Discontinuous-constituent phrase structure grammar

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

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

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):

${\displaystyle {\ce {S->VP\ NP_{subj}}}}$

${\displaystyle {\ce {VP->ITV~|~TV\ \_\ NP_{obj}}}}$

${\displaystyle {\ce {NP->{\it {{John}~|~{\it {{Susan}~|~...}}}}}}}$

${\displaystyle {\ce {ITV->{\it {{ran}~|~{\it {{danced}~|~...}}}}}}}$

${\displaystyle {\ce {TV->{\it {{saw}~|~{\it {{met}~|~...}}}}}}}$

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:

${\displaystyle {\ce {S->VP\ NP_{subj}->TV\ NP_{subj}NP_{obj}->{\mathit {saw}}\ NP_{subj}\ NP_{obj}->{\mathit {saw}}\ {\mathit {John}}\ NP_{obj}->{\mathit {saw}}\ {\mathit {John}}\ {\mathit {Mary}}}}}$