Title: EAI / 10_knowledge

Q: Where do knowledge and resoning play a crucial role?
A: In partially observable environments.

Q: What is the goal of knowledge represantation?
A: - represent implicit knowledge about a certain area in such a way that it can be processed by computers
- original knowledge is encoded in suitable data structures and algorithms

Q: What are the central components of knowledge-based agents?
A: - a knowledge base
- methods to add new sentences and methods to query what is known (\(\texttt{Tell}\), \(\texttt{Ask}\))

Explain the schematic architecture of knowledge-based agents.

Q: What must a knowledge agent be able to do? (5)
A: - represent states, actions, etc.
- incorporate new percepts
- update internal representations of the world
- deduce hidden properties of the world
- deduce appropriate actions

Q: What happens when the agent program is called?
A: 1. It \(\texttt{Tell}\)s the knowledge base what it percieves
2. It \(\texttt{Ask}\)s the knowledge base what action it should perform
3. It records it's choice with \(\texttt{Tell}\) and executes the action

Q: Explain entailment
A: Entailment means that one thing follows from another.
A knowledge base \(KB\) entails a sentence \(\alpha\), symbolically \(KB \models \alpha\), iff \(\alpha\) is true in all worlds where \(KB\) is true.

Q: Explain Inference.
A: \(KB \vdash_i \alpha: \Longleftrightarrow\) sentence \(\alpha\) can be derived from \(KB\) in proof system \(i\).

Q: Explain Soundness and Completeness.
A: Soundness:
\(i\) is sound if \(KB \vdash_i \alpha\) implies \(KB \models \alpha\)
Completeness:
\(i\) is comlete if \(KB \models \alpha \) implies \(KB \vdash_i \alpha\)

Q: What are the main connectives for \(\forall,\exists\)?
A: \(\forall: \quad\Rightarrow\)
\(\forall x(S(x) \Rightarrow P(x))\)
\(\exists:\quad \land\)
\(\exists x(S(x) \land P(x))\)

Q: Explain modus ponens (detachment rule).
A: \(\frac{\alpha \Rightarrow \beta \hspace{1cm} \alpha}{\beta}\)
Whenever any sentences of the form \(\alpha \Rightarrow \beta\) and \(\alpha\) are derivable, then the sentence \(\beta\) can be inferred.

Q: Explain the monotonicity property of inference relations.
A: if \(KB \vdash \alpha\) and \(KB \subseteq KB'\), then \(KB' \vdash \alpha\)
Once a conclusion \(\alpha\) is inferred, it can never be invalidated by additional knowledge.

Q: Explain the cut rule in inference relations.
A: \(KB \vdash \alpha\) and \(KB,\alpha \vdash \beta\), then \(KB \vdash \beta\)

Q: Explain the proof method resoultion.
A: complementary literals are removed in CNFs.
\(\dfrac{P \lor Q \hspace{1cm}\lnot Q}{P}\)