Situation calculus
In the situation calculus is a method of artificial intelligence. It will be described using the predicate logic effects of actions to situations in a model world. Is applied to the situation calculus, for example, in the language GOLOG, which is used among other things in robotics for action planning.
Description of the model world
The implementation of an action a leads to a succession situation, which is dependent on the previous situation and the action performed. This can be expressed formally by a binary function. Not every action can be performed in any situation. The feasibility can be defined, which is true in all situations in which the action is allowed by means of the predicate. For this definition situation-dependent predicates are often necessary. Relations which change their truth value over time are called fluents.
Example
As an example, a cabinet with several drawers. Articles from the drawers can be withdrawn, the drawers can be opened and closed. This situation can be described as follows:
- Closed drawers can be opened! → The disc tray can be s x open, where it is closed precisely in those situations.
- When you open a drawer, then it is open it! → If the drawer 's open x in a situation, it follows that it is no longer closed in the following situation.
- Items that are located in an open drawer can be removed! → The object y can be s x, strictly speaking, in situations out of the drawer, in which at the same time the drawer is not closed and the object is in the drawer.
- If you take out an object, then it is then no longer in the drawer! → If the object y in situation s from the drawer x taken as the object is located in the following situation no longer in the drawer.
- Open drawers can be closed! → The disc tray can be s x close, where it is not closed exactly in the situations.
- If you close a drawer, then it is closed then! → When the drawer is closed x in a situation s, it follows that it is closed in the following situation.
Frame problem
The previous example leads directly to the frame problem, since the clauses are not sufficient to describe the world. It still lacks trivial clauses, the only state that all other things are not changed by the actions. These clauses are extremely numerous even in small worlds: At 100 different actions with 50 fluents already approximately 10,000 terms used to describe necessary. Raymond Reiter has found a solution to this problem in 1991, which only requires a clause to display a fluents:
- If it is possible to perform an action a in a situation s, then it follows that the drawer is exactly then closed in succession situation when either the action a closing of the drawer was or if the drawer was previously closed, and it has acted in the action not to open the drawer.
This approach is known as the successor state axiom.
Axioms of the situation calculus
The axioms are the following clauses that apply in each world:
There is exactly one initial situation, no situation is the initial situation
Every situation is unique. When two conditions are the same, caused by the action of the situation and due to the action in a situation, then, both the situations, and the same, as well as the actions and.
A statement is true in all situations, if it is true in the initial situation, and the statement remains true in any situation, even after performing any action.
Some of the situations can be sorted. The comparison operator is defined recursively: A situation that is faced with a situation that results from performing the action in the situation, either the situation or a situation that lies ahead.
Remark
If you set as the initial condition that a ball is in the closed left-hand drawer, and a target that the ball is there no longer be located, can be made to calculate a plan taking into account all terms up to open the left drawer and the ball the drawer takes.
Documents
- Christoph Beierle, Gabriele core Isberner: methods of knowledge-based systems: foundations, algorithms, applications. Teubner -Verlag, 2008, p.304.
- Raymond Reiter: Knowledge in Action. Logical Foundations for Specifying and Implementing Dynamical Systems. 2001, ISBN 0-262-18218-1.
- Raymond Reiter: The frame problem- in the situation calculus: a simple solution ( sometimes ) and a complete ness result for goal regression. In Vladimir Lifschitz (ed.): Artificial Intelligence and Mathematical Theory of Computation: Papers in Honor of John McCarthy, pp. 359-380. Academic Press, New York, 1991. ISBN 0-124-50010-2.