A high-level approach to language description

Transcription

1 A high-level approach to language description Lionel Clément and Jérôme Kirman and Sylvain Salvati Université de Bordeaux - LaBRI INRIA Polymnie meeting 12 Mars 2014

2 Context and motivation Linguistic formalization Formal grammars

3 Context and motivation LFG HPSG Linguistic formalization Formal grammars

4 Context and motivation LFG HPSG Linguistic formalization Metagrammars Formal grammars

5 Context and motivation LFG HPSG Linguistic formalization Metagrammars Formal grammars Language

6 Context and motivation LFG HPSG Linguistic formalization Metagrammars Formal grammars Language

7 Goals on both ends Linguistic formalization High-level description of natural languages

8 Goals on both ends Linguistic formalization High-level description of natural languages Highly modular

9 Goals on both ends Linguistic formalization High-level description of natural languages Highly modular Close in spirit to meta-grammars

10 Goals on both ends Linguistic formalization High-level description of natural languages Highly modular Close in spirit to meta-grammars Target class of languages Mildly Context Sensitive Languages

11 Goals on both ends Linguistic formalization High-level description of natural languages Highly modular Close in spirit to meta-grammars Target class of languages Mildly Context Sensitive Languages Polynomial parsability

12 Working hypotheses Abstract Categorial Grammar: Abstract language (syntactic structure) Object language (word order)

13 Working hypotheses Abstract Categorial Grammar: Abstract language (syntactic structure) Object language (word order) Abstract structure = tree (hierarchy of syntactic components)

14 Working hypotheses Abstract Categorial Grammar: Abstract language (syntactic structure) Object language (word order) Abstract structure = tree (hierarchy of syntactic components) Description language = logic on trees (MTS)

15 Working hypotheses Abstract Categorial Grammar: Abstract language (syntactic structure) Object language (word order) Abstract structure = tree (hierarchy of syntactic components) Description language = logic on trees (MTS) Validity of an abstract structure conjunction of logical constraints Non-local phenomena logical long-distance relations Also helps defining the linearization

16 Working hypotheses Abstract Categorial Grammar: Abstract language (syntactic structure) Object language (word order) Abstract structure = tree (hierarchy of syntactic components) Description language = logic on trees (MTS) Validity of an abstract structure conjunction of logical constraints Non-local phenomena logical long-distance relations Also helps defining the linearization Linearization: mapping from abstract to surface structures = linear composition of lexical entries

17 Existing tools and results Base tools Logic (MSO or weaker on trees) λ-calculus (simply-typed, linear)

18 Existing tools and results Base tools Logic (MSO or weaker on trees) λ-calculus (simply-typed, linear) J. E. Doner. (MSOkS = FSTA) Decidability of the weak second-order theory of two successors. Notices Amer. Math. Soc., 12: , 1965.

19 Existing tools and results Base tools Logic (MSO or weaker on trees) λ-calculus (simply-typed, linear) J. E. Doner. (MSOkS = FSTA) Decidability of the weak second-order theory of two successors. Notices Amer. Math. Soc., 12: , B. Courcelle and J. Engelfriet. (HR are closed by MSO transductions) A logical characterization of the sets of hypergraphs defined by hyperedge replacement grammars. Mathematical Systems Theory, 28(6): , S. Salvati. (HR T 2 ACG lin T ) Encoding second order string acg with deterministic tree walking transducers. In S. Wintner, editor, Proceedings FG 2006: the 11th conference on Formal Grammars, FG Online Proceedings, pages CSLI Publications, 2007.

20 Example grammar Construct a simple grammar for French, that covers: Simple SVO structure Valency and ect-verb agreement

21 Example grammar Construct a simple grammar for French, that covers: Simple SVO structure Valency and ect-verb agreement Describe the semantics of the formalization as we go

22 Example grammar Construct a simple grammar for French, that covers: Simple SVO structure Valency and ect-verb agreement Describe the semantics of the formalization as we go Enrich the grammar to include Relative clauses as modifiers Complement clauses (for long distance wh-movement) Island constraints

23 Abstract structures Abstract language = set of abstract structure trees Trees have: Unlabelled internal nodes Labelled edges (bounded arity) Leaves are lexical entries or

24 Abstract structures Abstract language = set of abstract structure trees Trees have: Unlabelled internal nodes Labelled edges (bounded arity) Leaves are lexical entries or An abstract structure pensent voyageurs obj compl lit Paul journal Des voyageurs pensent que Paul lit le journal. obj

25 Lexical entries Lexical entries decorate leaves in the abstract structure tree Each entry has a set of associated properties (from a finite set)

26 Lexical entries Lexical entries decorate leaves in the abstract structure tree Each entry has a set of associated properties (from a finite set) A lexicon Entry le journal des voyageurs Paul lit lisent marche Properties noun, def, masculine, singular noun, indef, masculine, plural proper noun, masculine, singular verb, transitive, intransitive, singular, 3rd pers verb, transitive, intransitive, plural, 3rd pers verb, intransitive, singular, 3rd pers

27 Regular backbone Definition of abstract structures by a regular tree grammar (over-approximation)

28 Regular backbone Definition of abstract structures by a regular tree grammar (over-approximation) A simple over-approximation RTG C obj A noun proper noun verb A (A) Terminals are POS properties (any lexical entry with the right POS tag) Some arguments may be optional (between parentheses): (T ) T

29 Logical vocabulary (1/2) Variables (x, y, z,... ): positions in the tree

30 Logical vocabulary (1/2) Variables (x, y, z,... ): positions in the tree Predicates and relations: prop(x) := x is a lexical entry that has the property prop

31 Logical vocabulary (1/2) Variables (x, y, z,... ): positions in the tree Predicates and relations: prop(x) := x is a lexical entry that has the property prop none(x) := x = ; some(x) := none(x)

32 Logical vocabulary (1/2) Variables (x, y, z,... ): positions in the tree Predicates and relations: prop(x) := x is a lexical entry that has the property prop none(x) := x = ; some(x) := none(x) lbl(x, y) := x immediately dominates y by an arc labelled with lbl

33 Logical vocabulary (1/2) Variables (x, y, z,... ): positions in the tree Predicates and relations: prop(x) := x is a lexical entry that has the property prop none(x) := x = ; some(x) := none(x) lbl(x, y) := x immediately dominates y by an arc labelled with lbl regex(x, y) := x dominates y by a series of arcs l 1... l n L(regex) (with regex := ε lbl 1.lbl 2 lbl 1 + lbl 2 lbl )

34 Logical vocabulary (1/2) Variables (x, y, z,... ): positions in the tree Predicates and relations: prop(x) := x is a lexical entry that has the property prop none(x) := x = ; some(x) := none(x) lbl(x, y) := x immediately dominates y by an arc labelled with lbl regex(x, y) := x dominates y by a series of arcs l 1... l n L(regex) (with regex := ε lbl 1.lbl 2 lbl 1 + lbl 2 lbl ) Used to restrict the set of valid abstract structures: Sub-categorization, selection restrictions, etc. Regexps allow long-distance constraints

35 Logical vocabulary (2/2) Linguistic formalization by building additional predicates and relations

36 Logical vocabulary (2/2) Linguistic formalization by building additional predicates and relations Agreement relations numb agr(x, y) := singular(x) singular(y) plural(x) plural(y) gend agr(x, y) := masculine(x) masculine(y) feminine(x) feminine(y) third pers(x) := 3rd pers(x) (1st pers(x) 2nd pers(x)) pers agr(x, y) := 1st pers(x) 1st pers(y) 2nd pers(x) 2nd pers(y) third pers(x) third pers(y)

37 Logical vocabulary (2/2) Linguistic formalization by building additional predicates and relations Agreement relations numb agr(x, y) := singular(x) singular(y) plural(x) plural(y) gend agr(x, y) := masculine(x) masculine(y) feminine(x) feminine(y) third pers(x) := 3rd pers(x) (1st pers(x) 2nd pers(x)) pers agr(x, y) := 1st pers(x) 1st pers(y) 2nd pers(x) 2nd pers(y) third pers(x) third pers(y) Subject-verb agreement relation sv agr(x, y) := numb agr(x, y) pers agr(x, y)

38 Constraints on validity Valid abstract structures must satisfy additional constraints on the RTG

39 Constraints on validity Valid abstract structures must satisfy additional constraints on the RTG Constraints are logical formulas tied to the RHS of productions

40 Constraints on validity Valid abstract structures must satisfy additional constraints on the RTG Constraints are logical formulas tied to the RHS of productions Enforcing ect-verb agreement and valency C verb : v A : s obj (A) : o some(o) transitive(v) none(o) intransitive(v) sv agr(s, v)

41 Constraints on validity Valid abstract structures must satisfy additional constraints on the RTG Constraints are logical formulas tied to the RHS of productions Enforcing ect-verb agreement and valency C verb : v A : s obj (A) : o some(o) transitive(v) none(o) intransitive(v) sv agr(s, v) Filtered structures marche Paul obj journal marche voyageurs lit Paul

42 Constraints on validity Valid abstract structures must satisfy additional constraints on the RTG Constraints are logical formulas tied to the RHS of productions Enforcing ect-verb agreement and valency C verb : v A : s obj (A) : o some(o) transitive(v) none(o) intransitive(v) sv agr(s, v) Filtered structures marche Paul obj journal marche voyageurs lit Paul some(o) transitive(v)

43 Constraints on validity Valid abstract structures must satisfy additional constraints on the RTG Constraints are logical formulas tied to the RHS of productions Enforcing ect-verb agreement and valency C verb : v A : s obj (A) : o some(o) transitive(v) none(o) intransitive(v) sv agr(s, v) Filtered structures marche Paul obj journal some(o) transitive(v) marche voyageurs plural(v) singular(s) lit Paul

44 Constraints on validity Valid abstract structures must satisfy additional constraints on the RTG Constraints are logical formulas tied to the RHS of productions Enforcing ect-verb agreement and valency C verb : v A : s obj (A) : o some(o) transitive(v) none(o) intransitive(v) sv agr(s, v) Filtered structures marche Paul obj journal marche voyageurs lit some(o) transitive(v) plural(v) singular(s) OK Paul

45 Linearization rules Like constraints, linearizations will be based on the RTG productions

46 Linearization rules Like constraints, linearizations will be based on the RTG productions The realization attached to the LHS will depend on : Logical conditions Realizations of other nodes (mostly RHS leaves)

47 Linearization rules Like constraints, linearizations will be based on the RTG productions The realization attached to the LHS will depend on : Logical conditions Realizations of other nodes (mostly RHS leaves) A linearization rule C : c obj verb : v A : s (A) : o [ some(o) s.v.o c := none(o) s.v

48 Linearization rules Like constraints, linearizations will be based on the RTG productions The realization attached to the LHS will depend on : Logical conditions Realizations of other nodes (mostly RHS leaves) A linearization rule C : c obj verb : v A : s (A) : o c := s.v.o (lin( ) := ε)

49 Adding relative clauses (1/3) We enrich the previous grammar to include relative clauses

50 Adding relative clauses (1/3) We enrich the previous grammar to include relative clauses Lexical entries for french relative pronouns Entry Properties qui pronoun, rel pro, masculine, feminine, singular, plural, 1st, 2nd, 3rd pers., nom que pronoun, rel pro, masculine, feminine, singular, plural, 1st, 2nd, 3rd pers., acc

51 Adding relative clauses (1/3) We enrich the previous grammar to include relative clauses Lexical entries for french relative pronouns Entry Properties qui pronoun, rel pro, masculine, feminine, singular, plural, 1st, 2nd, 3rd pers., nom que pronoun, rel pro, masculine, feminine, singular, plural, 1st, 2nd, 3rd pers., acc Logical vocabulary for wh-movement and agreement in relatives wh path(x, y) := (x, y) obj(x, y) ext(x) := rel pro(x) rel(r) := np.mod(np, r) v.verb(v) (r, v) ap agr(a, p) := pers agr(a, p) numb agr(a, p) gend agr(a, p)

52 Adding relative clauses (1/3) We enrich the previous grammar to include relative clauses Lexical entries for french relative pronouns Entry Properties qui pronoun, rel pro, masculine, feminine, singular, plural, 1st, 2nd, 3rd pers., nom que pronoun, rel pro, masculine, feminine, singular, plural, 1st, 2nd, 3rd pers., acc Logical vocabulary for wh-movement and agreement in relatives wh path(x, y) := (x, y) obj(x, y) ext(x) := rel pro(x) rel(r) := np.mod(np, r) v.verb(v) (r, v) ap agr(a, p) := pers agr(a, p) numb agr(a, p) gend agr(a, p) antecedent(a, p) := np, r. (np, a) mod(np, r) wh path(r, p)

53 Adding relative clauses (2/3) A : np A : np mod M : m A : a pronoun : p M : m C : r np := np.m a := p m := wh path(r, p) ext(p) p.r

54 Adding relative clauses (2/3) A : np A : np mod M : m A : a pronoun : p M : m C : r rel pro(np ) np := np.m a := p m := wh path(r, p) ext(p) p.r

55 Adding relative clauses (2/3) A : np A : np mod M : m A : a pronoun : p M : m C : r rel pro(np ) np := np.m a := p m := wh path(r, p) ext(p) p.r Filtered out sentences - [NP+MOD] (SUJ+VB+OBJ) *[la pomme ([qui (que regarde Paul)] tombe)]

56 Adding relative clauses (2/3) A : np A : np mod M : m A : a pronoun : p M : m C : r rel pro(np ) rel pro(p) r.rel(r) wh path(r, p) a.antecedent(a, p) ap agr(a, p) np := np.m a := p m := wh path(r, p) ext(p) p.r Filtered out sentences - [NP+MOD] (SUJ+VB+OBJ) *[la pomme ([qui (que regarde Paul)] tombe)]

57 Adding relative clauses (2/3) A : np A : np mod M : m A : a pronoun : p M : m C : r rel pro(np ) rel pro(p) r.rel(r) wh path(r, p) a.antecedent(a, p) ap agr(a, p) np := np.m a := p m := wh path(r, p) ext(p) p.r Filtered out sentences - [NP+MOD] (SUJ+VB+OBJ) *[la pomme ([qui (que regarde Paul)] tombe)] *(qui tombe)

58 Adding relative clauses (2/3) A : np A : np mod M : m A : a pronoun : p M : m C : r rel pro(np ) rel pro(p) r.rel(r) wh path(r, p) a.antecedent(a, p) ap agr(a, p) nom(p) x.(x, p) acc(p) x.obj(x, p) np := np.m a := p m := wh path(r, p) ext(p) p.r Filtered out sentences - [NP+MOD] (SUJ+VB+OBJ) *[la pomme ([qui (que regarde Paul)] tombe)] *(qui tombe)

59 Adding relative clauses (2/3) A : np A : np mod M : m A : a pronoun : p M : m C : r rel pro(np ) rel pro(p) r.rel(r) wh path(r, p) a.antecedent(a, p) ap agr(a, p) nom(p) x.(x, p) acc(p) x.obj(x, p) np := np.m a := p m := wh path(r, p) ext(p) p.r Filtered out sentences - [NP+MOD] (SUJ+VB+OBJ) *[la pomme ([qui (que regarde Paul)] tombe)] *(qui tombe) *[la pomme (que tombe)] ; *[la pomme (qui Paul regarde)]

60 Adding relative clauses (2/3) A : np A : np mod M : m A : a pronoun : p M : m C : r rel pro(np ) rel pro(p) r.rel(r) wh path(r, p) a.antecedent(a, p) ap agr(a, p)!p.wh path(r, p) rel pro(p) nom(p) x.(x, p) acc(p) x.obj(x, p) np := np.m a := p m := wh path(r, p) ext(p) p.r Filtered out sentences - [NP+MOD] (SUJ+VB+OBJ) *[la pomme ([qui (que regarde Paul)] tombe)] *(qui tombe) *[la pomme (que tombe)] ; *[la pomme (qui Paul regarde)]

61 Adding relative clauses (2/3) A : np A : np mod M : m A : a pronoun : p M : m C : r rel pro(np ) rel pro(p) r.rel(r) wh path(r, p) a.antecedent(a, p) ap agr(a, p)!p.wh path(r, p) rel pro(p) nom(p) x.(x, p) acc(p) x.obj(x, p) np := np.m a := p m := wh path(r, p) ext(p) p.r Filtered out sentences - [NP+MOD] (SUJ+VB+OBJ) *[la pomme ([qui (que regarde Paul)] tombe)] *(qui tombe) *[la pomme (que tombe)] ; *[la pomme (qui Paul regarde)] *[la pomme (Paul regarde Marie)] ; *[Paul (qui que regarde)]

62 Adding relative clauses (3/3) C : c obj M : m C : r verb : v A : s (A) : o ext(s) v.o c := ext(o) s.v else s.v.o m := wh path(r, p) ext(p) p.r

63 Adding relative clauses (3/3) C : c obj M : m C : r verb : v A : s (A) : o ext(s) v.o c := ext(o) s.v else s.v.o m := wh path(r, p) ext(p) p.r Wh- movement account journal lit mod Paul obj que

64 Adding relative clauses (3/3) C : c obj M : m C : r verb : v A : s (A) : o ext(s) v.o c := ext(o) s.v else s.v.o m := wh path(r, p) ext(p) p.r Wh- movement account journal lit mod Paul obj que M : x 0 C : x 1 lit A : x 2 Paul A : x 3 que

65 Adding relative clauses (3/3) C : c obj M : m C : r verb : v A : s (A) : o ext(s) v.o c := ext(o) s.v else s.v.o m := wh path(r, p) ext(p) p.r Wh- movement account journal lit mod Paul obj que M : x 0 C : x 1 lit A : x 2 Paul A : x 3 que x 2 = Paul x 3 = que

66 Adding relative clauses (3/3) C : c obj M : m C : r verb : v A : s (A) : o ext(s) v.o c := ext(o) s.v else s.v.o m := wh path(r, p) ext(p) p.r Wh- movement account journal lit mod Paul obj que M : x 0 C : x 1 lit A : x 2 Paul A : x 3 que x 1 = Paul.lit x 2 = Paul x 3 = que

67 Adding relative clauses (3/3) C : c obj M : m C : r verb : v A : s (A) : o ext(s) v.o c := ext(o) s.v else s.v.o m := wh path(r, p) ext(p) p.r Wh- movement account journal lit mod Paul obj que M : x 0 C : x 1 lit A : x 2 Paul A : x 3 que x 0 = que.paul lit x 1 = Paul.lit x 2 = Paul x 3 = que

68 Adding complement clauses (1/2) verb : v C : c A : s obj compl (A) : o (C) : c some(o) transitive(v) none(o) intransitive(v) sv agr(s, v) some(c ) compl cl(v) ext(s) v.o.cc [ c := some(c ext(o) s.v.cc where cc = ) que.c else ε else s.v.o.cc

69 Adding complement clauses (1/2) verb : v C : c A : s obj compl (A) : o (C) : c some(o) transitive(v) none(o) intransitive(v) sv agr(s, v) some(c ) compl cl(v) ext(s) v.o.cc [ c := some(c ext(o) s.v.cc where cc = ) que.c else ε else s.v.o.cc Addition to the lexicon Entry Properties dit verb, intransitive, compl cl, singular, 3rd pers disent verb, intransitive, compl cl, plural, 3rd pers

70 Adding complement clauses (2/2) Updated logical definition of wh path (Island constraints) wh path(x, y) := (x, y) compl obj(x, y)

71 Adding complement clauses (2/2) Updated logical definition of wh path (Island constraints) wh path(x, y) := (x, y) compl obj(x, y) Final linearization example journal dit mod Paul lisent compl voyageurs obj que

72 Adding complement clauses (2/2) Updated logical definition of wh path (Island constraints) wh path(x, y) := (x, y) compl obj(x, y) Final linearization example journal dit mod Paul lisent compl voyageurs obj dit A : x 2 que Paul M : x 0 C : x 1 C : x 3 lisent A : x 4 A : x 5 voyageurs que

73 Adding complement clauses (2/2) Updated logical definition of wh path (Island constraints) wh path(x, y) := (x, y) compl obj(x, y) Final linearization example journal dit mod Paul lisent compl voyageurs obj dit A : x 2 que Paul M : x 0 C : x 1 C : x 3 lisent A : x 4 A : x 5 voyageurs que x 4 = voyageurs x 5 = que

74 Adding complement clauses (2/2) Updated logical definition of wh path (Island constraints) wh path(x, y) := (x, y) compl obj(x, y) Final linearization example journal dit mod Paul lisent compl voyageurs obj dit A : x 2 que Paul M : x 0 C : x 1 C : x 3 lisent A : x 4 A : x 5 voyageurs que x 2 = Paul x 3 = des voyageurs.lisent x 4 = voyageurs x 5 = que

75 Adding complement clauses (2/2) Updated logical definition of wh path (Island constraints) wh path(x, y) := (x, y) compl obj(x, y) Final linearization example journal dit mod Paul lisent compl voyageurs obj dit A : x 2 que Paul M : x 0 C : x 1 C : x 3 lisent A : x 4 A : x 5 voyageurs que x 1 = Paul.dit.que.des voyageurs lisent x 2 = Paul x 3 = des voyageurs.lisent x 4 = voyageurs x 5 = que

76 Adding complement clauses (2/2) Updated logical definition of wh path (Island constraints) wh path(x, y) := (x, y) compl obj(x, y) Final linearization example journal dit mod Paul lisent compl voyageurs obj dit A : x 2 que Paul M : x 0 C : x 1 C : x 3 lisent A : x 4 A : x 5 voyageurs que x 0 = que.paul dit que des voyageurs lisent x 1 = Paul.dit.que.des voyageurs lisent x 2 = Paul x 3 = des voyageurs.lisent x 4 = voyageurs x 5 = que

77 Conclusion In summary, we have : Provided a logic-based toolset for linguistic description Demonstrated possible uses for it through a simple grammar Hinted at an effective procedure to compile the descriptions

78 Conclusion In summary, we have : Provided a logic-based toolset for linguistic description Demonstrated possible uses for it through a simple grammar Hinted at an effective procedure to compile the descriptions Possible directions : Work towards a usable implementation Improve mapping to language semantics Implement linguistic knowledge into larger grammars