Lecture 8 (Knowledge systems)
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1
What are the two main components of a Knowledge-Based (KB) System?
Knowledge Base (KB) and Inference Engine.
2
What does the Knowledge Base (KB) in a KB system do?
It stores facts and rules about the world.
3
What does the Inference Engine in a KB system do?
It applies logical rules to the knowledge base to deduce new facts and draw conclusions.
4
What is the meaning (semantics) of Propositional Logic based on?
It is truth-functional; the truth of a complex formula is determined by the true/false values of its simple parts.
5
How do you read the operator \$p \wedge q\$ (and)?
"p and q". True only if both are true.
6
How do you read the operator \$p \vee q\$ (or)?
"p or q". True if at least one is true.
7
How do you read the operator \$\neg p\$ (not)?
"not p". Flips the truth value of p.
8
What concepts can Propositional Logic *not* represent?
Knowledge, Belief, Obligation, or Time.
9
What new operators does Modal Logic add to propositional logic?
\$\Box\$ (box) and \$\Diamond\$ (diamond).
10
How can \$\Box \varphi\$ be read?
"It is necessary that \$\varphi\$."
11
How can \$\Diamond \varphi\$ be read?
"It is possible that \$\varphi\$."
12
What is a tip for remembering the \$\Box\$ (Box) operator?
Think of "in ALL possible cases" or "I am certain that...". It's a strong, universal claim.
13
What is a tip for remembering the \$\Diamond\$ (Diamond) operator?
Think of "in SOME possible case" or "I cannot rule out that...". It's a weak, existential claim.
14
What is the relationship between \$\Box\$ and \$\Diamond\$ (duality)?
\$\Box \varphi \equiv \neg \Diamond \neg \varphi\$
15
What system is used to determine the meaning (semantics) of Modal Logic?
Kripke Models.
16
What are the three key parts of a Kripke model?
A set of possible worlds (W), an accessibility relation (R), and a valuation function (val).
17
What does the accessibility relation (R) in a Kripke model represent?
The arrows that connect worlds, defining which worlds are "possible" or "accessible" from a given world.
18
What does the valuation function (val) in a Kripke model do?
It tells us which simple propositions (like \$c\$ or \$s\$) are true inside each specific world.
19
How do you check if a \$\Box\$ (Box) formula (e.g., \$\Box_I \varphi\$) is true at a world?
Start at the world, follow ALL arrows for that agent (I), and check if \$\varphi\$ is true in EVERY SINGLE accessible world.
20
How do you check if a \$\Diamond\$ (Diamond) formula (e.g., \$\Diamond_{Other} \varphi\$) is true at a world?
Start at the world, follow ALL arrows for that agent (Other), and check if \$\varphi\$ is true in AT LEAST ONE accessible world.
21
What does Epistemic logic model?
Knowledge (Arrows point to worlds the agent considers possible).
22
What does Doxastic logic model?
Belief (Arrows point to worlds the agent believes are true).
23
What does Deontic logic model?
Obligation (Arrows point to "ideal" or "permissible" worlds).
24
What does Temporal logic model?
Time (Arrows point to future moments in time).
25
What is Multi-Agent Epistemic Logic?
A Kripke model with multiple accessibility relations, one for each agent.
26
What is the "Golden Rule" of Multi-Agent Logic?
Always use the correct set of arrows for the agent specified in the modal operator (e.g., \$\Box_I\$ uses "I" arrows).
27
What is the general strategy for solving nested modal logic formulas?
Work from the inside out.
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