[Solved]: How to decribe an action with STRIPS?

Problem Detail: 

The state space is decribed with 3 boolean variables $p,q$ and $r$ (so we have 8 states total). We have an action, let's say $a$. Action $a$ can be executed when $p=\text{False}$ and $q=\text{True}$ and the result is $p=\text{True}$, $q=\text{False}$ and $r=\text{False}$

How can we describe this action with STRIPS? My problem is this: since it isn't allowed on STRIPS to have negative literals, how can I describe it? For example, $\text{precondition}(a) = \{ \neg p,q \}$.

Asked By : Adasel Pomik

Answered By : Vor

An instance of propositional STRIPS planning is a quadruple $\langle P,O,I,G \rangle$

• $P$ is the set of atomic ground formulas;
• $O$ is the set of operators (actions); an operator $a \in O$ has the form $Pre \Rightarrow Post$, where $Pre$ is a satisfiable conjuction of positive ($a^+$) and negative preconditions ($a^-$) of the operator; $Post$ is a satisfiable conjunction of positive ($a_+$) and negative ($a_-$) postconditions of the operator ($a_+$ is called the add list, $a_-$ is called the delete list);
• $I \subseteq P$ is the initial state;
• $G = \langle G_+, G_- \rangle$, called the goals, is a satisfiable conjunction of positive and negative conjunctions;
• the state $S$ is a subset of $P$.

The result of applying operator (action) $a$ on state $S$ is:

• $(S \cup a_+) \setminus a_-\quad$ if $a^+ \subseteq S$ and $S \cap a^- = \emptyset$
• $S$ otherwise

In your example simply set: $$a^+ = \{q\}, \quad a^- = \{p\}$$ $$a_+ = \{p\}, \quad a_- = \{q,r\}$$

For a formal definition and a nice computational complexity characterizations of STRIPS with various constraints on the preconditions/postconditions see: The Computational Complexity of Propositional STRIPS Planning (1994), by Tom Bylander.

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Question Source : http://cs.stackexchange.com/questions/14066