Assignment Task

 

Q1)
Consider the following knowledge base, given in natural language: 
William was king. All kings have at least one ruthless son. All sons of kings are princes. William Rufus and Henry were sons of William. Henry was not ruthless, but William Rufus was. All ruthless princes become kings. No king who is ruthless or crazy is good. 

a) Translate the knowledge base into first-order logic, using one FOL sentence for each sentence above. You must use the following predicates and constants: 

Unary predicates; i.e. taking one argument: king, ruthless, prince, crazy, good 
Binary predicates; i.e. taking two arguments: son 
Constants; i.e. names of people: William, Henry, William Rufus (please note that ”William Rufus” is a single name referring to one person) 

b) We now want to prove that the assertion ”William Rufus was king, but not good” follows from the knowledge base above. Perform this proof by reasoning about the formalized sentences above, taking the semantics of quantifiers and connectives into account.  

c) Convert the formalized knowledge base to CNF and divide into clauses. You must follow the algorithm for conversion, which is given in section 9.5.1 in Russell & Norvig. Document every step of your conversion into clause form. 

d) Use first-order resolution to prove the assertion ”William Rufus was king, but not good” from the knowledge base


Q2)
Consider the following knowledge base, given in natural language: 
All innovators are mad, but it’s not the case that everyone who is mad is an innovator. Bill Gates is an innovator, as is Elon Musk. Everyone who is ahead of their time are misunderstood. Both Elon Musk and Bill Gates are ahead of their time. Elon Musk has not received a presidential medal, but Bill Gates has. Both of them have successful companies. Anyone who is an innovator and misunderstood are happy if they both have a successful company and have received a presidential medal, but unhappy otherwise. 

a) Translate the knowledge base into first-order logic, using one FOL sentence for each English sentence above. Carefully consider which predicates, functions and constants to use. Hint: for the last sentence, think carefully about finding a clear structure (what implies what?) and test your translation with some different models to check that it captures the intended meaning. 

b) We now want to prove that the assertion ”Bill Gates is happy, but Elon Musk is not happy” follows from the knowledge base. Conduct this proof by reasoning about the semantics of the logical sentences you wrote for task a) above. 

c) Convert the formalized knowledge base to CNF and divide into clauses. You must follow the algorithm for conversion, which is given in section 9.5.1 in Russell & Norvig. Document every step of your conversion into clause form. 

d) Use first-order resolution to prove the assertion ” Bill Gates is happy, but Elon Musk is not happy” from the knowledge base.

 

 

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  • Uploaded By : Brett
  • Posted on : April 19th, 2019

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