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Some of the operators are:
goto1(m):
robot goes to location m
goto2(m):
robot goes next to item m
pushto(m,n): robot pushes object m next to object
n
gothrudoor(k,l,m): robot goes thru door k from room l
to room m
turnlighton(m): robot turns on lightswitch m
Given a STRIPS system S , a plan
is defined as any finite sequence of its operators. Each plan
a = ( a1, ..., aN) defines a sequence of world models M0, M1,
..., MN, where M0 is the initial world model and
Mi = ( Mi-1 \ D ai) » A
ai (i = 1, ... , N) (2)
We say that a is accepted by
the system if
Mi-1 |- P ai (i = 1, ... , N)
(3)
In this case, MN is called result
executing a and denote it by R( a ).
So now to a first version of
a semantics for STRIPS. The world is described by a language,
L and at any instant in time in a certain state. One of the states,
s0, is selected as the intitial state. We assume that it is defined
for each state s which sentences of L are (known to be) satisfied
in this state, and that the set of sentences satisfied in state
s is closed under predicate logic (??) An action is a partial
function f from states to states. If f(s) is defined then we
say that f is applicable in state s, and that f(s) is the result
of the action. We assume that an action f a is associated with
each operator a. A STRIPS system along with this additional information
will be called an interpreted STRIPS system. A world model M
of an interpreted STRIPS system S is satisfied in a state s if
every element of M is satisfied in s. For each plan a = ( a1,
..., aN) of S, we define f a to be the composite action f aN
... f a1 .
Consider a fixed interpreted
STRIPS system S = (M0, {(Pa,Da,Aa)}aop). Under what conditions
can S be considered sound.
Definition A. An operator description
(P,D,A) is sound relative to an action f if, for every state
s such that P is satisfied in s,
(i) f is applicable in state
s,
(ii) every sentence which is
satisfied in s and does not belong to D is satisfied in f(s),
(iii) A is satisfied in f(s)
S is sound if M0 is satisfied
in the initial state s0, and each operator description (Pa,Da,Aa)
is sound relative to f a.
Soundness Theorem. If S is sound
and a plan a is accepted by S, then the action f a is applicable
in the initial state s0 , and the world model R( a ) is satisfied
in the state f a (s0 ).
Problem, Def. A eliminates all
the usual STRIPS systems as "unsound"....Problem is
with ii. To make the delete list complete it would have to include
all sentences that might become false which includes conjunctions
that include a statement in the delete set as well as the disjunction
of these sentences in the delete list, and in general any sentence
that includes a sentence from the delete list conjoined with
any sentence F where F is provable in predicate logic. (e.g.
push(k,m,n) not only ATR(m ), AT(k,m ) must be deleted, but also
ATR(m ) × AT(k,m ), ATR(m ) × F, etc.) So the delete
list will become infinite and perhaps even non-recursive!
Definition B. An operator description
(P,D,A) is sound relative to an action f if, for every state
s such that P is satisfied in s,
(i) f is applicable in state
s,
(ii) every atomic sentence which
is satisfied in s and does not belong to D is satisfied in f(s),
(iii) A is satisfied in f(s)
(iv) every non-atomic sentence
in A is satisfied in all states of the world
S is sound if
(v) M0 is satisfied in the initial
state s0,
(vi) every non-atomic sentence
in M0 is satisfied in all states of the world,
(vii)every operator description
(Pa,Da,Aa) is sound relative to f a.
The Soundness Theorem remains
valid for the new definition.
Definition C. An operator description
(P,D,A) is sound relative to an action f if, for every state
s such that P is satisfied in s,
(i) f is applicable in state
s,
(ii) every essential sentence
which is satisfied in s and does not belong to D is satisfied
in f(s),
(iii) A is satisfied in f(s)
(iv) every sentence in A which
is not essential is satisfied in all states of the world
S is sound if
(v) M0 is satisfied in the initial
state s0,
(vi) every sentence in M0 which
is not essential is satisfied in all states of the world,
(vii) every operator description
(Pa,Da,Aa) is sound relative to f a.
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