rewrite rules that permit a limited amount of wrapping, similar to that found in [[Head grammar]].
+{{tocright}}
-My name is Bess Yuill but everybody calls me Bess. I'm from United Kingdom. I'm studying at the university (final year) and I play the Viola for 7 years. Usually I choose songs from the famous films :D. <br>I have two sister. I like Baton twirling, watching movies and Games Club - Dungeons and Dragons, Monopoly, Etc..<br><br>Here is my web page :: [http://www.dumpgames.com/profile/dotuil Choosing the right ride for you mountain bike sizing.]
+==Description==
+Re''write rules of a '''DCPSG''' are identical to those of a CFG, with the addition of a meta-symbol, denoted here as an underscore. ''DCPSG'' rules therefore have the general form <math>X \to \alpha</math> where <math>\alpha</math> is a string of terminal symbols and/or non-terminal symbols and at most one underscore.
+The rewrite semantics of DCPSG are identical as those of a CFG when the rule being used does not contain an underscore: given a rule <math>X \to \alpha</math>, an occurrence of <math>X</math> may be rewritten as <math>\alpha</math>.
+For rules with an underscore, the rewrite semantics are slightly different: given a rule <math>X \to \alpha \_ \beta</math>, an occurrence of <math>X</math> can be rewritten as <math>\alpha</math>, with <math>\beta</math> being inserted immediately after the next non-terminal that is introduced at the same time. Using strict left-most productions, <math>\beta</math> is simply inserted immediately after the non-terminal that follows <math>X</math> prior to the rewrite.
+''
+==Example==
+We can characterize the gross sentence structure of a VSO language such as Irish with the following rules (substituting English words for Irish words, and using subscripts solely for demonstration of discontinuity):
+<math>S \to VP\ NP_{subj}</math>
+<math>VP \to ITV ~|~ TV \ \_ \ NP_{obj}</math>
+<math>NP \to John ~|~ Susan ~|~ ...</math>
+<math>ITV \to ran ~|~ danced ~|~ ...</math>
+<math>TV \to saw ~|~ met ~|~ ...</math>
+A derivation for the sentence ''saw John Susan'', where ''John'' is the subject, and ''Susan'' is the direct object forming a VP with ''saw'' is:
+<math>S \to VP\ NP_{subj} \to TV\ NP_{subj} NP_{obj} \to saw\ NP_{subj}\ NP_{obj} \to saw\ John\ NP_{obj} \to saw\ John\ Mary</math>
+==References==
+<references/>
+{{Formal languages and grammars}}
+{{DEFAULTSORT:Discontinuous-Constituent Phrase Structure Grammar}}
+[[Category:Formal languages]]
+[[Category:Grammar frameworks]]

Friendship paradox: Difference between revisions

Revision as of 05:04, 22 January 2014

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