Andrew Carnie, Structural Relations. The mathematical properties of phrase structure trees

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1 Structural Relations The mathematical properties of phrase structure trees

2 Important!

3 Important! Even if you have trouble with the formal definitions, try to understand the INTUITIVE idea behind them. Don t get lost in the details of the formalism.

4 Structural Relations Structural relations: the formal relationships between items of a tree Why should we care? We want to be able to talk about specific relationships in terms of structures. Structural relations are actually very simple! Don t let the formalism scare you!

5 Some basic terms M N O D E F G H J

6 Some basic terms M Branches N O D E F G H J

7 Some basic terms M Branches N O D E F G H J Labels: M,N,O,D,E,F,G,H,J

8 Some basic terms Branches M N O D E F G H J Labels: M,N,O,D,E,F,G,H,J Node: Any point with a label Andrew Carnie, 2006

9 Some basic terms M Root node Branches N O D E F G H J Labels: M,N,O,D,E,F,G,H,J Node: Any point with a label Andrew Carnie, 2006

10 Some basic terms M Root node Branches N O Non-terminal nodes D E F G H J Labels: M,N,O,D,E,F,G,H,J Node: Any point with a label Andrew Carnie, 2006

11 Some basic terms M Root node Branches N O Non-terminal nodes D E F G H J Labels: M,N,O,D,E,F,G,H,J Node: Any point with a label Terminal nodes Andrew Carnie, 2006

12 Domination

13 Domination Intuitively: this is containment. If a node contains another, then it dominates it:

14 Domination Intuitively: this is containment. If a node contains another, then it dominates it: A B C D E F G

15 Domination Intuitively: this is containment. If a node contains another, then it dominates it: A dominates B,C,D,E,F,G A B C D D dominates E,F,G E F G

16 Domination Intuitively: this is containment. If a node contains another, then it dominates it: A dominates B,C,D,E,F,G A [ A B C [ D E F G]] contained inside [ A ] B C D D dominates E,F,G E F G

17 Domination Intuitively: this is containment. If a node contains another, then it dominates it: A dominates B,C,D,E,F,G A [ A B C [ D E F G]] contained inside [ A ] B C D D dominates E,F,G E F G Another way to think of it: on top of Andrew Carnie, 2006

18 Domination

19 Domination A slightly more formal definition: Domination: Node A dominates node B if and only if A is higher up in the tree than B and if you can trace a line from A to B going only downwards.

20 Immediate Domination

21 Immediate Domination Node A immediately dominates node B if there is no intervening node G which is dominated by A, but dominates B. (in other words, A is the first node that dominates B)

22 Immediate Domination Node A immediately dominates node B if there is no intervening node G which is dominated by A, but dominates B. (in other words, A is the first node that dominates B) A B C D E F G

23 Immediate Domination Node A immediately dominates node B if there is no intervening node G which is dominated by A, but dominates B. (in other words, A is the first node that dominates B) A B C D Andrew Carnie, 2006 A dominates B,C,D,E,F,G but A immediately dominates only B,C,D E F G

24 Exhaustive Domination Node A exhaustively dominates a SET of TERMINAL nodes {B,C,,D}, provided it dominates all the members of the set (so that there is no member of the set that is not dominated by A) AND there is no terminal node G dominated by A that is not a member of the set.

25 Exhaustive Domination F A G B C D E H I

26 Exhaustive Domination F A G B C D E H I A exhaustively dominates the set {B,C,D,E}

27 Exhaustive Domination F A G B C D E H I A exhaustively dominates the set {B,C,D,E} A does NOT exhaustively dominate the set {B,C,D}

28 Exhaustive Domination F A G B C D E H I A exhaustively dominates the set {B,C,D,E} A does NOT exhaustively dominate the set {B,C,D} A does NOT exhaustively dominate the set {B,C,D,E,H}

29 A formal definition of constituency Andrew Carnie, 2006

30 A formal definition of constituency Constituent: The set of nodes exhaustively dominated by a single node

31 A formal definition of constituency Constituent: The set of nodes exhaustively dominated by a single node F A G B C D E H I

32 A formal definition of constituency Constituent: The set of nodes exhaustively dominated by a single node F A G B C D E H I

33 A formal definition of constituency Constituent: The set of nodes exhaustively dominated by a single node F A G B C D E H I

34 A formal definition of constituency Constituent: The set of nodes exhaustively dominated by a single node F A G B C D E H I

35 A formal definition of constituency Constituent: The set of nodes exhaustively dominated by a single node A F G {E, H} are NOT a constituent B C D E H I

36 Constituent vs Constituent of

37 Constituent vs Constituent of Constituent of does NOT mean the same thing as constituent.

38 Constituent vs Constituent of Constituent of does NOT mean the same thing as constituent. Essentially constituent of is the opposite of domination.

39 Constituent vs Constituent of Constituent of does NOT mean the same thing as constituent. Essentially constituent of is the opposite of domination. A dominates B, then we say B is a constituent of A.

40 Constituent vs Constituent of Constituent of does NOT mean the same thing as constituent. Essentially constituent of is the opposite of domination. A dominates B, then we say B is a constituent of A. immediate constituent of is the opposite of immediate domination.

41 Some Informal Terms

42 Some Informal Terms Mother: the node that immediately dominates another.

43 Some Informal Terms Mother: the node that immediately dominates another. Daughter: the node that is immediately dominated by another (is an immediate constituent of another).

44 Some Informal Terms Mother: the node that immediately dominates another. Daughter: the node that is immediately dominated by another (is an immediate constituent of another). Sisters: two nodes that share the same mother.

45 Root and Terminal Nodes

46 Root and Terminal Nodes Root node: A node with no mother

47 Root and Terminal Nodes Root node: A node with no mother Terminal node: A node with no daughters

48 Root and Terminal Nodes Root node: A node with no mother Terminal node: A node with no daughters TP VP Andrew Carnie, 2006 D N V the platypus laughed

49 Root and Terminal Nodes Root node: A node with no mother Terminal node: A node with no daughters TP Root Node VP Andrew Carnie, 2006 D N V the platypus laughed

50 Root and Terminal Nodes Root node: A node with no mother Terminal node: A node with no daughters TP Root Node VP Andrew Carnie, 2006 D N V the platypus laughed Terminal Nodes

51 Precedence

52 Precedence Precedence: Node A precedes node B if A is to the left of B. (informal definition)

53 Precedence Precedence: Node A precedes node B if A is to the left of B. (informal definition) But this runs into problems with trees which are badly drawn

54 Precedence excludes domination Andrew Carnie, 2006

55 Precedence excludes domination Note that if two nodes are in a domination relation they cannot be in a precedence relation

56 Precedence excludes domination Note that if two nodes are in a domination relation they cannot be in a precedence relation

57 Precedence excludes domination Note that if two nodes are in a domination relation they cannot be in a precedence relation Is the ball to the left or right of the box?

58 Precedence excludes domination Note that if two nodes are in a domination relation they cannot be in a precedence relation Is the ball to the left or right of the box? Neither! You can t precede or follow something that dominates (contains) you or you dominate (contain).

59 Precedence

60 Precedence Consider this poorly drawn tree

61 Precedence Consider this poorly drawn tree TP VP D the V kissed N clown D the N donkey

62 Precedence Consider this poorly drawn tree TP VP Does kiss precede clown? Obviously not! D the V kissed N clown D the N donkey

63 Precedence Consider this poorly drawn tree TP VP Does kiss precede clown? Obviously not! D the V kissed N clown D the N donkey What is crucial here is that the dominator of clown precedes the dominator of kissed

64 Sister-Precedence In order to define precedence we re going to need a more local relation that refers to dominance. This is sister-precedence: A sister-precedes B if and only if A and B are immediately dominated by the same node A appears to the left of B

65 Sister-Precedence TP VP D N V the man left

66 Sister-Precedence TP VP sister-precedes VP D N V the man left

67 Sister-Precedence TP VP sister-precedes VP D sister precedes N D N V the man left

68 Sister-Precedence TP VP sister-precedes VP D sister precedes N D N V the man left N does NOT sister precede V (nor does D)

69 Precedence A Precedes B if and only iff A does not dominate B and B does not dominate A AND Either: A sister-precedes B OR There is some node E that dominates A, and some node F that dominates B, and E sister-precedes F.

70 Sister-Precedence Immediate Precedence TP VP D N V the man left But N does immediately precede V

71 Sister-Precedence Immediate Precedence TP VP D N V the man left N does NOT sister-precede V But N does immediately precede V

72 No Crossing Branches Constraint If one node X precedes another node Y then X and all nodes dominated by X must precede Y and all nodes dominated by Y. M N O P R Q S

73 No Crossing Branches Constraint If one node X precedes another node Y then X and all nodes dominated by X must precede Y and all nodes dominated by Y. M N O P R Q S

74 Immediate Precedence Immediate Precedence: A immediately precedes B if there is no node G which follows A but precedes B.

75 Immediate Precedence Immediate Precedence: A immediately precedes B if there is no node G which follows A but precedes B. A B G

76 Immediate Precedence Immediate Precedence: A immediately precedes B if there is no node G which follows A but precedes B. A B G A G B

77 Sister-Precedence Immediate Precedence TP VP D N V the man left But N does immediately precede V

78 Sister-Precedence Immediate Precedence TP VP D N V the man left N does NOT sister-precede V But N does immediately precede V

79 C-command

80 C-command Intuitively: The relationship between a node and its sister, and all the daughters of its sister

81 C-command Intuitively: The relationship between a node and its sister, and all the daughters of its sister M A C D E F G H

82 C-command Intuitively: The relationship between a node and its sister, and all the daughters of its sister A M C A c-commands C,D,E,F,G,H D E F G H

83 C-command Intuitively: The relationship between a node and its sister, and all the daughters of its sister A M C A c-commands C,D,E,F,G,H D E F Note: D does NOT c command A Andrew Carnie, 2006 G H

84 C-command Node A c-commands node B if every node dominating A also dominates B, and A does not itself dominate B.

85 C-command Node A c-commands node B if every node dominating A also dominates B, and A does not itself dominate B. Sisterhood

86 C-command Node A c-commands node B if every node dominating A also dominates B, and A does not itself dominate B. Sisterhood you can t command something you dominate

87 Symmetric C-command

88 Symmetric C-command A symmetrically c-commands B, if A c-commands B AND B c- commands A

89 Symmetric C-command A symmetrically c-commands B, if A c-commands B AND B c- commands A SAME THING AS SISTERHOOD

90 Symmetric C-command A symmetrically c-commands B, if A c-commands B AND B c- commands A SAME THING AS SISTERHOOD M A B D E F G H

91 Symmetric C-command A symmetrically c-commands B, if A c-commands B AND B c- commands A A SAME THING AS SISTERHOOD M A & B symmetrically c-command one another B D E F G H

92 Symmetric C-command A symmetrically c-commands B, if A c-commands B AND B c- commands A A SAME THING AS SISTERHOOD M A & B symmetrically c-command one another B D E F G H

93 Symmetric C-command A symmetrically c-commands B, if A c-commands B AND B c- commands A A SAME THING AS SISTERHOOD M A & B symmetrically c-command one another B A does NOT symmetrically c-command D D E F G H

94 Asymmetric C-command A asymmetrically c-commands B, if A c-commands B but B does NOT c-command A. (intuitively -- A is B s aunt)

95 Asymmetric C-command A asymmetrically c-commands B, if A c-commands B but B does NOT c-command A. (intuitively -- A is B s aunt) M A C B E F G H

96 Asymmetric C-command A asymmetrically c-commands B, if A c-commands B but B does NOT c-command A. (intuitively -- A is B s aunt) M A C B E F G H

97 Grammatical Relations Subject: /CP daughter of TP Object of a Preposition: daughter of PP Direct Object: With verbs of type V[ ], V[ CP] and V[ PP], the or CP daughter of VP With verbs of type V[ {/CP}], an or CP daughter of VP that is preceded by another daughter of VP. (i.e., the second daughter of VP)

98 Grammatical Relations Indirect Object: This is the 1st object indicating the goal of a verb of transfer (a ditransitive) or the PP of the same kind of verb: With verbs of type V[ PP], the PP daughter of VP immediately preceded by an daughter of VP. With verbs of type V[ {/CP}], the daughter of VP immediately preceded by V (i.e. the first daughter of VP) Oblique: any other /PP in the sentence.

99 Grammatical Relations

100 Grammatical Relations TP VP N V N

101 Grammatical Relations TP Subject VP N V N

102 Grammatical Relations TP Subject VP N V Object N

103 Grammatical Relations TP Subject VP N V Object N PP P N

104 Grammatical Relations TP Subject VP N V Object N PP P Object of a Preposition N

105 Grammatical Relations

106 Grammatical Relations Andrew Carnie, 2006 I gave Adam the book

107 Grammatical Relations TP VP N V N N Andrew Carnie, 2006 I gave Adam the book

108 Grammatical Relations TP VP N V N N Direct Object Andrew Carnie, 2006 I gave Adam the book

109 Grammatical Relations TP VP N V N N Indirect Object Direct Object Andrew Carnie, 2006 I gave Adam the book

110 Grammatical Relations TP VP N V N N Indirect Object Direct Object Andrew Carnie, 2006 I gave Adam the book I gave the book to Adam

111 Grammatical Relations TP TP VP VP N V N V PP N N N P Indirect Object Direct Object N Andrew Carnie, 2006 I gave Adam the book I gave the book to Adam

112 Grammatical Relations TP TP VP VP N V N V PP N N N P Indirect Object Direct Object Direct Object N Andrew Carnie, 2006 I gave Adam the book I gave the book to Adam

113 Grammatical Relations TP TP VP VP N V N V PP N N N P Indirect Object Direct Object Direct Object N Indirect Object Andrew Carnie, 2006 I gave Adam the book I gave the book to Adam

114 Summary Structural Relations: relationships between nodes. Dominance (=containment) immediate dominance (=motherhood) exhaustive dominance (=constituent) Precedence ( to the left) immediate precedence (=adjacent & to the left)

115 Summary C-command: sisters & nieces Symmetric C-command: sisters Asymmetric C-command: Aunt asymmetrically c-commands nieces Grammatical Relations: Subject, Direct Object, Indirect Object, Object of a Preposition.

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