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Planning in situational calculus

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Situation Calculus

• The idea behind situation calculus is that (reachable) states are definable in terms of the actions required to reach them.

• These reachable states are called situations. What is true in a situation can be defined in terms of relations with the situation as an argument.

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Situation Calculus contd..

• Situation calculus is defined in terms of situations. A situation is either

• init, the initial situation, or • do(A,S), the situation resulting from doing

action A in situation S, if it is possible to do action A in situation S.

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Contd..

• Situations are connected by the Result function

• e.g. s1= Result(a,s0) is the function giving the situation that results from doing action a while in situation s0

• Here, we represent an action sequence (plan) by a list [first | rest ] where

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Contd..

• first is the initial action and rest is a list of remaining actions.

• PlanResult(p,s) generalizes Result to give the situation resulting from executing p starting from state s:

• ∀s PlanResult([],s) = s• ∀s,a,p PlanResult([a | p], s) = PlanResult(p,

Result(a,s))

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Contd..

• Provides a framework for representing change, actions and reasoning about them.

• Situational calculus:• - is based on FOPL;• - a situation variable models new stars of the

world;• - action objects model activities;• - uses inference methods developed for FOPL to

do the reasoning.

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Planning in Situational Calculus • Situational calculus is a dialect of first order predicate

calculus formalization of states, actions and the effects of actions on states.

• Actions:- every change requires actions. The constant and function symbols for actions are completely dependent on the application. Actions typically have preconditions.

• Situations:- denote possible world histories.

– Constant s0 and function symbol do are used, s0 denotes the initial situation before any action has been performed.

– do(a, s) denotes the new situation that results from the performing action a in situation s.

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SITUATIONAL CALCULUSSituational calculus is based on FOPL plus: Special variables: s,a – objects of type situation and action Action functions: return actions.

E.g., move(A, TABLE, B) represents a move action move(x, y, z) represents an action schema

Two special function symbols of type situation s0 – initial situation do(a,s) – denotes the situation obtained after

performing an action a in situation s.Situation-dependent functions and relations

also called fluents Relation: on(x, y, s) – object x is on object y in situation

s; Function: above(x, s) – object that is above x in

situation s.

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• Shopping Problem– “Get a liter of milk, a bunch of bananas and a variable-

speed cordless drill.”• Need to define– Initial state– Operations

• A planning problem represented in situational calculus by logical sentences

– initial state : For shopping problemat(Home,s0) ¬have(Milk, s0) ¬have(Banana, s0) ¬have(Drill,s)

– goal state: a logical querys: at(Home,s) have(Milk,s) have(Bananas,s) have(Drill,s)

Situational Calculus Example

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• Operators : description of actions a,s: have(Milk,Result(a,s)) [(a=buy(Milk)

at(Supermarket,s) (have(Milk,s) a drop(Milk))]

• Result’(l,s) means result from sequence of actions l starting in s.s: Result’([],s)=s a,p,s: Result’([a|p],s)=Result’(p,Result(a,s))

Operators in Situational Calculus

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• Solutions– solution : a plan that an agent guarantees achievement of

the goal– a solution is a complete and consistent plan– a complete plan : every precondition of every step is

achieved by some other step– a consistent plan : no contradictions in the ordering or

binding constraints. When we meet a inconsistent plan we backtrack and try another branch

Solutions in Situational Calculus

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• A solution to the shopping problem is a plan P, applied to so, that yields a situation satisfying the goal query :

at(Home, Result’(p,s0)) have(Milk,Result’(p, s0)) have(Bananas,

result’(p, s0) have(Drill,Result’ (p, s0))

P = [Go(Supermarket),Buy(Bananas),Go(HardwareStore),Buy(Drill),

Go(Home)]

• To make planning practical:1. Restrict the language2. use a special-purpose algorithm

Solutions in Situational Calculus: Example