Lecture 15: Review

# Artificial Intelligence

### Review

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# Exam

* Topics: Everything we have covered so far (Introduction - Logic)

* You can use the slides, videos, the book, etc. during the exam

* Ask **me** if anything is unclear, not your classmates

* The answers have to be **your own**

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# Review: Intelligence

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# Question

We talked about "Thinking Humanly" as one type of intelligence. Which other three types did we discuss?

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# Question

Define the PEAS for an agent playing Super Mario

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# Question

Draw a finite state machine for a vacuum robot

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# Review: Search

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## Question

Find a path from Science to the Library using Breadth-First Search

Find a path from Science to the CLA using Depth-First Search, when the neighbors are ordered in **reverse alphabetical** order (the alphabetically last neighbors is pushed onto the stack first).

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# Question

Find a path from Science to the Library using Greedy Search (and then A*) with the following heuristic values:

Science: 10, Offices: 9.5, Marketplace: 7.75, Education: 8.5, Engineering: 6, Cultural Center: 5, Library: 0, Art: 2, Rose Garden: 4, IBM: 5, CLA: 6, Student Services: 5.5

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# Question

You and an opponent choose bits until two zeros or two ones have been chosen in a row, or 5 digits have been chosen in total. If the resulting number is prime, you get that many points, 
otherwise you lose that many points. Draw the complete game tree for this game. What is your best first move?

Example: You pick a 1, then you opponent picks a 0, then you pick a 0, and the game ends because 2 zeros have been chosen in a row. The resulting number is 100b = 4, which is not prime, and you lose 4 points.

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# Question

Which four steps make up Monte Carlo Tree Search?

Briefly explain each of the four steps

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# Question

In Monte Carlo Tree Search, during Action Selection, we discussed several methods how to choose actions. Name and briefly explain two of them.

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# Review: Logic

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# Question

Given the interpretation

$$
W = \\{b, d, e\\}
$$

For each of the following formulas determine if W is a model for that formula:

$$
a \rightarrow b \\\\
(a \vee d) \rightarrow (c \wedge e)\\\\
(a \rightarrow \neg a) \rightarrow (\neg a \rightarrow a) \\\\
d \rightarrow ((b \wedge (e \rightarrow a)) \rightarrow ((b \wedge d) \rightarrow a))
$$

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# Question

Define an interpretation W that is a model for all of these formulas:

$$
\neg a \rightarrow \neg b\\\\
c \rightarrow a\\\\
((c \vee \neg c) \rightarrow c)\\\\
a \rightarrow ((b \vee d) \wedge e)\\\\
b \rightarrow \neg c
$$

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# Question

Given the interpretation

$$
W = \\{\mathit{nat}(c), \mathit{real}(c), \mathit{complex}(c), 
       \mathit{nat}(a), \mathit{nat}(b), \mathit{real}(b),\\\\
      \mathit{sum}(a,a,a), \mathit{sum}(a,b,b), \mathit{sum}(a,c,c), 
      \mathit{sum}(b,b,b), \mathit{sum}(b,c,c)\\}
$$

For each of the following formulas determine if W is a model for that formula over the domain `$D = \{a,b,c\}$`

$$
\forall x: \mathit{sum}(x,x,x)\\\\
\forall x: \mathit{nat}(x)\\\\
\forall x: \mathit{complex}(x) \rightarrow \forall y: \mathit{sum}(y,x,x)\\\\
\forall x: \mathit{complex}(x) \rightarrow (\mathit{real}(x) \wedge \mathit{nat}(x))\\\\
\exists x: \neg \mathit{nat}(x) \rightarrow (\mathit{real}(x) \vee \mathit{complex}(x))\\\\
\exists x: \mathit{sum}(x,x,x) \rightarrow (\exists y: \mathit{sum}(x,y,y) \rightarrow \mathit{real}(y))
$$

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# Question

Define an interpretation W over the domain `$D= \{a,b,c,d,e\}$` <br/>
that is a model for all of these formulas:

$$
\mathit{zero}(a)\\\\
\mathit{nat}(a)\\\\
\mathit{last}(e)\\\\
\forall x: \mathit{last}(x) \vee \exists y: \mathit{succ}(x,y) \wedge \mathit{nat}(y)\\\\
\neg \exists x: \mathit{succ}(x,a)\\\\
(P(a) \wedge (\forall x: \forall y: (P(x) \wedge \mathit{succ}(x,y)) \rightarrow P(y))) \rightarrow \forall x: P(x)\\\\
P(a)
$$

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# Question

How is an (AI) planning problem defined/what three "parts" does it consist of?

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# Question

Given the interpretation/state

$$
s_0 = \\{ \mathit{at}(a,m), \mathit{at}(b,m), \mathit{at}(c,n) \\}
$$
Apply the effect `$e_1$` to this state to obtain `$s_1$`, then apply the effect `$e_2$` to get `$s_2$`, and then apply the effect `$e_1$` **again** to get `$s_3$`

$$
e_1 = \forall x: \forall y: \text{when}\quad(\exists z: (\mathit{at}(x,z) \wedge \mathit{at}(y,z)))\quad \mathit{seen}(x,y)\\\\
e_2 = (\forall x: \text{when}\quad \mathit{at}(a,x)\quad \neg \mathit{at}(a,x)) \wedge \mathit{at}(a,n)
$$

Answer the following queries in `$s_3$`:

Has b seen c? `$\mathit{seen}(b,c)$`

Has b seen b? `$\mathit{seen}(b,b)$`

Has a seen everyone? `$\forall x: \mathit{seen}(a,x)$`