06. Logical Agents I

Question 1

A knowledge base is an ….

An inference engine …

Answer 1

organized collection of facts about the system’s domain (domain-specific content)

interprets and evaluates the facts in the knowledge base in order to provide an answer (domain-independent algorithms)

Question 2

What are some possibilities to gain knowledge for a knowledge base?

Answer 2

Inference–> Make it possible to derive new knowledge from old knowledge.

Declarative approach–> New knowledge is added from “outside” by providing knowledge

Perception–> New knowledge is added by the agent from its own perception

Question 3

Agents can be viewed at two different levels, explain.

Answer 3

knowledge level: what they know, regardless of how implemented

implementation level: data structures in the knowledge base and algorithms that manipulate them

Question 4

Wumpus world PEAS description

Answer 4

see slide 7

Why do we use the PEAS framework to describe this?

Question 5

Wumpus world characterisation

Answer 5

Observable: No – only local perception.
Deterministic: Yes – outcomes are exactly specified.
Episodic: No – sequential since actions change the environment. Static: Yes – Wumpus and pits do not move.
Discrete: Yes.
Single-agent: Yes – Wumpus is essentially a natural feature.
The main challenge is the initial ignorance of the environment; overcoming this ignorance seems to require logical reasoning.

Question 6

Differentiate between syntax, semantics and models.

Answer 6

Syntax
Specifies how correct sentences are formed

Semantics
The semantics defines the meaning of sentences, i.e., when a sentence is true.

Model
Models are differently defined depending on the discipline. Here, models are instances which evaluate sentences to true or false.

Question 7

Differentiate between satisfaction and entailment.

Answer 7

Satisfaction
If a sentence α is true in model m, we say that m satisfies α. We use the notation M(α) to mean the set of all models of α. => All models in which alpha is true?

Entailment
Entailment is the relationship between two sentences where the truth of one sentence requires the truth of the other sentence, which is written as
α |= β if α entails β.

Formally, entailment is defined as
α |= β if and only if M(α) ⊆ M(β).

Question 8

If every model in which KB is true, alpha is also true =>

P entails Q if and only if

Answer 8

KB entails alpha

P => Q is always true for any model

Question 9

Operator precedence in propositional logic:

Answer 9

negation, conjunction, disjunction, implication, biconditional (descending order)

Question 10

Truth tables: Explain the implication logic
P False, Q True: P=> Q

P True, Q False: P=> Q

Answer 10

True

False

Question 11

Logical equivalence
Two sentences α and β are logically equivalent if they are true in the same set of models, which is written as α ≡ β. Alternative definition: …

Answer 11

α ≡ β if and only if α |= β and β |= α.

Question 12

Validity
A sentence is valid … (e.g., P ∨ ¬P).
Valid sentences are also known as tautologies.

Satisfiability
A sentence is satisfiable if …, e.g., the expression P1 ∧ P2 is satisfiable for P1 = P2 = true, whereas P1 ∧ ¬P1 is not satisfiable.

Answer 12

if it is true in all models

it is true in some model

Question 13

Inference and Proofs

Modus Ponens

And-Elimination

Answer 13

Explain them.

Question 14

Logical Equivalences

Answer 14

Slide 36

Question 15

Automated Theorem Proving
The previous method was done “by hand”. How can one automate this?
We can use the previously introduced search methods on the following problem:
Initial state: …
Actions: all the inference rules applied to …
Result: the result of an action is to ….
Goal: a state that contains the sentence to prove.

In practical cases, finding a proof can be more efficient than enumeration because…

Answer 15

the initial knowledge base.

all the sentences that match the top half of the inference rule.

add the sentence in the bottom half of the inference rule.

not all possible models have to be generated.