Description

150pt

Objective: Learning about Propositional Logic

1) 20 pt – Decide whether each of the following sentences is valid, unsatisfiable, or satisfiable (not valid, but only satisfiable). Show how you come to that decision using truth table enumeration or logical equivalence rules.

▪ Smoke => Smoke …………… …………………………….. 10pt

Circle the correct answer: Valid, Satisfiable, Unsatisfiable

▪ Smoke => Fire ………………………………………….. 10pt

Circle the correct answer: Valid, Satisfiable, Unsatisfiable
2) 40pt – Truth Table Enumeration for Inference

Assume we have the knowledge base KB: Rain ∧ (Rain ⇒ Wet) ∧ (Snow ⇒ Cold) and the given propositions are the only ones in the KB.

a) 25 pts – How many possible worlds (truth value assignments to the propositions) are models of the KB? Show your work by filling the truth table for the KB.

b) 15pts – Extend the above truth table (use truth table enumeration method) to show whether the knowledge base entails =Wet.

State your answer here: Entails/ Does not Entail because …………………………………………

…………………………………………………………………………………………………………..

3) 90pt – AIMA 3rd Ed. Q. 7.2

a) 20pt – First state the English paragraph as a set of Propositional Logic sentences. Please use the given two-letter proposition names below. Be careful about what propositions to use
(especially for the the statement “mortal mammal”), considering all of the paragraph.

b) 20pt – Convert the above KB into Conjunctive Normal Form. Show your work clearly.

c) 50pt – See if the KB entails each of the following conclusions: “unicorn is mythical”,
“unicorn is magical”, “unicorn is horned”. Use the indicated method, if available.

For each of them, please indicate the inference method you are using and clearly indicate your conclusion at the beginning:

I. 10pts – “unicorn is mythical”:

Conclusion: Using …………………………………………………………..……, we can show

that we can conclude?/not conclude? (infer/not infer?) that the unicorn is mythical.

Show your work or state your argument: …………………………………………………

…………………………………………………………………………………………………

II. 30pt – “unicorn is horned”:

Use either:
– simple resolution: that is apply resolution many imes to see whether you can infr Horned, or
– resolution refutation (aka proof by contradiction): that is, add the negated form of whatever you want to check for entailment (e.g. ¬Horned), and see if you can reach a contradiction. This would show that the KB+negative is unsatisfiable, hence the conclusion can be inferred).

III. 10pt – “unicorn is magical”:

Use Modus Ponens method and state your conclusion.