5 - Logical Agents

Question 1

A sentence is VALID iff ________.

Answer 1

A sentence is valid iff IT IS TRUE FOR ALL MODELS (a = True).

Question 2

A sentence is SATISFIABLE iff ________.

Answer 2

A sentence is satisfiable iff IT IS TRUE IN SOME MODELS (M(a) != ø).

Question 3

Sentence alpha valid => Sentence alpha ________.

Answer 3

Sentence alpha valid => Sentence alpha SATISFIABLE.

Question 4

Valid sentences are ________.

Answer 4

TAUTOLOGIES

Question 5

Inference algorithm COMPLETE iff ________.

Answer 5

… it is able to derive KB |- a for all KB |= a.

Question 6

Inference algorithm SOUND iff ________.

Answer 6

… it is able to guarantee entailment KB |= a for all KB |- a (derived sentences).

Question 7

A knowledge-based agent is composed of a ________ and ________.

Answer 7

KNOWLEDGE BASE and an INFERENCE MECHANISM.

Question 8

Inference Mechanism

Answer 8

Infers new sentences for decision making

Question 9

Inference Rules

Answer 9

Patterns of sound inference to find proofs

Question 10

Forward and backward chaining are natural reasoning algorithms for ________.

Answer 10

Horn Clauses

Question 11

Forward Chaining

Answer 11

Data driven and automatic processing (Object Recognition)

Question 12

Backward Chaining

Answer 12

Goal driven and appropriate for problem solving (Where are my keys?)

Question 13

p => q

Answer 13

True

Question 14

p => ~q

Answer 14

False

Question 15

~p => q

Answer 15

True

Question 16

~p => ~q

Answer 16

True

Question 17

p <=> q

Answer 17

True

Question 18

p <=> ~q

Answer 18

False

Question 19

~p <=> q

Answer 19

False

Question 20

~p <=> ~q

Answer 20

True

Question 21

Resolution Algorithm

Answer 21

KB into CNF -> Proof unsatisfiability by solving KB & ~a -> KB |= a

Question 22

How can we prove logical equivalences?

Answer 22

ENUMERATION (truth tables)

Question 23

Why should we use Horn clauses?

Answer 23

Simplify the implementation of logic programming languages

Question 24

Horn Clause

Answer 24

Clause with at most one positive literal

Question 25

Can we convert all sentences in propositional logic into the Horn form?

Answer 25

NO.