Discontinuous-constituent phrase structure grammar

Template:One source 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). 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:TOC right

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 $X\to \alpha$ where $\alpha$ 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 $X\to \alpha$, an occurrence of $X$ may be rewritten as $\alpha$.

For rules with an underscore, the rewrite semantics are slightly different: given a rule $X\to \alpha \mathrm{\_}\beta$, an occurrence of $X$ can be rewritten as $\alpha$, with $\beta$ being inserted immediately after the next non-terminal that is introduced at the same time. Using strict left-most productions, $\beta$ 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):

$\mathrm{S}⟶\mathrm{V}\mathrm{P}\mathrm{N}\mathrm{P}{\phantom{A}}_{\mathrm{s}\mathrm{u}\mathrm{b}\mathrm{j}}$

$\mathrm{V}\mathrm{P}⟶\mathrm{I}\mathrm{T}\mathrm{V}|\mathrm{T}\mathrm{V}\mathrm{\_}\mathrm{N}\mathrm{P}{\phantom{A}}_{\mathrm{o}\mathrm{b}\mathrm{j}}$

$\mathrm{N}\mathrm{P}⟶𝐽𝑜ℎ𝑛\mathit{|}𝑆𝑢𝑠𝑎𝑛\mathit{|}\mathit{\dots }$

$\mathrm{I}\mathrm{T}\mathrm{V}⟶𝑟𝑎𝑛\mathit{|}𝑑𝑎𝑛𝑐𝑒𝑑\mathit{|}\mathit{\dots }$

$\mathrm{T}\mathrm{V}⟶𝑠𝑎𝑤\mathit{|}𝑚𝑒𝑡\mathit{|}\mathit{\dots }$

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:

$\mathrm{S}⟶\mathrm{V}\mathrm{P}\mathrm{N}\mathrm{P}{\phantom{A}}_{\mathrm{s}\mathrm{u}\mathrm{b}\mathrm{j}}⟶\mathrm{T}\mathrm{V}\mathrm{N}\mathrm{P}{\phantom{A}}_{\mathrm{s}\mathrm{u}\mathrm{b}\mathrm{j}}\mathrm{N}\mathrm{P}{\phantom{A}}_{\mathrm{o}\mathrm{b}\mathrm{j}}⟶𝑠𝑎𝑤\mathrm{N}\mathrm{P}{\phantom{A}}_{\mathrm{s}\mathrm{u}\mathrm{b}\mathrm{j}}\mathrm{N}\mathrm{P}{\phantom{A}}_{\mathrm{o}\mathrm{b}\mathrm{j}}⟶𝑠𝑎𝑤𝐽𝑜ℎ𝑛\mathrm{N}\mathrm{P}{\phantom{A}}_{\mathrm{o}\mathrm{b}\mathrm{j}}⟶𝑠𝑎𝑤𝐽𝑜ℎ𝑛𝑀𝑎𝑟𝑦$