Knowledge and Application

Question 1

Declarative approach

Answer 1

Tell the agent what it needs to know and let it use reasoning to deduce consequences

Question 2

Knowledge base

Answer 2

Contains facts, rules and general knowledge about the domain in some formal language

Question 3

Reasoning engine

Answer 3

Produces relevant consequences of the knowledge base

Question 4

Unary rule-based

Answer 4

Let Ka (assertions) contain:
CompetesInPremierLeague(LiverpoolFC)
CompetesInPremierLeague(EvertonFC)
Kr (rules):
CompetesInPremierLeague(x) -> CompetesInFACup(x)
Atomic assertions follow from K:
CompetesInFACup(Liverpool FC)
FootballCLub(Everton)

class(individual variable) -> individual is part of class

Question 5

K be knowledge base and A(b) an atomic assertion

Answer 5

K |= A(b)
if whenever K is true, then A(b) is true since Kr allows us to prove this (acts like a bridge).
Ka - {A1(a)}
Kr = {A1(x) -> A2(x), A2(x) -> A3(x)} if x is in a1, then it is in a3
K |= {A1(a), A2(a), A3(a)}

Question 6

Time Complexity

Answer 6

IndividualName*ClassName

Question 7

Relation Name

Answer 7

Peter is the son of John
John is the son of Joseph
Relation name R denotes a set of pairs of individual objects, also called binary predicates:
onOf
grandsonOf
sonOf(Peter, John) - R(a,b) is atomic assertion

Question 8

Propositional Logic

Answer 8

A statement that can be true or false.

Question 9

Proof

Answer 9

a and q = m therefore I(m) = 1 (1 being true, 0 being false)*
f = q
!p = a
I(p) exists {0,1} -> I is the interpretation

Question 10

=>

Answer 10

If P is false, then P=>Q is true.
If the first initial value is false.

Question 11

Satisfiable

Answer 11

Propositional formula is satisfiable if there exists an interpretation under which it is true.
A . !A is a contradiction, because everything in the truth table adds up to false.

Question 12

2^n interpretations

Answer 12

N propositional atoms creates combinatorial explosion.

Question 13

Propositional Knowledge Base

Answer 13

Is a finite set of propositional formulas.

Question 14

∧

Answer 14

And

Question 15

P=>Q

Answer 15

If P is false, Q is true.

Question 16

{(p1 and p2)} |= (p1 or p2)

Answer 16

True, because all elements of AND that are true are true in OR.

Question 17

{p1, p1 => p2} |= p2

Answer 17

True, because when p1 AND p1=>p2 is equal true, p2 is equal to true.

Question 18

∨

Answer 18

Or

Question 19

¬

Answer 19

Not

Answer 20

And

Question 21

P1 … Pn is in X
Q = p1 … pn AND ¬P
If Q is unsatisfiable then X |= P

Answer 21

Q is not satisfiable then P is true because
p1…pn implies P stands true
Q = X AND ¬P
if Q was satisfiable, then at one point ¬P would stand true
therefore Q needs to be non-satisfiable

Question 22

Rule-based approach

Answer 22

They cannot contain ors, ands or nots since if it only an if something holds then something else holds.
Only propositional logic can.
Propositional logic, however, cannot express ‘any’ but rule-based can.

Question 23

Propositional Atoms

Answer 23

They are just propositions.

Question 24

Interpretation

Answer 24

Is the rule.

I(P) = true under interpretation I

Question 25

Combinatorial Explosion

Answer 25

2^n, with n being propositions and 2 being either they are true (1) or false (0).

Question 26

=>

Answer 26

Implies
whatever is on the left side, which is true, implies the right side is true
the sky is overcast |= the sun is not visible