Eckhard Bick - VISL

Here, the variable ‘number’ can be instantiated with the values ‘singular’ or ‘plural’,
and all instances of the same variable in a rule have to “match” (or to be “unified”,
which is why such grammars are called unification grammars), that is, their values have
to be the same in order for the production to be legitimate (note, that in the second rule,
there are two different number-variables - for verb and direct object, respectively -, that
do not have to match!). While pure PSG has a certain appeal for isolating languages like
English - not least due to its pedagogical simplicity - unification grammars are
unavoidable where generative grammar is applied to inflexional languages like French
or German.
Higher level generative grammars, like HPSG, may incorporate other
subcategorisation information, like valency and selection restrictions, into the lexicon,
and thus build a more sophisticated rule set.
Traditionally, four levels of descriptional power are distinguished for generative
grammars:
Chomsky's hierarchy of grammar classes (Chomsky, 1959)
(low number: more powerful, high number: more restricted
0 unrestricted PSG
1 context sensitive PSG
x -> y [where y has more symbols than x, e.g. A B -> C D E]
or: x A z -> x y z [other notation with "visible" context]
2 context free PSG
A -> x
3 regular PSG = finite state grammars
left linear: A -> B t, A -> t
right linear: A -> t B, A -> t
[where: T = terminal; N = non-terminal; A,B, C, D, E ∈ Ν; t ∈ T; x,y,z = sequences of T and/or N]
The computationally most interesting grammars are the least powerful, - finite state
grammars, since they can be implemented as algorithmically very efficient transition
networks (reminiscent of the above described Markov Models, without the transition
probabilities). In such networks, the computer program starts from the start symbol and
moves along possible transition paths (arcs) between non-terminal symbols. Every path
is labelled with a non-terminal symbol (word or word class), and can only be taken, if
the word class or word in question is encountered linearly at the next position to the
right (in right linear grammars 94 ). When it encounters a “dead end” (i.e. a non-terminal
94 In left linear grammars, the algorithm would have to work from right to left, in order to avoid infinite loops created by the
possibility of reiterating non-terminal production of the type A -> A t, as in ADJP -> ADJP adj.
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