KB entails a sentence α (KB |= α) if and only if, in every model KB is true, α is true as well. M (KB) is a subset of M(α)

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KB entails a sentence α (KB |= α) if and only if, in every model KB is true, α is true as well. M (KB) is a subset of M(α)

Assignment due Sunday, March 17, 2024 by 11:00pm
Answer the following questions. You have to upload a PDF file as the primary resource. You can upload any additional file as a secondary resource. Please note that you need to provide clear and detailed explanations for all the solutions that you provide.
Answer the following questions. Upload your answers in a pdf file.
Question 1
KB entails a sentence α (KB |= α) if and only if, in every model KB is true, α is true as well. M (KB) is a subset of M(α). One way to implement the inference is to enumerate all the models and check that α is true in every model that KB is true.
Assume a simplified version of the problem with breezes and pits. Squares next to pits are breezy, and breezy squares are next to squares with pits.
The agent did not detect a breeze at square [1,1] (column, row). The agent detected a Breeze in [2,1]. Thus, your knowledge base is KB : (¬ B1,1) ∧ (B2,1), where Bx,y is true if there is a breeze in [x,y].
Below you can see all possible models of adjacent pits: A pit is represented as a black cell.
1.1. Surround with a line the possible worlds above that are models of KB
1.2. Consider the sentence α1 = “Square [1,2] does not have a pit.” Surround with a line the possible worlds below that are models of α1.
1.3. Does KB |= α1? Explain your answer
1.4. Consider the sentence α2 = “Square [2,2] does not have a pit.” Surround with a line the possible worlds below that are models of α2.
Question 2:
Assume that you are given the following configuration. Compute the probability P3,1. Each square other than [1,1] contains a pit with a probability of 0.3.
Hint: Use section 12.7 for a similar example.
2.1 What is the evidence?
2.2. Write the formula for the full joint distribution. How many entries are there?
2.2 Use conditional independence to simplify the summation.
Question 3:
Given the network below, calculate marginal and conditional probabilities P (¬p3), P(p2|¬p3), P(p1|p2, ¬p3) a P(p1|¬p3, p4). Apply inference by enumeration. P(p1)=0.4 P(p2/p1)=0.8, P(p3/p2)=0.2 P(p3/¬p2)=0.3, P(p4/p2)=0.8, P(p4/¬p2)=0.5. Optional: Can you consider the case of using variable elimination?
Assignment Information
Weight:20%
Learning Outcomes Added
LO1_FundamentalsAI: Identify key concepts relating to various AI techniques.
LO2_ReasoningAI: Apply logic, probabilistic reasoning, and knowledge representation strategies in solving AI problems.
Above is the assignment requirements, please note that i have completed the assignment and the task i need you to complete is review everything and fix any mistakes.

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