Artificial Intelligence: Wumpus World Problem
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Questions and Answers

What is a characteristic of the resolution rule?

  • It applies to conjunctions of literals
  • It applies only to disjunctions of literals (correct)
  • It applies to equivalences
  • It applies to implications

    • What is Conjunctive Normal Form (CNF)?

  • A disjunction of literals
  • A disjunction of conjunctions of literals
  • A conjunction of disjunctions of literals (correct)
  • A conjunction of literals

    • What is the first step in converting a sentence to CNF?

  • Eliminate equivalences (correct)
  • Eliminate implications
  • Move negations inwards
  • Apply the resolution rule

    • What is the purpose of applying the resolution rule?

    <p>To derive any conclusion entailed by a knowledge base</p> Signup and view all the answers

    What is the result of applying de Morgan's rules and double negation elimination?

    <p>Moving negations inwards</p> Signup and view all the answers

    What is the performance measure in the Wumpus World problem?

    <p>Gold +1000, death -1000, -1 per step, -10 for using the arrow</p> Signup and view all the answers

    What happens when the agent shoots the wumpus?

    <p>The wumpus is killed and the agent gets a reward.</p> Signup and view all the answers

    What is the probability of a pit in a square other than the start?

    <p>0.2</p> Signup and view all the answers

    What is the purpose of the 'Grab' action?

    <p>To pick up the gold</p> Signup and view all the answers

    Is the Wumpus World fully observable?

    <p>No, the agent only has local perception.</p> Signup and view all the answers

    What happens when the wumpus is killed?

    <p>The wumpus screams.</p> Signup and view all the answers

    What is the primary difference between model checking and application of inference rules in proof methods?

    <p>One generates new sentences, while the other uses model space enumeration.</p> Signup and view all the answers

    What is a sentence that is true in all models called?

    <p>Valid</p> Signup and view all the answers

    What is the connection between validity and inference?

    <p>KB ╞ α if and only if (KB → α) is valid.</p> Signup and view all the answers

    What is the relationship between satisfiability and inference?

    <p>KB ╞ α if and only if (KB ∧ ¬α) is unsatisfiable.</p> Signup and view all the answers

    What is the definition of logically equivalent sentences?

    <p>Sentences that are true in the same models.</p> Signup and view all the answers

    What is the abbreviation for the Modus Ponens rule?

    <p>mp</p> Signup and view all the answers

    What can be proved using the rules R1-R5?

    <p>¬P1,2</p> Signup and view all the answers

    What is the purpose of transforming sentences into normal form?

    <p>To use inference rules as operators in a standard search algorithm.</p> Signup and view all the answers

    Which type of clauses are often used in real-world knowledge bases?

    <p>Horn clauses</p> Signup and view all the answers

    What is the maximum number of positive literals in a Horn clause?

    <p>One</p> Signup and view all the answers

    What is the conclusion of a Horn clause implication?

    <p>A single positive literal</p> Signup and view all the answers

    What is the purpose of the Modus Ponens rule in Horn KBs?

    <p>To derive new conclusions</p> Signup and view all the answers

    What is the characteristic of a definite clause?

    <p>It has exactly one positive literal</p> Signup and view all the answers

    Which algorithm is used in forward chaining?

    <p>Forward chaining</p> Signup and view all the answers

    What is the condition to add a conclusion to the knowledge base in forward chaining?

    <p>When the count of a clause is zero</p> Signup and view all the answers

    What is the proof of soundness of forward chaining based on?

    <p>Modus Ponens</p> Signup and view all the answers

    What happens when Forward Chaining (FC) reaches a fixed point?

    <p>No new atomic sentences are derived</p> Signup and view all the answers

    What is the purpose of considering the final state as a model m in Forward Chaining?

    <p>To assign true/false to symbols</p> Signup and view all the answers

    Why is every definite clause in the original KB true in the model m?

    <p>To avoid contradictions</p> Signup and view all the answers

    What is the main idea of Backward Chaining (BC)?

    <p>To work backwards from the query</p> Signup and view all the answers

    What is the purpose of checking if a new subgoal is already on the goal stack in Backward Chaining?

    <p>To avoid loops</p> Signup and view all the answers

    What is the characteristic of Forward Chaining?

    <p>Data-driven</p> Signup and view all the answers

    What is the advantage of Backward Chaining over Forward Chaining?

    <p>It is more suitable for problem-solving</p> Signup and view all the answers

    What is an example of a situation where Backward Chaining is more suitable?

    <p>Finding a PhD program</p> Signup and view all the answers

    Study Notes

    Wumpus World Problem

    • Wumpus World is a problem that involves an agent navigating a 4x4 grid of rooms to find gold and avoid a Wumpus and pits.
    • The agent starts at [1,1] and can move left, right, forward, grab, release, shoot, or climb.
    • The agent has sensors that can detect stench, breeze, glitter, bump, and scream.
    • The goal is to maximize the performance measure, which is +1000 for gold, -1000 for death, -1 for each step, and -10 for using the arrow.

    Wumpus World Properties

    • The environment is fully observable, but the agent only has local perception.
    • The environment is deterministic, meaning that outcomes are exactly specified.
    • The environment is episodic, meaning that the agent's actions are sequential.
    • The environment is static, meaning that the Wumpus and pits do not move.
    • The environment is discrete, meaning that the agent's actions and perceptions are discrete.

    Proof Methods

    • Proof methods can be divided into two kinds: model checking and applying inference rules.
    • Model checking involves enumerating all possible models of the knowledge base and checking if the goal is true in all of them.
    • Applying inference rules involves generating new sentences from old ones using rules like modus ponens.

    Validity and Satisfiability

    • A sentence is valid if it is true in all models.
    • A sentence is satisfiable if it is true in some model.
    • A sentence is unsatisfiable if it is true in no models.
    • The deduction theorem states that KB entails alpha if and only if KB implies alpha is valid.

    Equivalence Rules

    • Two sentences are logically equivalent if they are true in the same models.
    • Alpha is equivalent to beta if and only if alpha entails beta and beta entails alpha.

    Inference Rules

    • Modus ponens: from R and R implies S, can derive S.
    • Modus tollens: from R implies S and not S, can derive not R.
    • Conjunction: from R and S, can derive R and S.
    • Simplification: from R and S, can derive R.
    • Addition: from R, can derive R or S.

    Resolution and CNF

    • Resolution rule applies only to disjunctions of literals.
    • Every sentence of propositional logic is logically equivalent to a conjunction of disjunctions of literals (CNF).
    • CNF is useful for applying the resolution rule.

    Conversion to CNF

    • Eliminate implies, replacing alpha implies beta with not alpha or beta.
    • Move not inwards using de Morgan's rules and double-negation.
    • Convert to CNF using the above steps.

    Horn Clauses

    • Horn clauses are a restricted form of clauses that can be written as an implication whose premise is a conjunction of positive literals and whose conclusion is a single positive literal.
    • Modus ponens is complete for Horn KBs.
    • Definite clauses are Horn clauses with exactly one positive literal.
    • Definite clauses form the basis for logic programming.

    Forward Chaining

    • Forward chaining is a method for deriving conclusions from a knowledge base.
    • It works by firing any rule whose premises are satisfied in the KB and adding its conclusion to the KB, until the query is found.
    • Forward chaining is sound and complete for Horn KB.

    Backward Chaining

    • Backward chaining is a method for deriving conclusions from a knowledge base.
    • It works by working backwards from the query q, checking if q is known already, or proving by backward chaining all premises of some rule concluding q.
    • Backward chaining is useful for problem-solving.

    Forward vs. Backward Chaining

    • Forward chaining is data-driven, automatic, and unconscious processing.
    • Backward chaining is goal-driven, appropriate for problem-solving.
    • Forward chaining may do lots of work that is irrelevant to the goal.

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    Description

    This quiz is about the Wumpus World problem in artificial intelligence, where an agent navigates a 4x4 grid of rooms to collect gold and avoid death. The agent's performance is measured based on its actions.

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