Frame Problem in Artificial Intelligence
PATRICK J. HAYES
By, Vinodkumar GangalRoll No-130913020
Overview Introduction Time & Change Frame Axioms Effects of actions Frame Problem
Qualification problem Ramification problem.
Some Partial Solutions Using Frame Rules. Frames Casual Connection StripsConclusionReferences05/03/23 2/29
Introduction A robot is an intelligent system equipped with sensory
capabilities, operating in an environment similar to the everyday world inhabited by human robots.
Belief is meant any piece of information which is explicitly stored in the robot's memory.
New beliefs are formed by (at least) two distinct processes: thinking and observation.
Thinking: involves operations which are purely internal to the belief system.
Observation: involves interacting with the world, that is, the external environment and, possibly, other aspects of the robot's own structure.
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Time and Change For him to think about the real world, the robot's beliefs
must handle time. This has two distinct but related aspects.
(a) There must be beliefs about time. For example, beliefs about causality.
(b) The robot lives in time: the world changes about him.
The first is solely concerned with thinking: the second involves observation
R(e,s)
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Effects of actions An action performed in a given situation results in a new
situation. The function Result(action, situation) is used to denote the
situation which results from performing the action action in the situation situation.
actions are specified in terms of their preconditions and postconditions(effects)
for example, the action of picking up or dropping a block in the blocks V x V s(clear(x) → holding(x, Result(pickup, s)))V x V s( ~holding(x, Result(drop, s)))
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Frame Axioms Effect axioms are not sufficient to keep track of whether
the agent is holding a block
V a V x V s( holding(x, s) & (a ≠ drop) → holding(x, Result(a, s)))
V a V x V s( ~holding(x, s) & (a ≠ pickup) → ~holding(x, Result(a, s)))
axioms which describe which parts of the world are not changed by an action are called frame axioms.
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The Frame problem Representational frame problem. The inferential frame problem refers to the need to
reason explicitly about things that don’t change.
when reasoning about sequences of actions, each property must be (re)derived for each new situation, even if the property hasn’t changed.
since each action usually changes only a few facts about a situation, this is very inefficient.
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The qualification problem in general, it is difficult to specify precisely the situations
in which an action will have the specified (intended) effect.
For example, it may not be possible to perform a pickup action if the block is slippery or glued to the table.
if these “side conditions” are left out of the effect and frame axioms, we may derive false beliefs about the consequences of executing an action.
how to qualify the “normal” effects of an action in “abnormal” circumstances is the qualification problem.
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The ramification problem In addition to the explicit consequences specified in their
definition, actions also have implicit consequences For example, picking up a box also picks up all the objects in
the box (if any), and if I take the box somewhere, I also take its contents etc.
the ramification problem can be seen as the derivation of the ultimate effects of an action.
may involve additional simple inferences (if the box is in the living room, then all the objects in the box are in the living room), reasoning about cause and effect (naive physics) and other kinds of consequences.
hard to know when to stop …05/03/23 9/29
The Frame Problem How to identify effectively which data are relevant in solving a
problem (without first solving the problem)?
Is relevant in the solution? find a solution with
No time to try all data!
• Make educated guesses (e.g. heuristics)• Abstract data (how?)
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The Frame Problem Frame problem
Can we let relevance emerge through interplay between problem concepts and specific data?• relevant concepts shapes the abstraction of data • specific data adapts relevance of concepts
French flagblue, white, red
circle, trapezoid
rectangle
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The Frame Problem The “frame problem”: assumes – that perception was
always accurate.
The problem of deciding what parts of the internal model to update when a change is made to the model or the external world.
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The Frame Problem A problem of determining which elements of a description
are consequentially altered after an event occurs. Named after cartoon animation in which a frame of
elements - chairs, walls, etc. - is kept static while the subjects of attention move around it. Which graphic elements can remain in the frame and which must be redrawn per cel?
Child brick ex: Child knows that other bricks will stay put.
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Some Partial Solutions Using Frame Rules Frames
- a finite number of monadic second-order predicates P,. If Pi(h) for a non-logical symbol h then we say that h is in the ith block of the frame.
The frame rule iswhere h1…hn, are all the non logical symbols which occur crucially in
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Some Partial Solutions Using Frame Rules Casual Connection:
- that there is a 3-place predicate ->(x,y,S) which has the intuitive meaning that if x is not connected to y, then any change to y does not affect x. - It seems reasonable that -> should be a partial ordering on its first two arguments (reflexive and transitive).
Strips
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STRIPS
•Stanford Research Institute Problem Solver (1970s)•Planning system for a robotics project.
•Knowledge Representation : First Order Logic.
•Algorithm : Forward chaining on rules.
•Any search procedure : Finds a path from start to goal.•Forward Chaining : Data-driven inferencing.•Backward Chaining : Goal-driven
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Forward & Backward Chaining•Rule : man(x) mortal(x)•Data : man(Shakespeare)
To prove : mortal(Shakespeare)
•Forward Chaining:man(Shakespeare) matches LHS of Rule.X = Shakespeare mortal( Shakespeare) added
-Forward Chaining used by design expert systems
•Backward Chaining: uses RHS matching- Used by diagnostic expert systems
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Example : Blocks World•STRIPS : A planning system – Has rules with precondition deletion list and addition list
AC
A
CBB
START GOAL
Robot hand
Robot hand
Sequence of actions : 1. Grab C2. Pickup C3. Place on table C4. Grab B5. Pickup B
6. Stack B on C7. Grab A8. Pickup A9. Stack A on B
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Example : Blocks World•Fundamental Problem :The frame problem in AI is concerned with the question of what piece of knowledge is relevant to the situation.
•Fundamental Assumption : Closed world assumptionIf something is not asserted in the knowledge base, it is assumed to be false.
(Also called “Negation by failure”)
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Example : Blocks World•STRIPS : A planning system – Has rules with precondition deletion list and addition list
on(B, table)on(A, table) on(C, A)hand emptyclear(C)clear(B)
on(C, table)on(B, C) on(A, B)hand emptyclear(A)
AC
A
CBB
START GOAL
Robot hand
Robot hand
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Rules•R1 : pickup(x)
Precondition & Deletion List : hand empty, on(x,table), clear(x)
Add List : holding(x)
•R2 : putdown(x)Precondition & Deletion List : holding(x)Add List : hand empty, on(x,table), clear(x)
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Rules•R3 : stack(x,y)
Precondition & Deletion List :holding(x), clear(y) Add List : on(x,y), clear(x)
•R4 : unstack(x,y)Precondition & Deletion List : on(x,y), clear(x)Add List : holding(x), clear(y)
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Plan for the block world problem
• For the given problem, Start Goal can be achieved by the following sequence :1. Unstack(C,A)2. Putdown(C)3. Pickup(B)4. Stack(B,C)5. Pickup(A)6. Stack(A,B)
• Execution of a plan: achieved through a data structure called Triangular Table.
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Triangular Table
holding(C)
unstack(C,A)
putdown(C)
hand emptyon(B,table) pickup(B)
clear(C) holding(B) stack(B,C)
on(A,table) clear(A) hand empty pickup(A)
clear(B) holding(A) stack(A,B)
on(C,table) on(B,C) on(A,B)clear(A)
clear(C)on(C,A)
hand empty
0 1 2 3 4 5 6
1
2
3
4
5
6
7
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Triangular Table
• For n operations in the plan, there are :• (n+1) rows : 1 n+1• (n+1) columns : 0 n
• At the end of the ith row, place the ith component of the plan. • The row entries for the ith step contain the pre-conditions for the
ith operation.• The column entries for the jth column contain the add list for the
rule on the top.• The <i,j> th cell (where 1 ≤ i ≤ n+1 and 0≤ j ≤ n) contain the pre-
conditions for the ith operation that are added by the jth operation.• The first column indicates the starting state and the last row
indicates the goal state.
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Search in case of planning
Ex: Blocks world
Triangular table leads to some amount of fault-tolerance in the robot
Start
S1 S2
Pickup(B) Unstack(C,A)
AC
BSTART
A CBAC B
WRONG
MOVE
NOT ALLOWED
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Conclusion In the long run, frame rules will be required
for non-trivial problems, corresponding respectively to the "strategic" and "tactical" aspects of computing descriptions of new situations.
One outstanding defect of present approaches is the lack of a clear model theory.
Even to begin such a project would seem to require deep insight into our pre-systematic intuitions about the physical world.
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References[1] F. Bacchus, J. Halpern, H.J. Levesque, Reasoning about noisy sensors and effectors in the situation calculus,Artificial Intelligence 111 (1999) 171–208.[2] C. Baral, T. Son, Formalizing sensing actions—A transition function based approach, Artificial Intelligence125 (2001) 19–91.[3] R. Bull, K. Segerberg, Basic modal logic, in: D. Gabbay, F. Guenther (Eds.), Handbook of PhilosophicalLogic, Vol. II, Chapter 1, D. Reidel, Dordrecht, 1984, pp. 1–88.[4] B.F. Chellas, Modal Logic: An Introduction, Cambridge University Press, Cambridge, 1980.[5] O. Etzioni, S. Hanks, D.Weld, D. Draper, N. Lesh,M.Williamson, An approach to planning with incompleteinformation, in: B. Nebel, C. Rich, W. Swartout (Eds.), Principles of Knowledge Representation andReasoning: Proceedings of the Third International Conference, Cambridge, MA, 1992, pp. 115–125.[6] R. Fagin, J.Y. Halpern, Y.O. Moses, M.Y. Vardi, Reasoning about Knowledge, MIT Press, Cambridge, MA,1995.[7] A. Frisch, R. Scherl, A general framework for modal deduction, in: J.A. Allen, R. Fikes, E. Sandewall(Eds.), Principles of Knowledge Representation and Reasoning: Proceedings of the Second InternationalConference, Morgan Kaufmann, San Mateo, CA, 1991, pp. 196–207.[8] J. Funge, Representing knowledge within the situation calculus using interval-valued epistemic fluents,J. Reliable Comput. 5 (1) (1999).[9] G. De Giacomo, H.J. Levesque, Projecting using regression and sensors, in: Proc. IJCAI-99, Stockholm,Sweden, 1999, pp. 160–165.[10] G. De Giacomo, H.J. Levesque, An incremental interpreter for high-level programs with sensing, in: LogicalFoundations for Cognitive Agents: Contributions in honor of Ray Reiter, Springer, Berlin, 1999, pp. 86–102.
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Thank you
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