COSC 4350 Artificial Intelligence

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COSC 4350Artificial Intelligence

• Deterministic Planning (Part I)
• Dr. Lappoon R. Tang

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Overview

• Introduction
• Logic based planning
• Situation Calculus
• Frame Problem
• Total order planning
• Linear planning
• State-space planning
• Partial order planning
• Non-linear planning
• Plan-space planning

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Readings

• R N Chapter 10
• Sec 10.3
• Skim through Solving the representational frame
  problem and the rest in Sec 10.3

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What is planning?

• Given
• A way to describe the world
• An initial state of the world
• A goal description
• A set of possible actions to change the world
• Find
• A prescription (i.e. a plan) for actions to
  change the initial state into one that satisfies
  the goal

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Applications

• Mobile robots
• Example finding a sequence of actions by the
  robot that achieve a specific goal (e.g. moving
  out of the classroom ?)
• An initial motivator, and still being developed
• A trip planner
• Finding the route to the destination that
  minimizes the costs
• Scheduling
• Example making a schedule for the planes to take
  off in an airport
• And more
• Factory automation, flying autonomous spacecraft,
  military planning,

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Issues in Planner Construction

• We need to provide to the planner
• A representation of the world
• How do we describe the world?
• What is considered a state of the world?
• A representation of the actions taken by the
  agent
• What are the pre-conditions that have to be
  satisfied before an action can be taken?
• What are the effects of the action if taken?
• A method for describing changes
• What changes are made to the world by an action?
• What remain the same after an action is taken?

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Approaches to Planning

• Primarily four approaches
• Logic based planning
• Using first order logic to represent states,
  actions, and causality (i.e. effects of actions)
• Operator based planning
• Still use logic for representation of world
  states but actions are operators (i.e. they have
  pre and post conditions)
• Planning is a state space search
• State-space planning
• Plan-space planning
• Case based planning
• Use a database of previously constructed plan to
  solve a new planning problem
• Reactive planning
• Use if-then like rules to encode sense-act
  cycles

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Logic based planning

• Intuition
• the agent keep a KB of true sentences (facts)
  about the world (e.g. At(tang,SETB 1.514)) and
  the state of being of itself at the current
  point (e.g. Stop(Agent,S0) Agent is not moving
  at state S0)
• actions make changes to the current state of the
  agent and its new state is asserted into the KB
• planning is finding a sequence of changes of
  state of the agent from the initial state S0 to
  the final state for achieving a certain goal
• Usually the final state is a state of being in
  which the robot has achieved the goal

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Logic based planning (contd)

• Representation of 1) the state of the agent and
  2) the actions
• A State is used as a parameter in a logical
  description of the state of being of the agent
• Example At(Agent,1,1,S0) the agent is at grid
  1,1 initially where S0 represents the initial
  state
• The properties (effects) of Actions are described
  using axioms If an action can be taken, what
  logical fact becomes true?
• Example If Agent can move-one-step to the grid
  at 1,2, then after the action is executed,
  At(Agent,1,2,S1) becomes true where S1 is the
  state resulted from S0
• Domain constraints are expressed in logic
• Example an object is movable only if the top is
  clear

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Logic based planning (contd)

• Since a state of an agent is a statement that is
  true about the agent and the effects of an action
  assert what becomes true afterward, Planning can
  therefore be reduced to theorem proving
• The current state is expressed as a sequence of
  actions starting from the initial state where
  each action in the sequence takes the current
  state to the resulting state after its
  application
• a3(a2(a1(S0))) represents S0 ? S1 ? S2 ? S3
• Million Q Can we infer a sequence of actions
  (by theorem proving) that achieves a certain goal
  given the agents initial KB of the world and a
  logical description of the agents initial state?

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Logic based planning (contd)

• A To infer a sequence of actions leading the
  initial state to the final state, one tries to
  prove the existence of a final state that
  satisfies a certain description and extract the
  sequence of actions out from the state itself
  Idea Can I find a state of the agent in which a
  certain description of the final state hold?
• Example ? s Holding(G,s)? Is there a state s
  such that the agent is holding the piece of gold
  G?
• Idea We use theorem proving to derive s that
  makes Holding(G,s) true, then we extract the
  sequence of actions from s itself

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Logic based planning (contd)

• Started out in the late 60s and regained
  popularity in the 90s
• Still an area of ongoing research despite that
  it is a pretty old paradigm
• Perhaps partly due to advancement in theorem
  proving technology?
• Now, logic based planning is almost completely
  obsolete
• Why are we learning it?
• It provides historical perspective on the subject
  and problems in this framework motivated the
  development of new theories in planning

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The situation calculus

• Introduced by John McCarthy in 1963
• Early approach to representing and reasoning
  about actions of an agent for logic based
  planning
• What have to be true for actions to be
  applicable? (pre-conditions)
• What changes do actions make to the world?
  (effects)
• Key idea to describe changes made by actions
  entirely in first order logic
• The name itself is reminiscent of logic
• Note propositional logic is aka propositional
  calculus
• Note first order logic is aka predicate calculus

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The situation calculus (key definitions)

• Situations
• the current state of being of the agent (a
  snapshot of the world) represented by logical
  terms consisting of the initial situation (s0)
  and all its following situations resulted from
  actions taken by the agent
• The function Result(a,s) represents the situation
  that results when action a is taken in situation
  s
• Example Result(Go(1,1,1,2),S0) denotes the
  situation resulted from taking the action
  Go(1,1,1,2) by the agent at situation S0
• Actions map situations to situations

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The situation calculus (key definitions)
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The situation calculus (key definitions)

• Fluents
• predicates whose values change from one situation
  to the next (e.g. location of the agent like a
  robot or a truck), there are two kinds
• 1) predicates that describe either the agent
• e.g. TruckAt(h,s) the truck is at house h in
  situation s
• TruckAt(h,s0) might be true while TruckAt(h,s1)
  false
• 2) or relevant objects in the world
• e.g. InHouse(i,h,s) the item i is in house h in
  situation s.

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Describing actions in Situation Calculus

• Each action is described by two axioms
• Possibility axiom
• Effect axiom
• Possibility Axiom
• Format Preconditions gt Poss(a,s)
• If preconditions are satisfied (at situation
  s), then it is possible for the agent to take
  action a in situation s
• Effect Axiom
• Format Poss(a,s) gt Fluents about new state of
  being of the agent
• If it is possible for the agent to take action a
  in situation s, then fluents about its new state
  of being become true.

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Describing actions in Situation Calculus Example
(Wumpus Domain)

• Possibility Axiom
• At(Agent,x,s) ? Adjacent(x,y) gt Poss(Go(x,y),s)
• Gold(g)? At(Agent,x,s)? At(g,x,s) gt
  Poss(Grab(g),s)
• Holding(g,s) gt Poss(Release(g),s)
• Effect Axiom
• Poss(Go(x,y),s) gt At(Agent,y,Result(Go(x,y),s))
• Poss(Grab(g),s) gt Holding(g,Result(Grab(g),s))
• Poss(Release(g),s) gt Holding(g,Result(Release(g)
  ,s))

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Frame Problem in Situation Calculus

• One can run into problems of not being able to
  successfully construct a proof simply because
  what remains true after an action is taken is not
  mentioned in the effect axioms
• Frame problem
• The problem of representing what stays the same
• Action effects only specify the changes

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Frame Problem Solutions

• STRIPS