# AIMA: Logical Agents

> Source: https://ollybritton.com/notes/textbooks/ai-a-modern-approach/knowledge-reasoning-and-planning/logical-agents/ · Updated: 2021-04-04 · Tags: notes, aima

## Flashcards
##### How do knowledge-based agents represent their knowlege??
Using a knowledge base.

##### What is a knowledge base (KB) made out of??
Sentences.

##### How are sentences represented in a knowledge base??
In a knowledge representation language.

##### What in the notation for $\alpha$ entailing $\beta$??
$$
\alpha \models \beta
$$
##### What is a model in logic??
A set of assignments for true and false.

##### What does it mean for a sentence to be valid??
Given true premises, the sentence is always true.

##### What does it mean for a sentence to be satisfiable??
There exists a model that makes the formula true.

##### How can you define entailment in terms of validity??
$\alpha \models \beta$ if the sentence $\alpha \implies \beta$ is valid.

##### How can you define entailment in terms of satisfiability??
$$\alpha \models \beta$$ if $(\alpha \land \neg\beta)$ is unsatisfiable.

##### What is a conjunction in logic??
$P \land Q$, and

##### What are the conjuncts of $P \land Q$??
$P$ and $Q$.

##### What is a disjunction in logic??
$P \lor Q$, or

##### What are the disjuncts of $P \lor Q$??
$P$ and $Q$.

##### What is the symbol for implication in logic??
$$
P \implies Q
$$

##### What is the premise/antecedent of $P \implies Q$??
$$
P
$$

##### What is the conclusion/consequent of $P \implies Q$??
$$
Q
$$

##### What is the symbol for if and only if in logic??
$$
P \iff Q
$$

##### How can you interpret $P \implies Q$??
If $P$ is true, then I am claiming that $Q$ is true; otherwise I am making no such claim.

##### Why is "5 is even implies Sam is smart" true in logic??
Because the premise of the implication is false, then the overall sentence is true.

##### Why is "5 is odd implies Tokyo is the capital of Japan" true in logic??
Because logic doesn't require causation or relevance between premises and conclusions.

##### How can you write $P \iff Q$ in terms of implication??
$$(P \implies Q) \and (Q \imples P)$$

##### What is $M(\alpha)$ for some sentence $\alpha$??
The set of all models for $\alpha$.

##### What is a sound inference algorithm??
One that only derives entailed sentences (never makes things up).

##### What is a complete inference algoirthm??
One that derives all sentences that are entailed.

##### What's the brute-force solution for entailment??
Model-checking, trying all the models possible.

##### What is a literal in logic??
An atom or its negation

$$
P, \neg P
$$

##### What is conjunctive normal form??
Logical sentences consisting only of conjunctions of clauses of literals.

##### When do forward chaining and backward chaining algorithms work??
When a knowledge base is expressed in Horn form.

##### What is forward chaining??
Making inferences to try and arrive at a conclusion.

##### What is backward chaining??
Making inferences backward from a conclusion to try match it to initial knowledge.

##### How can you do route finding using SAT solvers??
Formulate a sentence that contains assertions about the initial state, transitions and the goals and see if it can find a valid solution.

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