Situational calculus is a formal logic framework for representing states of the world and modeling how actions change those states. It defines situations as either the initial state or a new state resulting from an action. Relations and functions can be situation-dependent to represent properties that change with state. Planning problems are represented using logical sentences about initial states, actions, and goal states. Solutions are plans that through a sequence of actions guarantee achieving the goal state when started from the initial state.

1. Planning in situational calculus
1

2. 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.
2

3. 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.
3

4. 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
4

5. 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))
5

6. 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.
6

7. 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.
7

8. SITUATIONAL CALCULUS
Situational 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. 8

9. Situational Calculus Example
• 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 problem
at(Home,s0)  ¬have(Milk, s0)  ¬have(Banana, s0) 
¬have(Drill,s)
– goal state: a logical query
s: at(Home,s)  have(Milk,s)  have(Bananas,s)  have(Drill,s)
9

10. Operators in Situational Calculus
• 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))
10

11. Solutions in Situational Calculus
• 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
11

12. Solutions in Situational Calculus: Example
• 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 language
2. use a special-purpose algorithm
12