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Oct 19 In-Class Exercise Thread.

Please post your solutions to the Oct 19 In-Class Exercise to this thread.

Best, Chris

Please post your solutions to the Oct 19 In-Class Exercise to this thread. Best, Chris

-- Oct 19 In-Class Exercise Thread

There is not a pit in [1,1] ¬P1,1

There is not a breeze in [1,1] ¬B1,1

There is not a stench in [1,1] ¬S1,1

A square has a Wumpus iff there is a stench in the neighboring square. W1,2⇔(S1,1 and S2,2and S1,3)

There is not a Wumpus in [1,2] ¬W1,2

W2,1⇔(S1,1 and S2,2and S3,1)

There is not a Wumpus in [2,1] ¬W2,1

B1,1⇔(P1,2∨P2,1)

There is not a pit in [1,2] ¬P1,2

B2,1⇔(P1,1∨P2,2∨P3,1)

There is not a pit in [2,1] ¬P2,1

There is a breeze in [2,1] B2,1

There is not a stench in [2,1] ¬S2,1

There is not a wumpus in [2,2]

There is not a wumpus in [3,1]

There is a stench in [1,2] S1,2

There is not a breeze in [1,2] ¬B1,2

A square has a Wumpus iff there is a stench in the neighboring square. W1,3⇔(S1,2∨S2,3∨S1,4)

The Wumpus is not on square [2,2] ¬W2,2

The Wumpus is on square [1,3] W1,3

There is not a pit on square [2,2] ¬P2,2

A square is breezy iff there is a pit in a neighboring square. B2,1⇔(P1,1∨P2,2∨P3,1)

There is a pit on square [3,1] P3,1

(Edited: 2022-10-19)

There is not a pit in [1,1] ¬P1,1 There is not a breeze in [1,1] ¬B1,1 There is not a stench in [1,1] ¬S1,1 A square has a Wumpus iff there is a stench in the neighboring square. W1,2⇔(S1,1 and S2,2and S1,3) There is not a Wumpus in [1,2] ¬W1,2 W2,1⇔(S1,1 and S2,2and S3,1) There is not a Wumpus in [2,1] ¬W2,1 B1,1⇔(P1,2∨P2,1) There is not a pit in [1,2] ¬P1,2 B2,1⇔(P1,1∨P2,2∨P3,1) There is not a pit in [2,1] ¬P2,1 There is a breeze in [2,1] B2,1 There is not a stench in [2,1] ¬S2,1 There is not a wumpus in [2,2] There is not a wumpus in [3,1] There is a stench in [1,2] S1,2 There is not a breeze in [1,2] ¬B1,2 A square has a Wumpus iff there is a stench in the neighboring square. W1,3⇔(S1,2∨S2,3∨S1,4) The Wumpus is not on square [2,2] ¬W2,2 The Wumpus is on square [1,3] W1,3 There is not a pit on square [2,2] ¬P2,2 A square is breezy iff there is a pit in a neighboring square. B2,1⇔(P1,1∨P2,2∨P3,1) There is a pit on square [3,1] P3,1

-- Oct 19 In-Class Exercise Thread

`\neg`P_(1,1)

`\neg`W_(1,1)

`\neg`B_(1,1)

`\neg`S_(1,1)

`\neg`P_(2,1)

`\neg`W_(2,1)

`B_(2,1)

`\neg`S_(2,1)

`\neg`P_(1,1)

`\neg`W_(1,1)

`\neg`B_(1,1)

`\neg`S_(1,1)

`\neg`P_(1,2)

`\neg`W_(1,2)

`B_(1,2)

`S_(1,2)

(Edited: 2022-10-19)

@BT@\neg@BT@P_(1,1) @BT@\neg@BT@W_(1,1) @BT@\neg@BT@B_(1,1) @BT@\neg@BT@S_(1,1) <br> @BT@\neg@BT@P_(2,1) @BT@\neg@BT@W_(2,1) @BT@B_(2,1) @BT@\neg@BT@S_(2,1) <br> @BT@\neg@BT@P_(1,1) @BT@\neg@BT@W_(1,1) @BT@\neg@BT@B_(1,1) @BT@\neg@BT@S_(1,1) <br> @BT@\neg@BT@P_(1,2) @BT@\neg@BT@W_(1,2) @BT@B_(1,2) @BT@S_(1,2)

-- Oct 19 In-Class Exercise Thread

a. `S_(1,2)` <=> (`W_(1,3)` `vv` `W_(2,2)`) \\ b. `\neg``W_(1,3)` \\ c. `\neg``B_(1,2)` \\ d. `\neg``P_(1,2)` \\ e. `\neg``G_(1,2)` \\ f. `B_(2,1)` <=> (`P_(3,1)` `vv` `P_(2,2)`) \\ g. `\neg``W_(2,1)` \\ h. `\neg``P_(2,1)` \\ i. `\neg``G_(2,1)` \\ j. `P_(3,1)`

(Edited: 2022-10-19)

a. @BT@S_(1,2)@BT@ <=> (@BT@W_(1,3)@BT@ @BT@vv@BT@ @BT@W_(2,2)@BT@) \\ b. @BT@\neg@BT@@BT@W_(1,3)@BT@ \\ c. @BT@\neg@BT@@BT@B_(1,2)@BT@ \\ d. @BT@\neg@BT@@BT@P_(1,2)@BT@ \\ e. @BT@\neg@BT@@BT@G_(1,2)@BT@ \\ f. @BT@B_(2,1)@BT@ <=> (@BT@P_(3,1)@BT@ @BT@vv@BT@ @BT@P_(2,2)@BT@) \\ g. @BT@\neg@BT@@BT@W_(2,1)@BT@ \\ h. @BT@\neg@BT@@BT@P_(2,1)@BT@ \\ i. @BT@\neg@BT@@BT@G_(2,1)@BT@ \\ j. @BT@P_(3,1)@BT@

-- Oct 19 In-Class Exercise Thread

 There is no pit in 1,1 `\neg` `P_(1,1)` 
 There is no wumpus in 1,1 `\neg``W_(1,1)`
 There is no stench in 1,1 `\neg``S_(1,1)`
 There is no breeze in 1,1 `\neg``B_(1,1)`
 There is no wumpus in 1,2 `\neg``W_(1,2)`
 There is no breeze in 1,2 `\neg``B_(1,2)`
 There is a stench in 1,2 `S_(2,1)`
 There is no pit in 1,2 `\neg``P_(1,2)`
 There is no pit in 2,1 `\neg` `P_(2,2)`
 There is a breeze in 2,1 `B_(2,2)`
 There is no stench in 2,1 `\neg``S_(2,1)`
 There is no wumpus in 2,1 `\neg``W_(2,1)

(Edited: 2022-10-19)

There is no pit in 1,1 @BT@\neg@BT@ @BT@P_(1,1)@BT@ There is no wumpus in 1,1 @BT@\neg@BT@@BT@W_(1,1)@BT@ There is no stench in 1,1 @BT@\neg@BT@@BT@S_(1,1)@BT@ There is no breeze in 1,1 @BT@\neg@BT@@BT@B_(1,1)@BT@ There is no wumpus in 1,2 @BT@\neg@BT@@BT@W_(1,2)@BT@ There is no breeze in 1,2 @BT@\neg@BT@@BT@B_(1,2)@BT@ There is a stench in 1,2 @BT@S_(2,1)@BT@ There is no pit in 1,2 @BT@\neg@BT@@BT@P_(1,2)@BT@ There is no pit in 2,1 @BT@\neg@BT@ @BT@P_(2,2)@BT@ There is a breeze in 2,1 @BT@B_(2,2)@BT@ There is no stench in 2,1 @BT@\neg@BT@@BT@S_(2,1)@BT@ There is no wumpus in 2,1 @BT@\neg@BT@@BT@W_(2,1)

-- Oct 19 In-Class Exercise Thread

`R_1`: `\neg` `P_{1,1}`

`R_2`: `S_{1,2}` `\iff` `W_{1,1}` `\vv` `W_{2,2}` `\vv` `W_{1,3}`

`R_3`: `S_{2,1}` `\iff` `W_{1,1}` `\vv` `W_{2,2}` `\vv` `W_{3,1}`

`R_4`: `B_{2,1}` `\iff` `P_{1,1}` `\vv` `P_{2,2}` `\vv` `P_{3,1}`

`R_5`: `B_{1,2}` `\iff` `P_{1,1}` `\vv` `P_{2,2}` `\vv` `P_{1,3}`

`R_6`: `\neg` `W_{1,1}`

`R_7`: `\neg` `W_{2,1}`

`R_8`: `\neg` `W_{1,2}`

`R_9`: `\neg` `W_{2,2}`

(Edited: 2022-10-19)

@BT@R_1@BT@: @BT@\neg@BT@ @BT@P_{1,1}@BT@ @BT@R_2@BT@: @BT@S_{1,2}@BT@ @BT@\iff@BT@ @BT@W_{1,1}@BT@ @BT@\vv@BT@ @BT@W_{2,2}@BT@ @BT@\vv@BT@ @BT@W_{1,3}@BT@ @BT@R_3@BT@: @BT@S_{2,1}@BT@ @BT@\iff@BT@ @BT@W_{1,1}@BT@ @BT@\vv@BT@ @BT@W_{2,2}@BT@ @BT@\vv@BT@ @BT@W_{3,1}@BT@ @BT@R_4@BT@: @BT@B_{2,1}@BT@ @BT@\iff@BT@ @BT@P_{1,1}@BT@ @BT@\vv@BT@ @BT@P_{2,2}@BT@ @BT@\vv@BT@ @BT@P_{3,1}@BT@ @BT@R_5@BT@: @BT@B_{1,2}@BT@ @BT@\iff@BT@ @BT@P_{1,1}@BT@ @BT@\vv@BT@ @BT@P_{2,2}@BT@ @BT@\vv@BT@ @BT@P_{1,3}@BT@ @BT@R_6@BT@: @BT@\neg@BT@ @BT@W_{1,1}@BT@ @BT@R_7@BT@: @BT@\neg@BT@ @BT@W_{2,1}@BT@ @BT@R_8@BT@: @BT@\neg@BT@ @BT@W_{1,2}@BT@ @BT@R_9@BT@: @BT@\neg@BT@ @BT@W_{2,2}@BT@

-- Oct 19 In-Class Exercise Thread

 Knowledge base for the bottom left square for figure 7.4:
 Visited Squares: (1,1) (1,2) and (2,1)
 P(1,1) is F
 W(1,1) is F
 B(1,1) is F
 S(1,1) is F
 
 P(1,2) is F
 W(1,2) is F
 B(1,2) is F
 S(1,2) is T
 
 P(2,1) is F
 W(2,1) is F
 B(2,1) is T
 S(2,1) is F
 
 Rules: format (fact we learned about the square) => (something we don't know)
 B(1,1) <=> P(1,2) or P(2,1)
 B(2,1) <=> P(1,1) or P(2,2) or P(3,1)
 B(1,2) <=> P(1,1) or P(2,2) or P(1,3)

 S(1,1) <=> W(1,2) or W(2,1)
 S(2,1) <=> W(1,1) or W(2,2) or W(3,1)
 S(1,2) <=> W(1,1) or W(2,2) or W(1,3)

(Edited: 2022-10-19)

Knowledge base for the bottom left square for figure 7.4: Visited Squares: (1,1) (1,2) and (2,1) P(1,1) is F W(1,1) is F B(1,1) is F S(1,1) is F P(1,2) is F W(1,2) is F B(1,2) is F S(1,2) is T P(2,1) is F W(2,1) is F B(2,1) is T S(2,1) is F Rules: format (fact we learned about the square) => (something we don't know) B(1,1) <=> P(1,2) or P(2,1) B(2,1) <=> P(1,1) or P(2,2) or P(3,1) B(1,2) <=> P(1,1) or P(2,2) or P(1,3) S(1,1) <=> W(1,2) or W(2,1) S(2,1) <=> W(1,1) or W(2,2) or W(3,1) S(1,2) <=> W(1,1) or W(2,2) or W(1,3)

-- Oct 19 In-Class Exercise Thread

(Edited: 2022-10-19)

((resource:884B9A15-7385-44CD-A431-BA408699D387.png|Resource Description for 884B9A15-7385-44CD-A431-BA408699D387.png))

-- Oct 19 In-Class Exercise Thread

 no pit,breeze,stench in [1,1] ¬P_(1,1), [1,1] ¬B_(1,1), [1,1] ¬S_(1,1)
 we move to next grid [1,2]
 no pit,stench in [1,2] ¬P_(1,2), [1,2] ¬S_(1,2)
 breeze in [1,2] [1,2] B_(1,2) -> indicates B_(1,2) <=> (P_(2,2)V P_(3,1))
 next safe state is [1,2]

no pit,breeze,stench in [1,1] ¬P_(1,1), [1,1] ¬B_(1,1), [1,1] ¬S_(1,1) we move to next grid [1,2] no pit,stench in [1,2] ¬P_(1,2), [1,2] ¬S_(1,2) breeze in [1,2] [1,2] B_(1,2) -> indicates B_(1,2) <=> (P_(2,2)V P_(3,1)) next safe state is [1,2]

-- Oct 19 In-Class Exercise Thread

`\negP1, 1` No pit in 1, 1

`\negB1, 1` No breeze in 1, 1

`\negS1, 1` No stench in 1, 1

`\negP1, 2` No pit in 1, 2

`\negB1, 2` No breeze in 1, 2

S1, 2 Stench at 1, 2

`\negP2, 1` No pit in 2, 1

B2, 1 Breeze in 2 1

`\negS2, 1` No stench in 2, 1

---

For a wumpus to be on a square all adjacent squares must have a stench.

W1,3 <-> (S1, 2 V S2, 3 V S1, 4)

S1, 2 <-> (W1, 3 V W2, 2 V W1, 1)

`\negW2, 2` Because S2, 1 is false

And because W2, 2 is false, so we can say `W1, 3`

---

Likewise, there is only a pit if all squares surrounding a square is breezy.

Because B1, 2 is false, P2, 2 is false so `\negP2, 2`

A square is breezy is if there is a pit on a surrounding square.

Since `\negP2, 2` and B2, 1 and `negP1, 1`, P3, 1 is true

B2, 1 <-> (P1, 1 V P2, 2 V P3, 1)

(Edited: 2022-10-19)

@BT@\negP1, 1@BT@ No pit in 1, 1 @BT@\negB1, 1@BT@ No breeze in 1, 1 @BT@\negS1, 1@BT@ No stench in 1, 1 @BT@\negP1, 2@BT@ No pit in 1, 2 @BT@\negB1, 2@BT@ No breeze in 1, 2 S1, 2 Stench at 1, 2 @BT@\negP2, 1@BT@ No pit in 2, 1 B2, 1 Breeze in 2 1 @BT@\negS2, 1@BT@ No stench in 2, 1 --- For a wumpus to be on a square all adjacent squares must have a stench. W1,3 <-> (S1, 2 V S2, 3 V S1, 4) S1, 2 <-> (W1, 3 V W2, 2 V W1, 1) @BT@\negW2, 2@BT@ Because S2, 1 is false And because W2, 2 is false, so we can say @BT@W1, 3@BT@ --- Likewise, there is only a pit if all squares surrounding a square is breezy. Because B1, 2 is false, P2, 2 is false so @BT@\negP2, 2@BT@ A square is breezy is if there is a pit on a surrounding square. Since @BT@\negP2, 2@BT@ and B2, 1 and @BT@negP1, 1@BT@, P3, 1 is true B2, 1 <-> (P1, 1 V P2, 2 V P3, 1)