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1661CS 771 Artificial Intelligence Homework 1 (50 points) 人工智能代写 1.For each of the following assertions, say whether it is true or false and support your answer with examples or counterexa...
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自动推理代写 1. [8 pts] Show that the following sentences are consistent by identifying a world which satisfieseach sentence: • (¬A⇒B) ∧ (A⇒¬B).• (A ∧ B)⇒
Show that the following sentences are consistent by identifying a world which satisfies each sentence:
2.[8 pts]
Show that the following sentences are valid by showing that each is true at every world:
3.[8 pts]
Prove from the definitions of Boolean quantifiers ∃ and ∀ that (a) ∃P · (∆ ∨ Γ) is equivalent to (∃P · ∆) ∨ (∃P · Γ), and (b) ∀P · (∆ ∧ Γ) is equivalent to (∀P · ∆) ∧ (∀P · Γ).
4.[8 pts]
Convert the following knowledge base into clausal form:
∆ = A⇒B, ¬A⇒(¬B ∧ C), (B ∨ C)⇒D.
Show that if we have a polynomial-time procedure for model counting, and another for clausal entailment on a knowledge base Γ, then we have a polynomial-time procedure for testing the equivalence between Γ and CNF ∆.
6.[10 pts]
Show using resolution that D ∨ E is entailed by the knowledge base:
∆ = ¬A⇒B, A⇒¬C, ¬D⇒¬B ∧ ¬C, A⇒E.
7.[12 pts]
Show the termination tree for dpll when run on the following KB, assuming that variables are tested according to the order A, B, C, D, E and true expanded before false:
Note that dpll does not use conflict-directed backtracking.
8.[12 pts]
Show a trace of dpll+ on the above KB, assuming that decisions are made according to the constraints given above. At each conflict, show the decision sequence, implication graph, conflict-driven clause, and its assertion level. Assume that conflict-driven clauses are generated using the first-UIP method of Section 3.6.2.
9.[12 pts]
Consider the following knowledge base.
∆ = A⇒B, ¬A⇒(¬B ∧ C), (B ∨ C)⇒D.
Show how you can count the number of models of ∆ using cdpll and draw the termination tree. Assume that you are expanding variables according to the order A, B, C, D and always expand true before false.
Consider the following knowledge base:
∆ = P1 ∨ P2 ∨ P3, P1⇒Q, P2⇒Q, P3⇒Q.
a. Convert ∆ into clausal form.
b. Apply directed resolution to the clausal form using the variable order P1, P2, P3, Q.
c. Construct a decision tree for ∆ and use it to count the number of models of ∆.
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CS 771 Artificial Intelligence Homework 1 (50 points) 人工智能代写 1.For each of the following assertions, say whether it is true or false and support your answer with examples or counterexa...
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