Oct 3, 2003
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- Now that we know how to do proofs
	- lets revisit some important steps

- Key approach
	- define predicate vocabulary
	- write given sentences
	- convert to clausal form
	- resolve

- Example proof tree
	- long "sticky" thingy
		 - possible when KB consists of
		   horn clauses
	- "bushy" proofs
		- general case

- Looking at structure of resolution-refutation proofs
	- input resolution
		- complete for Horn clauses
	- unit resolution
		- complete for Horn clauses
	- linear resolution
		- complete
	- set-of-support resolution
		- complete, if set chosen properly

- Unifiers
	- find substitutions that make one
	  statement equivalent to another

- Examples
	- MGU(Knows(John,x),Knows(y,Bill))
	- MGU(Knows(John,x),Knows(y,Mother(y)))
	- MGU(Knows(John,x),Knows(y,z))
		- has many Us

- Examples where MGU doesn't exist
	- MGU(Knows(John,x),Knows(Bill,y))
	- MGU(Knows(John,x),Knows(Elizabeth,x))

- Occurs-check
	- a check to see if a variable being substituted
	  already occurs elsewhere in the same formula
		- omitted by some systems, such as PROLOG