Situation calculus

Question 1

Briefly describe situation calculus.

Answer 1

In situation calculus:

• The world consists of sequences of situations.
• Over time, an agent moves from one situation to another.
• Situations are changed as a result of actions.
• A situation argument is added to items that can change over time. For example, At(location, s).
• Items that can change over time are called fluents, and those that don’t are called eternal. They don’t need situation arguments.
• Situation calculus uses a function result(action, s) to denote the new arising situation.

Question 2

What is a possbility axiom?

Answer 2

It specifies when particular actions are possible.

For example, for action ‘grab’ to be possible we need something to grab on at this location. This can be modelled as a possibility axiom:

Question 3

What does effect axiom do?

Answer 3

They describe what is true in the situation that results from performing an action. For example, to keep track of whether EVIL ROBOT has the gold we need effect axioms to describe the effect of picking it up:

Question 4

What is a frame axiom?

Answer 4

It describes describe the way in which the world stays the same. For example, the code below shows the effect of having object o and not discarding it.

Question 5

Define successor state axioms.

Answer 5

A mixture of effect and frame axioms, used to solve the representational frame problem.

Basic concept: If it is possible to do action a, then after performing a, you can make a predicate p true iff

• p is true before and you haven’t made it false this turn, OR
• you made p true in this turn.

Question 6

Describe the following problems:

• Representational frame problem
• Inferential frame problem
• Qualification problem
• Ramification problem

Answer 6

• Representational frame problem: a large number of frame axioms are required to represent the many things in the world which will not change as the result of an action.
• Inferential frame problem: when reasoning about a sequence of situations, all the unchanged properties still need to be carried through all the steps.
• Qualification problem: we are in general never completely certain what conditions are required for an action to be effective.
• Ramification problem: actions tend to have implicit consequences that are large in number.

Question 7

What are Unique names axioms and Unique actions axioms?

What are their purposes?

Answer 7

Unique names axioms state that each pair of distinct items in our model of the world must be different.

Unique actions axioms state that pairs of distinct actions are different as well.

The purpose is to prevent interpretations from assigning different variables to the same thing in FOL.

Question 8

How do you modify the successor state axiom to solve the ramification problem?

Answer 8

This is rather unbearable…