1. FMZ Elaborazione del linguaggio naturale Fabio Massimo Zanzotto

2. FMZ Part six Tree Adjoining Grammars

3. FMZ Our Aim Lines of development Grammatical Representation Power: Build a formalism/model able to give the possibility of reducing the unnecessary interpretations Grammar Use: Build a formalism (and an associated algorithm) able to represent partial analysis

4. FMZ Our Aim Lines of development Grammatical Representation Power: CFG (context free grammars) DCG Feature Structures Grammar Use: CYK Chart and Early Algorithm

5. FMZ Lesson learnt Lexicon (i.e. words) is a very important piece of the Language and of the language model Words carry meaning and govern the syntactic structure of sentences

6. FMZ What we observed Toy Examples:... La vecchia porta la sbarra...... Il vecchio porta la sbarra...... Flying planes can be dangerous...... Flying planes is dangerous...

7. FMZ Continuing the observation of the languages Some more toy examples:... Il ragazzo mangia la mela con il coltello...... Luomo guarda il monitor con gli occhi stralunati...... Le azioni della acme inc aumentano in tre settimane da 2 euro a 3 euro... How many interpretations are possible for these sentences?

8. FMZ Subcategorisation frames Necessary subcategorisation frames:... Il ragazzo mangia la mela con il coltello... ((NP) mangiare (NP) (PP(con)))... Luomo opera il paziente di appendicite... ((NP) operare (NP) (PP(di)))... Le azioni della acme inc aumentano in tre settimane da 2 euri a 3 euro... ((NP) aumentare (PP(da)) (PP(a)))

9. FMZ Modelling Subcat Frames in CFGs Target Frame: ((NP) mangiare (NP) (PP(con))) S NP VP | NP VP(mangiare) NP NP SBAR VP VerbX NP | VerbX NP PP VerbX Verb | Modal Verb VP(mangiare) VerbX(mangiare) NP | VerbX (mangiare) NP PP(con) VerbX(mangiare) Verb(mangiare) | Modal Verb(mangiare) NP Art Noun | Art Adj Noun | Noun | Verb Noun | NP PP PP Prep NP

10. FMZ Observations Il ragazzo mangia la mela a mezzogiorno con il coltello How do we modify those(?): VP(mangiare) VerbX(mangiare) NP | VerbX (mangiare) NP PP(con) VerbX(mangiare) Verb(mangiare) | Modal Verb(mangiare)

11. FMZ Summing up We understood that subcategorisation can indicate preferred sentence readings We want to build lexicalised rules, that is, rules governed by lexical elements (words) We want to empower the grammar

12. FMZ Idea!!! Lexicalised rules may be partial tree! ((NP) aumentare (PP(da)) (PP(a))) aumentare V VP S NP PP IN daa NP

13. FMZ Defining better our aim We want a lexicalised grammar –each rule (partial tree) has to at least a lexical item We want a grammar equivalent to the a given grammar –weak equivalence: equivalence in the language recognised –strong equivalence: equivalence in generated trees with respect to input sentences... remember that the structure define the meaning

14. FMZ Operations in CFG in the derivation, no terminal symbols are substituted with rewriting rules headed by the same symbol may be understood as tree substitution no terminal symbols are substituted with trees headed by the same symbol is it sufficient to obtain the strong equivalence?

15. FMZ Investigating strong equivalence Given the grammar and the sequence aaaa, one of the interpretations is:

16. FMZ Lets build the lexicalised grammar Given the tree collection the interpretation cannot be obtained!

17. FMZ Another example Given the grammar it can be lexicalised as follows: strange rule!!!

18. FMZ Another example The same grammar may be lexicalised also however, what about this

19. FMZ Tree Adjoining Grammars

20. FMZ What do we need? A new operation!!! the Tree Adjoining operation

21. FMZ Tree Adjoining Example

22. FMZ Again the substitution The well know operation

23. FMZ Substitution example

24. FMZ Tree Adjoining again Does it solve the problem of obtaining the strong equivalence? This is the solution to the example problem!!!

25. FMZ Tree Adjoining again successive adjoining of ( 4 )

26. FMZ More examples may give the interpretation:

27. FMZ What is a grammar now? It is a collection of: initial trees, represent the lexicon, e.g., auxiliary trees, represent grammatical rules, e.g.,

28. FMZ Do you remember? copy-language structures: Pino, Gino e Rino sono rispettivamente fratello, zio e babbo di Nino may be read as: a 1 a 2 a 3 b 1 b 2 b 3 Exercise: Find a model in TAG for this problem

29. FMZ What we have done? we have worked on the representation power of the grammar we introduced: –lexicalised rules –the adjoining operation where do we pay? –on the parsing algorithm?

30. FMZ Question Have we resolved the problem of selecting between different readings (sentence interpretations)?