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Parenthetical Grammar

In formal linguistics it is essential to realise that the laws of associativity hold neither in lexical nor in syntactic strings. Their lack and absence advances a strong argument for parenthetisation. The structuring and inner hierarchy in the following German and English expressions is much easier to understand from the use of parentheses.

‘‘Parenthetical grammar’’ is a formal rewriting system that applies parentheses for expressing the grammatical relations of dependency and semantic subordination. It provides the simplest method of syntactic parsing without requiring very demanding means of visual representation. It employs a simple apparatus of left brackets (‘{’, ‘[’ or ‘(’) in order to demark the initial boundary of linguistic expressions and right brackets (‘}’, ‘]’ or ‘)’) that delimit their end. As seen in the phrase a ladies’ dress parenthetisation induces considerable differences in meaning:

a ladies’ dress = a (ladies’ dress) ¹ (a lady’s) dress = a lady’s dress .

The expression on the left describes a dress for ladies, whereas the phrase structure on the right refers to a particular lady’s garment.

A simple example of sentence analysis is given by the collocation Such an extremely long journey exhausted our energy. Its parenthetical articulation grammar segments couples of heads and dependents into the ensuing hierarchy:

((((Such (an ((extremely long) journey))) (exhausted (our energy))).

When rendered in terms of phrase structures, its decomposition proceeds as follows:

S ® NP VP ® ((AP NP) VP) ® ((Adv AP NP) VP) ® ((D A NP) VP) ® ((D A NP) (V NP)) .

Another telling illustration is supplied by the string Little Red Riding-Hood went to her grandmother in another village:

((Little (Red Riding-Hood))) (went (to (((her grandmother)) (in (another village)))).

The main reason for introducing such adjustments in syntactic theory is not only that it saves space and simplifies analysis. Its most important theoretical facility consists in opening the second dimension of syntactic hierarchy. Parenthetical grammars turn linear sequences into 2D-patterns embedding strings into a two-dimensional Cartesian space. Its basic horizontal axis x depicts the linear sequencing of symbols, while the second vertical axis y plots strings with the scaled hierarchy of phrase-structures according to different levels of syntactic validity.6