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.

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

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

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

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

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

TV ⟶ saw | met | ⋅ ⋅ ⋅ {\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:

S ⟶ VP NP subj ⟶ TV NP subj NP obj ⟶ saw NP subj NP obj ⟶ saw John NP obj ⟶ saw John Mary {\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}}}}}