CSE 472/572, Spring 2002

#### HW #8: KNOWLEDGE REPRESENTATION

1. R&N, Ch. 8, p. 262: #8.8
• This exercise concerns the representation of temporal information.

2. Translate each of the following sentences into the language of first-order predicate calculus. Be sure to give your syntax and semantics.

a) Mary gave Michael an ice-cream cone.

c) Robert cut down the tree with an axe.

d) All the ingredients are in a bowl and mixed thoroughly.

3. Here is the syntax and semantics for some generic SNePS case frames.

EnglishexamplelogicSNePS example
x is a YJohn is a computer scientist Y(x)
or:
x \epsilon Y
       M
/ \
/   \
member class
/       \
/         \
|           |
V           V
x           Y

        M
/ \
/   \
member class
/       \
/         \
|           |
V           V
John      computer
scientist
x is YJohn is rich Y(x)
       M
/ \
/   \
object property
/       \
/         \
|           |
V           V
x           Y
        M
/ \
/   \
object property
/       \
/         \
|           |
V           V
John        rich
x stands in the relation R to y John is taller than Ann R(x,y)
        M
/|\
/ | \
/  |  \
arg1 rel arg2
/    |    \
/     |     \
|      |      |
V      V      V
x      R      y
         M
/|\
/ | \
/  |  \
arg1 rel arg2
/    |    \
/     |     \
|      |      |
V      V      V
John  taller  Ann
than      
(This generalizes to:)R(t1,...,tn)
        M
/|\
/ | \
/  |  \
/   |   \
rel arg1..argn
/     |     \
/      |  ..  \
|       |       |
V       V       V
R       t1  ..  tn
All As are BsAll dogs are animals \forall x [A(x) => B(x)]
                  M
/| \
/ |  \
/  |   \
/   |    \
ant   |     cq
/     |      \
/      |       \
|     forall     |
V       |        V
P1       |       P2
/\       |       /\
/  \      |      /  \
/    \     |     /    \
class  member  |  member  class
/        \   |   /        \
/          \  |  /          \
/            \ | /            \
/              \|/              \
|                |                |
V                V                V
A                x                B
[dog]                       [animal]


Here's an extended example, with 2 corresponding, but slightly different, SNePS networks (one with default'' arc labels, as above, and one with more descriptive arc labels):

John bought a book from Mary

                M1----time--->past
/ \
/ | \
/ / \ \
/  | |  \
/  /   \  \
/   |   |   \
/   /     \   \
rel  arg1  arg2 arg3
/    /       \    \
/     |       |     \
/     /         \     \
/      |         |      \
/      /           \      \
|      |             |      |
V      V             V      V
^
|
|
member
|
|
M2---class--->book

                M2----time--->past
/ \
/ | \
/ / \ \
/  | |  \
/  /   \  \
/   |   |   \
/   /     \   \
act agent object from
/    /       \    \
/     |       |     \
/     /         \     \
/      |         |      \
/      /           \      \
|      |             |      |
V      V             V      V
^
|
|
member
|
|
M2---class--->book

Now, translate each of the sentences from the previous question into SNePS. Be sure to give your syntax and semantics.

 DUE: AT THE START OF LECTURE: WEDNESDAY, MAY 1