A Logic of Capabilities

In this paper a logic of capabilities is introduced. We start by defining a language in which not only knowledge and actions of a set of agents can be expressed but also their abilities. To formalize the planning of the agents a Can-predicate and a Cannotpredicate are used. The former indicates that an agent knows that he can achieve a given goal by performing a given action, the latter indicates that the agent knows that he cannot achieve the given goal by performing the given action. We will define two classes of models, of which one is a restricted version of the other. Using these classes a semantics for the language is defined. For the second class of models a sound and complete axiomatization is given. We define the notion of action transformation, a function that transforms actions into other actions. The semantics that we define is such that two actions that can be transformed into one another have equivalent results and that the abilities of an agent are closed under the action transformations. It turns out that the possibility to express the abilities of an agent provides for a flexible and intuitively appealing framework.