Fractional Grammars

The formal apparatus of parenthetical grammars shares many inadequacies encountered in immediate constituent analysis. It chains subsequent neighbouring words into pairs but does not specify their grammatical interrelations expressed by their mutual syntactic dependency. A convenient solution is offered by the so-called fractional grammars. They combine the convenient properties of constituency and dependency by indicating the subordinate position of dependents by slash signs ‘/’ and ‘\’. This is how it is possible to analyse a simple sentence The extremely long journey exhausted our energy:

(((The\((extremely\long)\journey))\(exhausted/(our\energy))).

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

The right slash in V/NP means that in accusative object constructions the noun phrase the NP functions as a dependent of the head V (verb). It is efficient especially in indicating the syntactic status of incongruent attributes following the governing nominal head. Its treatment of attribute constructions is illustrated by the phrase structure the flower of many colours:

(the\flower)/(of(different\colours)) .

NP® (D\N)/NP ® (D\N)/(A\N) .

The replacement of cancellation by subtraction seems convenient since it permits exploiting slash marks for designating other important string operations. One possible usage might serve for designating relations of syntactic dependency. The inner structure of a word would be comprehensible if we combined dependency with parenthetisation. The afore-mentioned phrases would beam with clarity and explicitness if they were segmented neatly by parentheses determining the hierarchy of terms:

Rücksichtslosigkeit » ‘inconsiderateness’ ,

((((Rück\sichts)\los)\ig)\keit) » ‘(in\((consider)\ate)\ness)’ .

In such lexical derivations suffixes act as the governing head because they explicitly give the whole expression its categorial and part-of-speech standing. If a lexical root is preceded by a few prefixes and appended by several suffixes, we do not consider the order of its etymological composition but the hierarchy of syntactic values. Etymologically speaking, in ‘boldness’ the adjective ‘bold’ is primary but in lexical analysis it is secondary because the part-of-speech value of ‘boldness’ is determined by the suffix ‘-ness’.