Representing problems with propositional schemas

- Consider representing fact in Wumpus World, "there is a breeze next to a pit".
	- Very lengthy!
		PITij,  BREEZEij
	- Need: compact way to specify a large set of clauses.  Answer: SCHEMAS.

	- Introduce CONSTRUCTED PROPOSITIONS
		(predicate TERM TERM ...)
			each TERM is a CONSTANT or a VARIABLE.

	- Example of BREEZE using schemas with FORALL RANGE

(forall VARIABLE (range LOW HIGH) TEST CLAUSE)

- Example: 8-queens problems.  

	-- What are the constraints in English?

	-- What propositions are needed?  How many?

	-- "No queens attack"
		-- What is schema?
		-- How many clauses result?

	-- "At least one queen in each row"
		
		-- forall doesn't help!

		-- Introduce:  (forsome VARIABLE (range LOW HIGH) TEST CLAUSE)

	-- Suppose we find a MODEL for these clauses.  How do we read off the solution to the
	  original 8-queens problem?

- Another example: GRAPH COLORING.  

	-- 4-color theorem

	-- Draw a map of NY, NJ, PA, MASS, VT, CONN

	-- Convert to a graph

	-- What variables need to represent coloring the graph?  RED, BLUE, GREEN,
           YELLOW.

	-- Introduce:  (define TYPE (CONSTANT CONSTANT ...))

	-- Introduce: (forall VARIABLE TYPE TEST CLAUSE)

- Homework:  create SCHEMA for a CROSSWORD PUZZLE.  Assignment should be done in TEAM
  of TWO or THREE. 
	-- Match up.  Who is left?  Match them.