Tree-Adjoining Grammars
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1 Tree Adjoining Grammars Tree-Adjoining Grammars Department of Computer Science University of Helsinki Department of Computer Science, University of Helsinki Page 1
2 Tree Adjoining Grammars Outline Introduction: formalisms for linguistic purposes. Basics of TAGs: elementary structures and operations, derivation. Formal properties of grammars and TAGs TAG variants Multicomponent TAGs (MC-TAG) Synchronous TAGs (S-TAG) TAG parsing Department of Computer Science, University of Helsinki Page 2
3 Tree Adjoining Grammars Formal systems for linguistic theories Basis of any formal system: elementary structures and combining operations. Context-free grammars (CFG): terminal and nonterminal symbols, and rewrite rules. CFG example rules as elementary structures. 1. S V really V likes John Lyn Department of Computer Science, University of Helsinki Page 3
4 Tree Adjoining Grammars Derivation in CFGs The phrase structure tree S John really V likes Lyn For each nonterminal node, the daughters record which rule was used to rewrite it. Department of Computer Science, University of Helsinki Page 4
5 Tree Adjoining Grammars Tree Substitution Grammars (TSG) Both elementary objects and derivations are trees. TSG example. S S John Lyn V John V likes likes Lyn Elementary structures are combined by substitution. Condition: The nonterminal node must have the same label as the root node of the substituted tree. Department of Computer Science, University of Helsinki Page 5
6 Tree Adjoining Grammars Domain of locality CFGs and TSGs are weakly equivalent. They generate the same string languages, but the derived structures have a different Domain of locality. Local restrictions are valid in the domain of locality: a CFG rule or a tree grammar tree. Examples: V agreement, subcategorisation. TSGs (and other tree grammars) have an Extended domain of locality. Department of Computer Science, University of Helsinki Page 6
7 Tree Adjoining Grammars Lexicalisation A grammar is lexicalised, if every elementary structure is associated with exactly one lexical item, and every lexical item of the language is associated with a finite set of elementary structures in the grammar. CFGs cannot be lexicalised in a linguistically meaningful manner, but let s try. S likes No place for really? Instead of merging two rules into one, we can combine them into a tree structure TSG. Still no place for really. Solution: Adjunction operation. A formalism in which the elementary structures of a grammar are trees and in which the combining operations are adjunction and substitution is called a Tree Adjoining Grammar (TAG). When lexicalised, we have a Lexicalised Tree Adjoining Grammar (LTAG). Department of Computer Science, University of Helsinki Page 7
8 Tree Adjoining Grammars Elementary structures Elementary trees are maximal syntactic projections of lexical items. Initial tree: Auxiliary tree: X X X Alpha trees. Recursion is not allowed in initial trees. Lexicalised trees have anchors on the frontier of the tree. Beta trees. Recursion allowed. Root and foot node must have the same label. Department of Computer Science, University of Helsinki Page 8
9 Tree Adjoining Grammars Operations Substitution: only for initial trees or lexical items. Y 2 X Y 1 => X Y 2 Adjunction: only for auxiliary trees. Y 2 Y 3 X Y 1 => X Y 2 Y 3 Department of Computer Science, University of Helsinki Page 9
10 Tree Adjoining Grammars Adjunction example Adjunction of really into initial tree: S S really * John V John really likes Lyn V likes Lyn Department of Computer Science, University of Helsinki Page 10
11 Tree Adjoining Grammars Derived trees and derivation trees A string-rewriting formalism, e.g. a CFG, derives a set of strings. A tree-rewriting formalism, e.g. a TAG, derives a tree: derived tree. Linguistic TAGs derive phrase structure trees. A derivation tree records how the derived string (CFG) or derived tree (TAG) was assembled from elementary rules (CFG) or elementary tree (TAG). Derivation tree for John really likes Lyn: (like) (John) (Lyn) (really) Department of Computer Science, University of Helsinki Page 11
12 Tree Adjoining Grammars Derivation tree examples When derived treed are ambiguous, derivation trees might show the difference. Elementary tree for an idiomatic expression and two derivation trees for Mary pull John s leg: To pull s leg Literal reading Idiomatic reading S pull-n0vn1 pull-leg-n0vdn1n 0 Mary- leg- Mary- John- V s-d pull D N John- 1 s leg Department of Computer Science, University of Helsinki Page 12
13 Tree Adjoining Grammars Adjunction constraints and features Elementary tree nodes can be annotated with adjunction constraints. Selective adjoining constraint (SA): list of accepted trees. Null adjoining constraint (NA): empty list. Obligatory adjunction constraint (OA): boolean value. Nonterminal and terminal nodes? NA nodes are nonterminal nodes that are not rewritten. OA nodes are nonterminal nodes that must be rewritten. SA nodes are either terminal or nonterminal nodes for tree rewriting. Department of Computer Science, University of Helsinki Page 13
14 Tree Adjoining Grammars Comparison of formal grammars Chomsky hierarchy for string rewriting systems Grammar Languages Automaton Production rules Type-0 Recursively enumerable Turing machine No restrictions Type-1 Context-sensitive Linear-bounded non-deterministic Turing machine A Type-2 Context-free Nondeterministic A pushdown automaton Type-3 Regular Finite state automaton A A ab a Tree Adjoining Grammars are sronger than CFGs, but weaker than Context-sensitive grammars. Department of Computer Science, University of Helsinki Page 14
15 (TAG) Tree Adjoining Grammars Formal properties of TAGs The set of languages generated by a TAG, context-free grammar, (CFG). (TAG), includes the set of languages generated by a Inclusion is proper, e.g. COUNT-4= a n 0 (CFG) Moreover, (TAG) (CSG), e.g. COUNT-5 (CSG) (TAG) Automaton: Embedded Pushdown Automaton with a stack of stacks of stack symbols as the pushdown store. Tree-Adjoining Languages (TAL) are polynomially parsable, time complexity O(n ). Department of Computer Science, University of Helsinki Page 15
16 Tree Adjoining Grammars Extending the Power of TAG TAG cannot always provide a satisfactory analysis for linguistic constructions, e.g. This building, John bought a picture of. This building is the complement of the noun picture and should be substituted into an node in the same elementary tree as the head noun picture. Illegal adjuntion: S S 0 PP V 1* Det N P 1 buy picture of Illegal auxiliary tree Department of Computer Science, University of Helsinki Page 16
17 Tree Adjoining Grammars Multicomponent TAGs (MC-TAG) Elementary sets are sets of trees rather than single trees. In a tree-local multicomponent TAG, all members of an elementary set must adjoin simultaneously into a single elementary tree. In a set-local multicomponent TAG, all members of a derived set of trees must adjoin simultaneously into trees from a single elementary set. S S S* PP 0 Det N P 1 V 1 picture of buy Department of Computer Science, University of Helsinki Page 17
18 Tree Adjoining Grammars Synchronous TAGs (STAG) A Synchronous TAG relates the tree-adjoining grammars of two different languages. Definitions for node to node correspondence, lexical entries, feature transfer. Application areas include machine translation, language generation, semantic analysis, etc. A typical transfer algorithm for machine translation: Parse the source sentence according to the source grammar. Map each elementary tree in the source derivation tree with a tree in the target derivation tree according to the transfer lexicon. Read the target sentence off the target derivation tree. Example. Department of Computer Science, University of Helsinki Page 18
19 Tree Adjoining Grammars TAG recognition and parsing A bottom-up chart parser proceeds bottom-up in recognising the elementary trees used in a derivation and assembling the elementary trees into a derivation. Worst and best case time complexity O(n ). Earley-style algorithms combine bottom-up parsing with top-down prediction on derived trees. Worst case time complexity O(n ) O(n ), faster in an average case. Head-driven algorithms extends parses along the path from the anchor of an elementary tree to its root by performing adjunctions. Worst case time complexity O(n Algorithms based on kernel grammars (a CFG) parse the input twice. In the second step, TAGincompatible derivations are eliminated from the context-free parse forest. Worst case time complexity O(n ). Several other parsing algorithms exist. ). Department of Computer Science, University of Helsinki Page 19
20 Tree Adjoining Grammars Today... Project work topics introduction and selection. Presentation schedule. Delivery of exercises for next week. Department of Computer Science, University of Helsinki Page 20
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