Sep 11, 2006
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- Recap
	- solving a CSP using constraint propagation
		- can just 'read off' the answer
	- solving a CSP using search

- Recap 3 node graphs
	- example 1: maintaining arc consistency 'cleans' up the domains
	- example 2: after maintaining arc consistency, must still search

- Arc consistency is really short-hand for
	- "2-consistency"

- What is 3-consistency?
	- Fix values for two variables, there must be a legal value 
		for the 3rd

- Strong K-consistency is equivalent to
	- 1-consistency
	- 2-consistency
	- ...
	- (K-1)-consistency
	- K-consistency

- In general to just 'read off' the answer
	- can try to maintain strong n-consistency
	  for a graph with n nodes

- Sometimes k<n is sufficient
	- example of a 3 node graph where arc-consistency
	  is enough 

- How do we determine k?
	- k should be set just > width of the constraint graph

- Computing the width of the constraint graph
	- first identify all orderings (top to bottom) of the graph
		- where constraints are from a node to some node before it
	- for each ordering
		- find the max degree of a node
	- find min degree across all max degrees

- A different sounding approach is given in your book
	- but it is really the same thing

- For Sudoku
	- can try to do strong-81 consistency
		- overkill
	- some intermediate level might be sufficient

- Next topic: knowledge representation and reasoning

- Representation and Reasoning
	- given KB (facts)
	- try to derive conclusions (more facts)

- General theme
	- setup an interpretation
	- setup an inference procedure

- Logics
	- many kinds
	- mostly we will study monotonic logic
		- propositional logic
		- predicate logic

- Non-monotonic logic
	- "Tweety is a canary."
	- "A canary is a bird."
	- "Birds fly."
		- can infer "Tweety flies."
	- but, if we add
		- "Tweety's wings are broken."
		- need to retract earlier conclusion
		- cannot do this in propositional
		  (or predicate) logic

- Propositional logic
	- propositions: p, q, r
	- AND, OR, NOT
	- p=>q is the same as (NOT p OR q)
	- p<=>q is the same as (p=>q AND q=>p)

- Which of these operators are really important?
	- can we remove some so that others can be derived from it?
		- yes! (which ones?)