ID/LP Grammars are a subset of Phrase Structure Grammars, differentiated from other formal grammars by distinguishing between immediate dominance (ID) and linear precedence (LP) constraints. Whereas traditional phrase structure rules incorporate dominance and precedence into a single rule, ID/LP Grammars maintains separate rule sets which need not be processed simultaneously. ID/LP Grammars are used in Computational Linguistics. For example, a typical phrase structure rule such as S ⟶ NP VP {\displaystyle {\ce {S -> NP \; VP}}} , indicating that an S-node dominates an NP-node and a VP-node, and that the NP precedes the VP in the surface string. In ID/LP Grammars, this rule would only indicate dominance, and a linear precedence statement, such as N P ≺ V P {\displaystyle NP\prec VP} , would also be given. The idea first came to prominence as part of Generalized Phrase Structure Grammar; the ID/LP Grammar approach is also used in head-driven phrase structure grammar, lexical functional grammar, and other unification grammars. Current work in the Minimalist Program also attempts to distinguish between dominance and ordering. For instance, recent papers by Noam Chomsky have proposed that, while hierarchical structure is the result of the syntactic structure-building operation Merge, linear order is not determined by this operation, and is simply the result of externalization (oral pronunciation, or, in the case of sign language, manual signing).
Defining Dominance and Precedence
Immediate Dominance Immediate dominance is the asymmetrical relationship between the mother node of a parse tree and its daughters, where the mother node (to the left of the arrow) is said to immediately dominate the daughter nodes (those to the right of the arrow), but the daughters do not immediately dominate the mother. The daughter nodes are also dominated by any node that immediately dominates the mother node, however this is not an immediate dominance relation. For example, the context free rule A → B C D {\displaystyle A\rightarrow B\ C\ D} , shows that the node labelled A (mother node) immediately dominates nodes labelled B, C, and D, (daughter nodes) and nodes labelled B, C, and D can be immediately dominated by a node labelled A.
Linear Precedence Linear precedence is the order relationship of sister nodes. LP constraints specify in what order sister nodes under the same mother can appear. Nodes that surface earlier in strings precede their sisters. LP can be shown in phrase structure rules in the form A → B C D {\displaystyle A\rightarrow B\ C\ D} to mean B precedes C precedes D, as shown in the tree below.
A rule that has ID constraints but not LP is written with commas between the daughter nodes, for example A → B , C , D {\displaystyle A\rightarrow B,\ C,\ D} . Since there is no fixed order for the daughter nodes, it is possible that all three of the trees shown here are generated by this rule.
Alternatively, these relationships can be expressed through linear precedence statements, such as B ≺ C {\displaystyle B\prec C} , to mean that anytime B and C are sisters, B must precede C. The principle of transitivity can be applied to LP relations which means that if B ≺ C {\displaystyle B\prec C} and C ≺ D {\displaystyle C\prec D} , then B ≺ D {\displaystyle B\prec D} as well. LP relationships are asymmetric: if B precedes C, C can never precede B. An LP relationship where there can be no intervening nodes is called immediate precedence, while an LP where there can be intervening nodes (those derived from the principle of transitivity) are said to have weak precedence.
Grammaticality in ID/LP Grammars For a string to be grammatical in an ID/LP Grammar, it must belong to a local subtree that follows at least one ID rule and all LP statements of the grammar. If every possible string generated by the grammar fits this criterion, than it is an ID/LP Grammar. Additionally, for a grammar to be able to be written in ID/LP format, it must have the property of Exhaustive Constant Partial Ordering (ECPO): namely that at least part of the ID/LP relations in one rule is observed in all other rules. For example, the set of rules: (1) A → B C D {\displaystyle A\rightarrow B\ C\ D} (2) B → D C A {\displaystyle B\rightarrow D\ C\ A} does not have the ECPO property, because (1) says that C must always precede D, while (2) says that D must always precede C.
Advantages of ID/LP Grammars Since LP statements apply regardless of the ID rule context, they allow us to make generalizations across the whole grammar. For example, given the LP statement V ≺ D P {\displaystyle V\prec DP} , where V is the head of a VP, this means that in any clause in any sentence, V will always surface before its DP sister in any context, as seen in the following examples.Lucy won the race.Ava told Sara to read a book. This can be generalized into a rule that holds across English, X ≺ Y P {\displaystyle X\prec YP} , where X is the head of any phrase and YP is its complement. Non-ID/LP Grammars are unable to make such generalizations across the whole grammar, and so must repeat ordering restrictions for each individual context.
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