October 13th, 2003

(all 6's in these notes are to represent a Greeek small delta, and all 0's except s0's represent capital phi)


From previous class
----------------------------
D  :  a causes f if p1 .. pm, -q1 .. -qn.

O  :  initially f.

querry f after a1 .. an.


how do you define that from (D, O) |= f after a1 .. an.

0: states x action -> states
60: intial state

-----------------------------
load causes loaded
shoot causes -alive if loaded.

intially alive.
-----------------------------

0(6, a) = things true in the world before a plus the fluent results from a (or removed if a resutls in a negative fluent).

0(6, a) = ( 6 U Pa6 ) \ Na6 if Pa6 intersection Na6 = 0
otherwise undefined.

Pa6 = {f : a causes f if p1 ... pm, -q1 ... -pn exists in D
p1 ... pm are in 6, none of q1 ... qn are in 6
q1 ... qn} intersection 6= 0 }

Na6 = {-f : a causes f if p1 ... pm, -q1 ... -qn exists in D
p1 ... pm are in 6, none of q1 ... qn are in 6
q1 ... qn} intersection 6= 0 }


60 is an intial state for (D, O)
if (i) for all intially f in 0    f exists in 60
and (ii) for al initally -f in O  f not exists in 60


(D, O) |= f after a1 .. an
if and only if for all intially states 60 of (D, O)
f is true in 0( ... 0(0(60, a1), a2 ... an)

------------------------------------------------------------
example:

-Assume O is complete.

assume closed world

holds(alive, s0).                   
s0 - intial situation.

holds(loaded, res(load, S)) <- .        
res(a, s) - situation reached after executing a in situation s.

ab(alive, shoot, S) <- holds(loaded, S).
  
holds(F, res(A, S)) <- holds(F, S), not ab(F, A, S).

-alive is proved by the closed world assumption, because alive can not be proved in S after shoot.

can not be proven. holds(alive, res(shot, res(load, s0)))

holds(alive, res(load, s0)), can be proven by the frame rule, but alive can not be proven after shoot.