LING 200 Lecture Notes - Lecture 14: Downward Entailing

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blueherring748

23 Jun 2018

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C-command def:

X commands Y just in case X does not dominate Y, but every node that dominates X dominates

Dominate def:

A node X dominated Y if you can draw a line going from X to Y always going down

-Tree example:

A dominated all other nodes

B dominated C, D, E, F

M dominates N, K, L, G, I, H, J

N dominates G, I, H, J

G dominates H

A c-commands NOTHING

B c-commands M and what M dominates (N, K, L, G, I, H, J)

C c-commands D, F

N c-commands K, L

K c-commands N and what N dominates (N, G, I, H, J)

Hypothesis 5: An anaphor must be c-commanded by a co-indeed DP in its minimal clause (S)

The DP [ a friend of Emma’s ] c-commands DP [herself]

DP [Emma’s] does not c-command the DP [herself]

There is at least one node (E.g. PP) that dominates [Emma] but not the anaphor

DP [Emma’s friend] c-commands DP [herself]

*Subjects are great antecedents

DP [Emma’s] does not c-command the DP [herself]

-Binding

We call a DP that is c-commanded by a co-indexed DP “bound”

Binding def:

X binds Y just in case X and Y are co-indexed and

X c-commands Y

Condition on anaphors

Binding condition A:

An anaphor must be bound in its minimal clause (smallest S)

Three things must be satisfied:

Is there a co-indexed DP (an antecedent?)

Does this co-indexed DP c-command the anaphor? (binding?)

Is binder contained in same minimal S node as anaphor ? (locality?)

We call a DP that is c-command by a co-indexed DP “bound”

Binding def:

X binds Y just in case X and Y are co-indexed and X c-commands Y

Condition on anaphors:

Binding condition A-

An anaphor must be bound in it’s minimal clause

(1) *Herself went to Madrid —> no antecedent

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Document Summary

X commands y just in case x does not dominate y, but every node that dominates x dominates. A node x dominated y if you can draw a line going from x to y always going down. M dominates n, k, l, g, i, h, j. B c-commands m and what m dominates (n, k, l, g, i, h, j) K c-commands n and what n dominates (n, g, i, h, j) Hypothesis 5: an anaphor must be c-commanded by a co-indeed dp in its minimal clause (s) The dp [ a friend of emma"s ] c-commands dp [herself] Pp) that dominates [emma] but not the anaphor. Dp [emma"s] does not c-command the dp [herself] We call a dp that is c-commanded by a co-indexed dp bound . X binds y just in case x and y are co-indexed and. An anaphor must be bound in its minimal clause (smallest s) Does this co-indexed dp c-command the anaphor? (binding?)

Related Questions

1.Write a function encipher(s, n) that takes as inputs an arbitrary string s and a non-negative integer n between 0 and 25, and that returns a new string in which the letters in s have been "rotated" by n characters forward in the alphabet, wrapping around as needed. For example:

>>> encipher('hello', 1) result: 'ifmmp'

>>> encipher('hello', 2) result: 'jgnnq'

>>> encipher('hello', 4) result: 'lipps'

Upper-case letters should be "rotated" to upper-case letters, even if you need to wrap around. For example:

>>> encipher('XYZ', 3)

result: 'ABC'

Lower-case letters should be "rotated" to lower-case letters:

>>> encipher('xyz', 3)

result: 'abc'

Non-alphabetic characters should be left unchanged:

>>> encipher('#caesar!', 2)

result: '#ecguct!'

Hints/reminders:

You can use the built-in functions ord and chr convert from single-character strings to integers and back:

>>> ord('a')

result: 97

>>> chr(97)

result: 'a'

You can use the following test to determine if a character is between 'a' and 'z' in the alphabet:

if 'a' <= c <= 'z':

A similar test will work for upper-case letters.

We recommend writing a helper function rot(c, n) that rotates a single character c forward by n spots in the alphabet. We have given you a template for this helper function in ps3pr3.py that checks to ensure that c is a single-character string. We wrote rot13(c) in lecture; rot(c, n) will be very close to rot13(c)! You can test your rot(c, n) as follows:

>>> rot('a', 1)

result: 'b'

>>> rot('y', 2)

result: 'a'

>>> rot('A', 3)

result: 'D'

>>> rot('Y', 3)

result: 'B'

>>> rot('!', 4)

result: '!'

Once you have rot(c, n), you can write a recursive encipher function.

Once you think you have everything working, here are three more examples to try:

>>> encipher('xyza', 1)

result: 'yzab'

>>> encipher('Z A', 2)

result: 'B C'

>>> encipher('Caesar cipher? I prefer Caesar salad.', 25)

result: 'Bzdrzq bhogdq? H oqdedq Bzdrzq rzkzc.'

2.Write a function decipher(s) that takes as input an arbitrary string s that has already been enciphered by having its characters "rotated" by some amount (possibly 0). decipher should return, to the best of its ability, the original English string, which will be some rotation (possibly 0) of the input string s. For example:

>>> decipher('Bzdrzq bhogdq? H oqdedq Bzdrzq rzkzc.')

result: 'Caesar cipher? I prefer Caesar salad.'

Here are two more examples:

>>> decipher('Hu lkbjhapvu pz doha ylthpuz hmaly dl mvynla lclyfaopun dl ohcl slhyulk.')

result: 'An education is what remains after we forget everything we have learned.'

>>> decipher('python')

result: 'eniwdc'

------------------------------------

def rot(c, n):
""" your docstring goes here """
# check to ensure that c is a single character
assert(type(c) == str and len(c) == 1)

def letter_prob(c):
""" if c is the space character (' ') or an alphabetic character,
returns c's monogram probability (for English);
returns 1.0 for any other character.
adapted from:

"""
# check to ensure that c is a single character
assert(type(c) == str and len(c) == 1)

if c == ' ': return 0.1904
if c == 'e' or c == 'E': return 0.1017
if c == 't' or c == 'T': return 0.0737
if c == 'a' or c == 'A': return 0.0661
if c == 'o' or c == 'O': return 0.0610
if c == 'i' or c == 'I': return 0.0562
if c == 'n' or c == 'N': return 0.0557
if c == 'h' or c == 'H': return 0.0542
if c == 's' or c == 'S': return 0.0508
if c == 'r' or c == 'R': return 0.0458
if c == 'd' or c == 'D': return 0.0369
if c == 'l' or c == 'L': return 0.0325
if c == 'u' or c == 'U': return 0.0228
if c == 'm' or c == 'M': return 0.0205
if c == 'c' or c == 'C': return 0.0192
if c == 'w' or c == 'W': return 0.0190
if c == 'f' or c == 'F': return 0.0175
if c == 'y' or c == 'Y': return 0.0165
if c == 'g' or c == 'G': return 0.0161
if c == 'p' or c == 'P': return 0.0131
if c == 'b' or c == 'B': return 0.0115
if c == 'v' or c == 'V': return 0.0088
if c == 'k' or c == 'K': return 0.0066
if c == 'x' or c == 'X': return 0.0014
if c == 'j' or c == 'J': return 0.0008
if c == 'q' or c == 'Q': return 0.0008
if c == 'z' or c == 'Z': return 0.0005
return 1.0

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LING 200 Lecture Notes - Lecture 14: Downward Entailing

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