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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