1What are the two main components of a Knowledge-Based (KB) System?
Knowledge Base (KB) and Inference Engine.
2What does the Knowledge Base (KB) in a KB system do?
It stores facts and rules about the world.
3What does the Inference Engine in a KB system do?
It applies logical rules to the knowledge base to deduce new facts and draw conclusions.
4What 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.
5How do you read the operator \$p \wedge q\$ (and)?
"p and q". True only if both are true.
6How do you read the operator \$p \vee q\$ (or)?
"p or q". True if at least one is true.
7How do you read the operator \$\neg p\$ (not)?
"not p". Flips the truth value of p.
8What concepts can Propositional Logic *not* represent?
Knowledge, Belief, Obligation, or Time.
9What new operators does Modal Logic add to propositional logic?
\$\Box\$ (box) and \$\Diamond\$ (diamond).
10How can \$\Box \varphi\$ be read?
"It is necessary that \$\varphi\$."
11How can \$\Diamond \varphi\$ be read?
"It is possible that \$\varphi\$."
12What 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.
13What 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.
14What is the relationship between \$\Box\$ and \$\Diamond\$ (duality)?
\$\Box \varphi \equiv \neg \Diamond \neg \varphi\$
15What system is used to determine the meaning (semantics) of Modal Logic?
Kripke Models.
16What are the three key parts of a Kripke model?
A set of possible worlds (W), an accessibility relation (R), and a valuation function (val).
17What 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.
18What 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.
19How 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.
20How 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.
21What does Epistemic logic model?
Knowledge (Arrows point to worlds the agent considers possible).
22What does Doxastic logic model?
Belief (Arrows point to worlds the agent believes are true).
23What does Deontic logic model?
Obligation (Arrows point to "ideal" or "permissible" worlds).
24What does Temporal logic model?
Time (Arrows point to future moments in time).
25What is Multi-Agent Epistemic Logic?
A Kripke model with multiple accessibility relations, one for each agent.
26What 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).
27What is the general strategy for solving nested modal logic formulas?
Work from the inside out.